Repository of a selection of papers related to COVID-19 outbreak operated by Centre Borelli (ENS Paris-Saclay, CNRS, Université de Paris, SSA)
The repository prioritizes papers presenting mathematical models with practical impact, use of empirical data, strategy of containment policy, open and reproducible implementation of the model.
The repository compiles the key elements of each paper such as: type of model, main assumptions, input parameters, output of the model, open source implementation, etc. The complete table can be found under three different formats:
- Interactive dashboard-like table under Kibana
- A spreadsheet --> Comments are allowed
- List with clickable entries below.
List of characteristics is provided for each paper : see characteristics description
A glossary of technical terms is available.
Authors: Marie Garin, Myrto Limnios, Alice Nicolaï, Nicolas Vayatis
Contributors: Stephen Chick, Theodoros Evgeniou, Mathilde Fekom, Anton Ovchinnikov, Raphaël Porcher, Camille Pouchol
Credits for technical support: Olivier Boulant, Amir Dib, Christophe Labourdette.
If you wish to suggest an article to be added to the review, please contact us via email at [email protected] and we will proceed with the new entry after an internal assessment.
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| Title | Authors | Description |
|---|---|---|
| Epidemiological monitoring and control perspectives: application of a parsimonious modelling framework to the COVID-19 dynamics in France | Mircea T. Sofonea et al. | here |
| Epidemic Models for Personalised COVID-19 Isolation and Exit Policies Using Clinical Risk Predictions | Theodoros Evgeniou et al. | here |
| Predictive Monitoring of COVID-19 | Jianxi Luo et al. | here |
| Projections for first-wave COVID-19 deaths across the US using social-distancing measures derived from mobile phones | Spencer Woody et al. | here |
| COVID-19: One-month impact of the French lockdown on the epidemic burden | Jonathan Roux et al. | here |
| Forecasting the impact of the first wave of the COVID-19 pandemic on hospital demand and deaths for the USA and European Economic Area countries | IHME COVID-19 health service utilization forecasting team et al. | here |
| Estimating the burden of SARS-CoV-2 in France | Henrik Salje et al. | here |
| Temporal dynamics in viral shedding and transmissibility of COVID-19 | Eric H. Y. Lau et al. | here |
| Policy brief : Analyse coût‐bénéfice des stratégies de déconfinement | Christian Gollier et al. | here |
| Expected impact of lockdown in Ile-de-France and possible exit strategies | Laura Di Domenico et al. | here |
| Physical distancing is working and still needed to prevent COVID-19 resurgence in King, Snohomish, and Pierce counties | Niket Thakkar et al. | here |
| Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies | Cesar Manchein et al. | here |
| First-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a modelling impact assessment | Kathy Leung et al. | here |
| Modeling strict age-targeted mitigation strategies for COVID-19 | Maria Chikina et al. | here |
| Prediction of COVID-19 Disease Progression in India: Under the Effect of National Lockdown | Sourish Das et al. | here |
| Scenario analysis of non-pharmaceutical interventions on global COVID-19 transmissions | Xiaohui Chen et al. | here |
| Generic probabilistic modelling and non-homogeneity issues for the UK epidemic of COVID-19 | Anatoly Zhigljavsky et al. | here |
| COVID-19: Analytics Of Contagion On Inhomogeneous Random Social Networks | T. R. Hurd et al. | here |
| Locally informed simulation to predict hospital capacity needs during the COVID-19 pandemic | Gary E. Weissman et al. | here |
| A simple planning problem for covid-19 lockdown | Fernando Alvarez et al. | here |
| Machine learning the phenomenology of covid-19 from early infection dynamics | Malik Magdon-Ismail et al. | here |
| Coronavirus Covid-19 spreading in Italy: optimizing an epidemiological model with dynamic social distancing through Differential Evolution | I. De Falco et al. | here |
| Quantifying the effect of quarantine control in Covid-19 infectious spread using machine learning | Raj Dandekar et al. | here |
| Planning as Inference in Epidemiological Models | Frank Wood et al. | here |
| Using generalized logistics regression to forecast population infected by Covid-19 | Villalobos Arias et al. | here |
| Bayesian semiparametric time varying model for count data to study the spread of the COVID-19 cases | Arkaprava Roy and Sayar Karmakar et al. | here |
| Adaptive cyclic exit strategies from lockdown to suppress COVID-19 and allow economic activity | Omer Karin et al. | here |
| Monitoring Italian COVID-19 spread by an adaptive SEIRD model | Elena Loli Piccolomini et al. | here |
| Optimal COVID-19 epidemic control until vaccine deployment | R. Djidjou-Demassea et al. | here |
| Stochastic modeling and estimation of COVID-19 population dynamics | Nikolay M. Yanev et al. | here |
| Evolving epidemiology and transmission dynamics of coronavirus disease 2019 outside Hubei province, China: a descriptive and modelling study | Juanjuan Zhang et al. | here |
| Predicting the Spread of the COVID-19 Across Cities in China with Population Migration and Policy Intervention | Jiang Zhang et al. | here |
| Total Variation Regularization for Compartmental Epidemic Models with Time-varying Dynamics | Wenjie Zheng et al. | here |
| A modified sir model for the covid-19 contagion in italy | Giuseppe C. Calafiore et al. | here |
| Optimising Lockdown Policies for Epidemic Control using Reinforcement Learning | Harshad Khadilkar et al. | here |
| Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries | Seth Flaxman et al. | here |
| Estimates of the severity of coronavirus disease 2019: a model-based analysis | Robert Verity et al. | here |
| A simple stochastic SIR model for COVID 19 infection dynamics for Karnataka: Learning from Europe | Ashutosh Simha et al. | here |
| Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact | Alexis Akira Toda et al. | here |
| Optimal covid-19 quarantine and testing policies | Facundo Piguillem et al. | here |
| The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study | Kiesha Prem et al. | here |
| Modèle SIR mécanistico-statistique pour l'estimation du nombre d'infectés et du taux de mortalité par COVID-19 | Lionel Roques et al. | here |
| The effect of human mobility and control measures on the COVID-19 epidemic in China | Moritz U. G. Kraemer et al. | here |
| Composite Monte Carlo Decision Making under High Uncertainty of Novel Coronavirus Epidemic Using Hybridized Deep Learning and Fuzzy Rule Induction | Simon James Fong et al. | here |
| Optimal Timing and Effectiveness of COVID-19 Outbreak Responses in China: A Modelling Study | Anthony Zhenhuan Zhang et al. | here |
| On a quarantine model of coronavirus infection and data analysis | Vitaly Volpert et al. | here |
| Predicting the number of reported and unreported cases for the COVID-19 epidemic in South Korea, Italy, France and Germany | P. Magal et al. | here |
| Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China | Joseph T. Wu et al. | here |
| Mathematical Predictions for COVID-19 As a Global Pandemic | Victor Alexander Okhuese et al. | here |
| Short-term predictions and prevention strategies for COVID-2019: A model based study | Sk Shahid Nadim et al. | here |
| Transmission potential and severity of COVID-19 in South Korea | Eunha Shim et al. | here |
| COVID-19: Forecasting short term hospital needs in France | Clement Massonnaud et al. | here |
| Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand | Neil M Ferguson et al. | here |
| Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2) | Ruiyun Li et al. | here |
| Expected impact of school closure and telework to mitigate COVID-19 epidemic in France | Laura Di Domenico et al. | here |
| Rational evaluation of various epidemic models based on the COVID-19 data of China | Wuyue Yang et al. | here |
| Early dynamics of transmission and control of COVID-19: a mathematical modelling study | Adam J Kucharski et al. | here |
| Modeling the control of COVID-19: Impact of policy interventions and meteorological factors | Jia Jiwei et al. | here |
| Modeling of COVID-19 epidemic in the United States | GLEAM Team et al. | here |
| The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak | Matteo Chinazzi et al. | here |
| Evaluating the impact of international airline suspensions on the early global spread of COVID-19 | Aniruddha Adiga et al. | here |
| Evaluating the impact of international airline suspensions on COVID-19 direct importation risk | Aniruddha Adiga et al. | here |
| A Time-dependent SIR model for COVID-19 with Undetectable Infected Persons | Yi-Cheng Chen et al. | here |
| Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data | Z. Liu et al. | here |
| Estimation of the epidemic properties of the 2019 novel coronavirus: A mathematical modeling study | Jinghua Li et al. | here |
| Estimation of the final size of the coronavirus epidemic by the SIR model | Milan Batista et al. | here |
| Preparedness and vulnerability of African countries against importations of COVID-19: a modelling study | Marius Gilbert et al. | here |
| Estimation of the final size of coronavirus epidemic by the logistic model | Milan Batista et al. | here |
| Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data | Natalie M. Linton et al. | here |
| Assessing the impact of reduced travel on exportation dynamics of novel coronavirus infection (COVID-19) | Asami Anzai et al. | here |
| Predictions of 2019-ncov transmission ending via comprehensive methods | Tianyu Zeng et al. | here |
| A time delay dynamic system with external source for the local outbreak of 2019-nCoV | Yu Chen et al. | here |
| Understanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions | Z. Liu et al. | here |
| Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study | Joseph T Wu et al. | here |
Epidemiological monitoring and control perspectives: application of a parsimonious modelling framework to the COVID-19 dynamics in France
Authors : Mircea T. Sofonea, Bastien Reyné, Baptiste Elie, Ramsès Djidjou-Demasse, Christian Selinger, Yannis Michalakis, Samuel Alizon
Publication date : 05/24
Paper : Available here
Code available : null
Epidemic Models for Personalised COVID-19 Isolation and Exit Policies Using Clinical Risk Predictions
Authors : Theodoros Evgeniou, Mathilde Fekom, Anton Ovchinnikov, Raphael Porcher, Camille Pouchol, Nicolas Vayatis
Publication date : 05/03
Paper : Available here
Code available : https://reine.cmla.ens-cachan.fr/boulant/seair/
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRData used for the model
France - from 17/03 to 03/05 ICU beds capacityGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
1) enable for differential policies according to a risk-prediction model (distinction between severe and mild cases); 2) consider gradual softening of individuals isolation level according to their predicted classOutputs
estimation of the efficiency of a differential exit policy based on a risk-prediction modelHow intervention strategies are modelled
susceptible divided by low/high isolation recommendation; non pharmaceutical intervention strategy: reduction in contact rates according to the predicted class (mild or severe) by a factor that can be either estimated or defined as a function of 3 parameters indicating the degree of isolationAdditional Assumptions
1) recovered are life-immune, 2) isolation level different according to the risk-predicted type (low or high risk)Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classical parameters; initial state conditions of the systemOther parameters
health care capacity; risk-prediction model’s parametersHow parameters are estimated
data-driven; literatureDetails on parameters estimation
1) beta prior for proportion of mild cases if infected and uniform for initial populations size; 2) ABC using RMSE wrt to the number of ICU beds occupancy to estimate initial conditions and proportion of individuals that would require an ICU bedAuthors : Jianxi Luo
Publication date : 05/02
Paper : Available here
Code available : https://www.mathworks.com/matlabcentral/fileexchange/74658-fitviruscovid19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRData used for the model
World - data on the daily number of infections from Our World in DataGlobal approach
evolution forecast; epidemiological parameter estimationDetails of approach
provide a web page with daily updated predictions of the number of infections and epidemic end dateOutputs
prediction of the infected compartment dynamicsProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemHow parameters are estimated
data-drivenDetails on parameters estimation
uses the method described in https://www.researchgate.net/publication/339311383_Estimation_of_the_final_size_of_the_coronavirus_epidemic_by_the_SIR_model; nonlinear LSE between the actual and predicted number of casesProjections for first-wave COVID-19 deaths across the US using social-distancing measures derived from mobile phones
Authors : Spencer Woody, Mauricio Garcia Tec, Maytal Dahan, Kelly Gaither, Michael Lachmann, Spencer Fox, Lauren Ancel Meyers, James G Scott
Publication date : 04/26
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : phenomenological
Model sub-category
negative binomial regression; time-varying covariates; deaths modeling; spatially-structured; mixed-effects modelData used for the model
all US states - local data from mobile-phone GPS traces from SafeGraphGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
provide a web page with mortality projections in the US https://covid-19.tacc.utexas.edu/projections/Outputs
prediction of the death curve dynamicsHow intervention strategies are modelled
state-based time-varying covariates computed by a weighted average of social-distancing metrics that capture the variation of visitation patterns to public space and of the time spend at home versus at workProblem Formulation
GLM predictionOther parameters
maximum daily expected death rate; the day on which the expected death rate achieves its maximum; slope at the inflection point of the death-rate curveHow parameters are estimated
data-drivenDetails on parameters estimation
mixed-effects negative-binomial generalized linear model fitted by MCMCComment/issues
1) model constructed starting from an already developed model of the IHME, with the idea to improve some aspects and overcome the violation of the assumptions of independent errors in the IHME model; 2) cannot project longer-term epidemiological dynamics beyond the initial wave of mitigated transmissionAuthors : Jonathan Roux, Clément Massonnaud, Pascal Crépey
Publication date : 04/22
Paper : Available here
Code available : bbmle package in R
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR H; multistage; age-structured; spatially-structured; symptoms/severity structuredData used for the model
France - 03/20 to 03/28 - regional data on hospitalisations, ICU admissions, and deaths from Santé Publique France; data on ICU beds capacity per French RegionGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) retrospective estimate of the effect of a one-month long lockdown in France on hospital requirements and mortality rate; 2) forecast hospital needs for each of the 13 French metropolitan regionsOutputs
pre-lockdown reproduction number per region, prediction of the number of new hospitalisations, the number of required hospitalisation beds, the number of new ICU admissions, the number of required ICU beds and the number of new hospital deaths in each regionHow intervention strategies are modelled
modeling of the contact matrix, isolation of people over 70 years oldAdditional Assumptions
1) each region has its specific dynamic; 2) infected hospitalized considered as non-infectious (due to their isolation in hospital rooms and the protection of the hospital’s staff)Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
infectivity rate per compartment; infection through contact probability per region; incubation period; presymptomatic incubation period; presymptomatic infectious period; symptomatic period; prediagnostic period; asymptomatic period; length of stay in hospital; length of stay in ICU; pre and post-ICU lenth of stay; risk of ICU admission; risk of death in ICU or hospital; initial state conditions of the systemOther parameters
contact matrix; introduction date of the virus per regionHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) contact matrices for the French population estimated in https://journals.plos.org/ploscompbiol/article?rev=2&id=10.1371/journal.pcbi.1005697 2) hospitalisation rate and incubation period from https://spiral.imperial.ac.uk:8443/handle/10044/1/77482; infectivity of the asymptomatic cases from https://science.sciencemag.org/content/early/2020/04/09/science.abb6936.abstract; data-driven: probability of infection by region, other parameters from the APHP 3) introduction date of the virus and other parameters are estimated as MLE assuming some specific distributions for the hospitalisation data, the occupation of hospitalisation beds, the ICU and deaths dataComment/issues
1) takes into account age, region, location 2) confidence intervals providedForecasting the impact of the first wave of the COVID-19 pandemic on hospital demand and deaths for the USA and European Economic Area countries
Authors : IHME COVID-19 health service utilization forecasting team, Christopher JL Murray
Publication date : 04/21
Paper : Available here
Code available : Python; https://github.com/ihmeuw-msca/CurveFit
Deterministic or stochastic model : stochastic
Model category : phenomenological
Model sub-category
time-varying covariates; ERF curve; deaths modeling; mixed-effects model; spatially-structuredData used for the model
Europe, US - data on confirmed deaths from WHO and governments websites and data on hospital capacity and utilisation from publicly available sources and government websites; Hubei, Italy, Korea, US - average age pattern of mortality rates; Social mobility data from Descartes Labs3, SafeGraph4 and Google (via their COVID19 Community Mobility Reports)Global approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) estimate and forecast deaths across locations as a function of the implementation of social distancing measures with an online display tool https://covid19.healthdata.org/united-states-of-america; 2) forecast health service needs (hospital admissions, ICU admissions, length of stay, and ventilator need)Outputs
prediction of the deaths dynamics across regions, forecast of the health service needs (hospital admissions, ICU admissions, length of stay, and ventilator need)How intervention strategies are modelled
region-stratified inflection time parameters, depending on a weighted average of 6 social-distancing metrics per region, which encodes the timing and behavioral impact of social distancingAdditional Assumptions
1) change of the curve trend depends on both the timing and the effects of the implementation of social distancing; 2) all social distancing measures that are in place will stay in place; 3) any remaining restriction start within a fixed number of daysProblem Formulation
GLM predictionOther parameters
maximum asymptotic level that the rate can reach; time at which the rate of mortality is maximal; slope at the infection point of the death-rate curveHow parameters are estimated
data-drivenDetails on parameters estimation
GLM with mixed effects; estimated via nonlinear LSE regression of the cumulative number of deaths, use of L-BFGS-B algorithmComment/issues
1) model with random effects specific to the region, integrating real time covariates relative to the implementation of interventions; 2) analysis of the predictive performance; 3) cannot project longer-term epidemiological dynamics beyond the initial wave of mitigated transmissionAuthors : Henrik Salje, Cécile Tran Kiem, Noémie Lefrancq, Noémie Courtejoie, Paolo Bosetti, Juliette Paireau, Alessio Andronico, Nathanaël Hoze, Jehanne Richet, Claire-Lise Dubost, Yann Le Strat, Justin Lessler, Daniel Bruhl, Arnaud Fontanet, Lulla Opatowski, Pierre-Yves Boëlle, Simon Cauchemez
Publication date : 04/20
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEI ICU; symptoms/severity structured; age-structuredData used for the model
France - daily hospitalisations, ICU admissions, deaths and information on patients hospitalised in public and private hospitals, from the SI-VIC web portal, completed by data from OSCOURGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
1) estimate the impact of the lockdown and current population immunity; 2) estimate the risk of infection and severe outcomes by age and genderOutputs
probability of hospitalisation, ICU and death by age and gender; estimation of the distribution of delays from hospitalisation to death by age; estimation of the distribution of delays from hospitalisation to ICU; prediction of the dynamics of daily new infections, daily ICU admissions and number of ICU beds, prediction of the proportion of the population infected by May 11th for each of the 13 regions in metropolitan FranceHow intervention strategies are modelled
modeling of 5 hypothetis contact matrix; 2 values for R0: before and after lockdownProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
mean cumulative probability of having been infected across the entire population; relative risk of infection for an individual in a specific age group; probability of hospitalisation and admission in ICU depending on age; latent period; incubation period; infectious period; time between symptoms onset and admission in ICU: initial state conditions of the system; mean time spent in ICUHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) latent period; incubation period; infectious period and time between symptoms onset and admission in ICU from literature-
for the relative risk of getting infected for a specific age group: the mean number of contacts that an individual of this age group has on a daily basis as measured in France, weighted by the proportion of the population that is within this age group;
-
mean cumulative probability of having been infected across the entire population; age-dependent probabilities hospitalisation and admission to ICU are fitted by MLE (Poisson distribution on the number of ICU by age and gender, and the number of hospitalisations by age and gender);
-
initial number of exposed and mean time spent in ICU are jointly estimated via MH-MCMC, assuming a specific distribution on the number of ICU beds occupied
Comment/issues
1) couples hospitalisation data with the complete dataset from the Princess Diamond to disentangle the risk of being hospitalized in those infected from the underlying probability of infection 2) suite of sensitivity analysis and simulations where the true parameters are known to assess the performance of the estimationAuthors : Eric H. Y. Lau, Peng Wu, Xilong Deng, Jian Wang, Xinxin Hao, Yiu Chung Lau, Jessica Y. Wong,Yujuan Guan, Xinghua Tan, Xiaoneng Mo, Yanqing Chen, Baolin Liao, Weilie Chen, Fengyu Hu, Qing Zhang, Mingqiu Zhong, Yanrong Wu, Lingzhai Zhao, Fuchun Zhang, Benjamin J. Cowling, Fang Li, Gabriel M. Leung
Publication date : 04/15
Paper : Available here
Code available : code in R on https://github.com/ehylau/COVID-19
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
parametric distribution estimationData used for the model
1) Temporal patterns of viral shedding of patients in hospital 2) timing of symptoms onset from infector - infectee transmission pairs (two confirmed cases such that one case was highly likely to have been infected by the other) from publicly available dataGlobal approach
epidemiological parameter estimationDetails of approach
1) decompose the sequence of transmission between an infector and an infectee; 2) estimate the variations across time of infectiousness for an infected individual 3) estimate the distribution of incubation period 4) estimate the distribution of the generation timeOutputs
estimation of the dynamics of infectiousness in an infected individual (probability that the transmission event would occur); estimation of the incubation time distribution; simulation of the generation time as a function of the start of the infectionAdditional Assumptions
infected cases would considered infectious before or after illness onsetProblem Formulation
maximizing the likelihood of the observed generation time, assuming the distribution of the generation time is a convolution between assumed gamma distribution of the date of transmission and the assumed lognormal distribution of the incubation period, to estimate the parameters of the date of transmission event distributionEpidemiological parameters
incubation period distribution parameters; date of transmission distribution parameters,How parameters are estimated
literatureDetails on parameters estimation
incubation period distribution from literature (https://www.nejm.org/doi/full/10.1056/NEJMoa2001316, data from Wuhan)Comment/issues
model at a micro-scale to understand the dynamics in transmission between two individualsAuthors : Christian Gollier
Publication date : 04/12
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRD; isolated/non-isolated structuredData used for the model
no dataGlobal approach
evolution forecast; modeling of various intervention strategies; model introducing economic componentsDetails of approach
simulations under various scenarios of intervention and evaluation of the economic impact of lockdown to assess cost-benefit of each strategyOutputs
prediction of compartments dynamics under different scenariosHow intervention strategies are modelled
susceptible divided into working and lockdown subpopulations; lockdown modeled by the reduction of the working population (teleworking) and the reduction of the transmission rate for lockdown populationProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
proportion of individuals that are locked down; proportion of individuals that are testedHow parameters are estimated
literatureComment/issues
1) simulation of different scenarios (no intervention, suppression by a long-term quarantine, stop-and-go) and cost-benefit analysis of choosing one or the other, systematic testing of non-confined individuals; 2) not enough explanations of how the parameters are fixed; 3) half of lockdown population breaking the rulesAuthors : Laura Di Domenico, Giulia Pullano, ChiaraE.Sabbatini, Pierre-Yves Boëlle, Vittoria Colizza
Publication date : 04/12
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SEIRD H ICU; age-structured; multistage; symptoms/severity structured; (I: divided into prodromic, asymptomatic, paucisymptomatic, infectious with mild or severe symptoms)Data used for the model
Ile-de-France - up to 04/03 - hospital admission data before lockdown from French hospital data APHPGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) prediction of propagation dynamics, admission of ICU, number of ICU beds required under various intervention scenarios; 2) estimation of the reproduction number under various intervention scenariosOutputs
prediction of propagation dynamicsHow intervention strategies are modelled
social distancing measures expressed via changes in the age-location contact matricesAdditional Assumptions
1) children are assumed to become either asymptomatic or paucisymptomatic only; 2) children and adults are considered to be equally susceptibleProblem Formulation
numerical schemeSolving Method
forward scheme, 100 stochastic runsEpidemiological parameters
incubation period; prodromal phase period; latency period; serial period; infectious period per compartment; probability of being asymptomatic; probabilities (for a symptomatic) of being paucisymptomatic; probability of developing mild symptoms or severe symptoms; probability of going in ICU if severe symptomsOther parameters
location-specific contact matrices per scenarioHow parameters are estimated
literature; data-drivenDetails on parameters estimation
admission of ICU, number of ICU beds required depending on the scenario calibrated on Ile-de-France hospitalisation data; R0 depending on the scenario computed from the dynamical system, using next-generation matrix methodComment/issues
1) addresses the question of ICU and hospital capacity; 2) simulates the impact of lockdown of different durations and exit strategies; 3) exploits the structure of contacts in function of age, activity and placePhysical distancing is working and still needed to prevent COVID-19 resurgence in King, Snohomish, and Pierce counties
Authors : Niket Thakkar, Roy Burstein, Daniel Klein, Jen Schripsema, and Mike Famulare
Publication date : 04/10
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRData used for the model
Washington, King and Snohomish counties - 02/28 to 03/30; Pierce county - 03/05 to 03/30 - lab testing data from WADoH through the WDRS, mobility data from Facebook Data For Good Project - Disease Prevention MapsGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) estimation of the impact of physical distancing on the effective reproduction number; 2) prediction of infected cases for three different evolutions of the reproduction numberOutputs
daily point estimation of the effective reprodution number; prediction of the compartments dynamicsHow intervention strategies are modelled
estimation of Re dynamic as consequence of social distancing measures imposed in Washington, include schools lockdown, prohibiting large groups gatherings, non-essential workplaces lockdown and providing public information on how to adapt its behaviourAdditional Assumptions
1) reporting rate or case-to-infection rate per country assumed unknown and constant i.e. the probability of testing an infectious is constant for the modeled period per country; 2) probability to be tested follows a binomial distributionProblem Formulation
multi-step processEpidemiological parameters
classic parameters; latent and infectious periods fixedOther parameters
constant reporting rate to evalutate the total number of infected peopleHow parameters are estimated
data-drivenDetails on parameters estimation
infection rate estimated by regression of movement covariate against case-based estimatesComment/issues
1) conservative assumption of the constant reporting rate; 2) mobility data to measure changes in mobility and places where people spend time by the mobility covariate; 3) mobility data used to make more reliable the estimations; 4) 95% confidence interval for all the estimations; 5) mortality data not yet used; 6) based on a previous report https://covid.idmod.org/data/Social_distancing_mobility_reductions_reduced_COVID_Seattle.pdfStrong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies
Authors : Cesar Manchein, Eduardo L. Brugnago, Rafael M. da Silva, Carlos F.O. Mendes, Marcus W. Beims
Publication date : 04/08
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRQ; symptoms/severity structured; isolated/non-isolated structured; several I states (divided into asymptomatic and symptomatic populations); (Q: identified and isolated)Data used for the model
Asia, Europe, North and South Amercia until 03/27 from WHOGlobal approach
evolution forecast; modeling of various intervention strategies; optimisation of intervention strategiesDetails of approach
1) analysis a general shape for all countries of the cumulative rate of confirmed infected to predict the optimal control strategy for each coutry; 2) analysis of the correlation between countriesOutputs
optimal intervention strategy for each countryHow intervention strategies are modelled
modeled by the state Q respresenting the identified and isolated population (cf Republic of Korea); interactions modeled by a multiplicative constant to R0 per region; simulation with different levels of interactionsAdditional Assumptions
power-law (a + t^m) increase of the cumulative number of positive patients where m is region-dependentProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; features of the power-law growth for the cumulative number of infectedHow parameters are estimated
data-drivenDetails on parameters estimation
1) power-law features per country; 2) Distance Correlation to estimate the correlation between countriesComment/issues
1) data-based estimation of R0/region; 2) estimates similarity of the cumulative infected confirmed patients evolution using distance correlation metric; 3) interesting conclusion wrt the policyFirst-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a modelling impact assessment
Authors : Kathy Leung, Joseph T Wu, Di Liu, Gabriel M Leung
Publication date : 04/08
Paper : Available here
Code available : R; package EpiEstim
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRData used for the model
all Chinese provinces - confirmed cases; Beijing, Shanghai, Shenzhen, Wenzhou - individual delays between symptom onset and reporting when available, time between onset and death or the time between admission and death when availableGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
simulation of the effect of relaxing interventions after the epidemic has been initially brought under control but not eliminatedOutputs
estimated trajectory of the Re from the trajectory of the number of cases and symptoms onsets; evolution of the number of cases when interventions are successively relaxed, then re-implemented; relative case count compared with no relaxation of interventions; duration of aggressive interventions required to push prevalence back to pre-relaxation level, all in function of the Re at relaxation timeHow intervention strategies are modelled
time-varying R0Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; mean generation time; effective number per intervention type; effective number when interventions are relaxed (R2); effective number at the end of a first soft re-implementation of intervention phase (R4) = at the beginning of the more aggressive interventions; initial state conditions of the systemHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: mean generation time; 2) data-driven: distribution between symptoms onset and reporting by MCMC, then this distribution is taken into account to construct the adjusted curve of cases by date of symptoms onsets, then uses the method from https://academic.oup.com/aje/article/160/6/509/79472 to estimate the Re over time (MLE using the distribution of the generation time), this Re guides choices of R2 and R4; 3) distribution of time of onset-to-report and onset-to-death lognormal for sensitivity analysis and gamma for simulationsComment/issues
addresses the question of the consequences on relaxing strategies as a function of the Re when relaxingAuthors : Maria Chikina, Wesley Pegden
Publication date : 04/08
Paper : Available here
Code available : http://math.cmu.edu/~wes/pub.html
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRD; age-structuredData used for the model
no dataGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
prediction of the effects of age-heterogeneous mitigations on infections, ICU admissions and deathsOutputs
prediction of the number of infections and ICU cases as a function of various interventions strategiesHow intervention strategies are modelled
intervention strategies are expressed through the age contact matrixAdditional Assumptions
a fraction of people under the age threshold are subject to relaxed restrictions because: people of different ages often live in the same household, and other risk factors might also be used to inform mitigation effortsProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; mortality rate for each group; rate of ICU admissions per infection; initial state conditions of the system; total populationOther parameters
age-based contact matrixHow parameters are estimated
literatureDetails on parameters estimation
1) age contact matrix from https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005697; 2) mortality rate and rate of ICU admissions per infection from Report 9 of the team at Imperial College LondonComment/issues
1) examine the potential effects of age-heterogeneous mitigations 2) sensitivity analysis in function of the R0Authors : Sourish Das
Publication date : 04/07
Paper : Available here
Code available : https://github.com/sourish-cmi/Covid19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRData used for the model
India, China, US, Iran, South Korea, Japan, Italy, France, Germany, and Spain - from JHU and Covid19IndiaGlobal approach
epidemiological parameter estimation; evolution forecastDetails of approach
1) estimation of the different R0 per state in India to identify the areas where strong actions should be taken; 2) estimation of the effect of lockdown on the number of deathsOutputs
prediction of the compartments dynamics without lockdown at national and state levelsHow intervention strategies are modelled
modeling without lockdown; lockdown effect estimated by the difference between predicted infected cases by the model trained with before-lockdown datas and reported numbers of infected casesAdditional Assumptions
1) individuals are assumed to be immune to re-infection in the short term; 2) generation processProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; parameters of the generation process distributionHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) generation processComment/issues
1) simple model without lockdown assumptions 2) provide an estimate of the number of deaths if there had been no lockdownAuthors : Xiaohui Chen, Ziyi Qiu
Publication date : 04/07
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; spatially-structuredData used for the model
Italy, Spain, Germany, France, the UK, Singapore, South Korea, China, the US - 01/22 to 04/03 - historical data and data on timings and types of interventionsGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
1) estimation of the impact of different interventions with the simultaneous fit on several countries; 2) forward projection under the interventions estimated efficientOutputs
prediciton of the country-level compartments dynamics depending on the implemented strategiesHow intervention strategies are modelled
time-dependent infection rate for each country; the introduction of each strategy in a country introduces a decreasing factor in the transmission rate which decays the transmission rate more or less slowly depending on a parameter reflecting the time-lag to see the intervention effectAdditional Assumptions
1) each intervention has the same effect on the disease transmission rate across countries and over time 2) time-lag for the interventions impacts controlled by a scaling parameter in the exponential decayProblem Formulation
numerical schemeSolving Method
Euler methodEpidemiological parameters
recovery rate for each country; country-level fixed in the transmission rate; initial state conditions of the systemOther parameters
start date of interventions per country; scaling parameter controlling time-lag effect of interventions; country-independent effect of intervention parameters on the infection rateHow parameters are estimated
literature; data-drivenDetails on parameters estimation
OLS for: country-level fixed in the transmission rate; country-independent effect of intervention parameters on the infection rate; recovery rate for each countryComment/issues
1) multilevel model stratified by countries; 2) evaluate the effects of different strategies from mask wearing to quarantine, effects that are shared by all countries; 3) confidence intervals for parameters estimation; 4) interpretation of simultaneously fitted parameters not evidentAuthors : Anatoly Zhigljavsky, Roger Whitaker, Ivan Fesenko, Kobi Kremnizer, Jack Noonan, Paul Harper, Jonathan Gillard, Thomas Woolley, Daniel Gartner, Jasmine Grimsley, Edilson de Arruda, Val Fedorov, Tom Crick
Publication date : 04/07
Paper : Available here
Code available : See Appendix (R and Julia)
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
age-structured; SIRData used for the model
simulated data adapted to the UKGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) derive a generic epidemic model with a finite number of subpopulations; 2) forcast of the epidemic model applied to age subpopulations, under various public health interventionsOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
constant-by-parts time-dependent R0 depending on the timing of the interventions set up; introduction of a parameter representing the strength of the isolation for the most sensitive subgroup; level of the isolation strategies depending on the subpopulation and application to: homogeneous subgroups but different intervention start time, heterogenerous age-based subgroups (modeled by the strengh parameter);Additional Assumptions
1) time to infectionProblem Formulation
numerical schemeSolving Method
R and JuliaEpidemiological parameters
classic parameters; initial R0 fixed per intervention; distribution parameters fixedOther parameters
level of intervention per scenario; subgroup sizes; strengh of the isolation per subgroupHow parameters are estimated
literatureDetails on parameters estimation
sensibility analysis: 1) time to infectionComment/issues
1) estimation of age-based case death ratio; 2) model that could include refined susceptibility to the virus or medical pre-hisotry as the model is generic; 3) parameter sensitivity analysis of some epidemic variables; 4) models of spatial heterogeneity of the population and asynchronous timing of the epidemic through various areasAuthors : T. R. Hurd
Publication date : 04/07
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : individual-level
Model sub-category
network-based; SI; SIR; SEIRD; random network; social networkData used for the model
simulated data with a network from facebookGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
1) provide a purely analytical toolkit for networks; 2) analysis of SI(ER) model on an inhomogeneous random social network; 3) forecast the epidemic model through infection cascade mechanismOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
representation of social relations by a network with types that represent people’s important attributes, such as age, gender, living arrangement, profession, country and locationAdditional Assumptions
1) each individual has a random “immunity buffer”; 2) if one is infected, a random viral load will be transmitted to each of his/her social contacts; 3) network types are constantProblem Formulation
numerical scheme with cascade mechanismSolving Method
FFTEpidemiological parameters
classic parametersOther parameters
calibrated network (IRSN)How parameters are estimated
simulatedComment/issues
1) extensive theory; 2) introduction of an inhomogeneous random social network as a structure for infection cascade mechanism and the modeling of immunity; 3) advocate for the use of network-based modelsAuthors : Gary E. Weissman, Andrew Crane-Droesch, Corey Chivers, ThaiBinh Luong, Asaf Hanish, Michael Z. Levy, Jason Lubken, Michael Becker, Michael E. Draugelis, George L. Anesi, Patrick J. Brennan, Jason D. Christie, C. William Hanson III, Mark E. Mikkelsen, Scott D. Halpern
Publication date : 04/07
Paper : Available here
Code available : https://github.com/Code
ForPhilly/chime/
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIRData used for the model
China and other regions- temporal serie of infections; Pennsylvania : local information about the regional populationGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
display the projected epidemic course and clinical demand across a broad range of assumptions about parameters and interventison strategies, available at https://penn-chime.phl.io/Outputs
prediction of the compartments dynamics; prediction of the demand for total hospital beds, ICU beds, and ventilatorsHow intervention strategies are modelled
social distancing indirectly modeled through the modification of the doubling timeProblem Formulation
numerical schemeSolving Method
Monte Carlo simulation (1000 draws from probability distributions of model parameters)Epidemiological parameters
doubling time, distribution of the proportion of infections requiring hospitalisation; distribution of the proportion of hospitalised patients requiring ICU care; distribution of the proportion of ICU patients requiring mechanical ventilation; distribution of hospital length of stay; distribution of ICU length of stay; distribution of the proportion of ICU time on mechanical ventilation; distribution of the recovery timeOther parameters
1) regional population size; hospital market share (expected proportion of the population served by the hospitals in question); currently hospitalized patients; currently known regional infections; 2) percentage of social distancing; date of social distancing measures effect (may be delayed from implementation)How parameters are estimated
literatureDetails on parameters estimation
given by the literature or direct data, epidemiological parameters can be modified in the websiteComment/issues
1) provides comparison with other models; 2) limited to short term forecasting, only applicable during the period prior to a region’s peak infectionsAuthors : Fernando Alvarez, David Argente, Francesco Lippi
Publication date : 04/06
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; optimal controlData used for the model
countries with at least 100 cases - daily cases, recoveries and deaths, total deaths from WHO, JHUGlobal approach
evolution forecast; modeling of various intervention strategies; model introducing economic components; optimisation of intervention strategiesDetails of approach
prediction of the optimal lockdown trajectory to apply to minimize the economic lossOutputs
prediction of the optimal lockdown trajectory; prediction of the compartments dynamics under the optimal lockdown scenarioHow intervention strategies are modelled
time-dependent infection rate as function of the lockdown level and effectivenessAdditional Assumptions
possible increase of the death rate due to an overload of the hospitalsProblem Formulation
minimisation of an economic cost in terms of production lost induced by lockdown and deathsSolving Method
Optimal control algorithm with the use of a Hamilton-Jacobi-Bellman equationEpidemiological parameters
classic paratemers; probability of getting a vaccine and cureOther parameters
effectiveness of lockdown; ability of testingHow parameters are estimated
literature; data-drivenDetails on parameters estimation
literature or simple calibrationComment/issues
1) gives the optimal trajectory of lockdown level that must be adopted to minimize the economic loss; 2) need of some economic parameters as the value of life.Authors : Malik Magdon-Ismail
Publication date : 04/06
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; symptoms/severity structured; (I: divided into mild, serious and asymptomatic populations)Data used for the model
USA - European CDC - from 01/21 to 03/14Global approach
epidemiological parameter estimation; evolution forecastDetails of approach
estimation of the "virulence" (portion of mild cases that becomes serious) and the number of asymptomatic infected population on early dataOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
confirmed infected population is fully quarantined (infection rate equal to zero)Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parametersHow parameters are estimated
data-drivenDetails on parameters estimation
GD using a combination of RMSE and root-mean-squared-percentage-error between observed dynamics and model predictionsComment/issues
1) simple and robust application of the SIR model from early data; 2) asymptomatic cases approach and comparison of SIR parameters with economic and demographic data from several countries; 3) time-stamping of the predictions 4) use of economic and demographic data from several countries in order to evaluate its influence on the epidemiological parametersCoronavirus Covid-19 spreading in Italy: optimizing an epidemiological model with dynamic social distancing through Differential Evolution
Authors : I. De Falco, A. Della Cioppa, U. Scafuri, and E. Tarantino
Publication date : 04/06
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRDData used for the model
Italy, Lombardy and Campania - until 03/29 - from Italian Ministry for Health free repositoryGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
estimation of the model parameters through Differential Evolution to predict I population (peak, end of spreading)Outputs
prediction of the compartments dynamicsHow intervention strategies are modelled
infection rate multiplied by a time-dependent factorProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parametersOther parameters
social distancing time-dependant factor for social distancingHow parameters are estimated
data-drivenDetails on parameters estimation
optimisation via Differential Evolution an optimisation technique that randomly creates an initial set of possible solutions and chooses the best one by minimisation of RMSEComment/issues
1) efficient model with a relevant approach that considers that the rate of social distancing is not fixed but a time-varying functionAuthors : Raj Dandekar, George Barbastathis
Publication date : 04/06
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIR; SEIR; SEIRQ; (Q: Quarantine); combined with a NNData used for the model
Wuhan - 01/24 to 03/03 from CDC, Italy - 02/24 to 03/23, South Korea - 02/22 to 03/17, USA - 03/08 to 04/01 from CSSE and JHUGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) learn and predict the epidemic model; 2) augment a first principles-derived epidemiological model with a data-driven NN; 3) comparison of the intervention strategies in the different countries through the impact on the control of R0; 4) predictions of the dynamics for multiple modelsOutputs
prediction and comparison of the dynamics for the optimal choice of: time-dependent quarantine wrt the strength and effective time-dependent repoduction numberHow intervention strategies are modelled
nonlinear time-dependent infection rate per country (representing the strength of the policy) and estimated by a neural networkProblem Formulation
NN (10 units in hidden layer and ReLu activation function) weights and epidemic rates minimising the MSE loss function through local adjoint sensitivity analysis of the infected and recoveredSolving Method
ADAM optimizerEpidemiological parameters
classic parameters; initial state conditions of the systemHow parameters are estimated
data-drivenDetails on parameters estimation
1) data-driven for the NN on infected population public data per region; 2) rates of the compartments for SIR, SEIR, estimated by minimisation of the MSE loss function through local adjoint sensitivity analysis of the infected and recovered, using the ADAM optimizer.Comment/issues
1) lack of reproducibility by NN; 2) NN ables to introduce quarantine strategies and to predict stagnation in the infected numbers, that does not show classic SIR model (comparison showed); 3) effective reproduction number dynamic deduced directly from the infectious rate (or quarantine strength) dynamic; 4) based on Rackauckas et al.( 2020, 2019); 5) indepth detailed procedure and parameter estimationAuthors : Frank Wood, Andrew Warrington, Saeid Naderiparizi, Christian Weilbach, Vaden Masrani, William Harvey, Adam Scibior, Boyan Beronov, Ali Nasseri
Publication date : 04/06
Paper : Available here
Code available : https://github.com/plai-group/covid
Deterministic or stochastic model : deterministic; stochastic
Model category : compartmental
Model sub-category
SEIR; multistage; symptoms/severity structured; (I: divided into mild, severe and critical cases)Data used for the model
simulated dataGlobal approach
evolution forecast; modeling of various intervention strategies; optimisation of intervention strategiesDetails of approach
using existing epidemiological dynamics models to infere the policies that are more likely to be effective, given explicit constraints (such as threshold of infected population)Outputs
number of people infected wrt the impact of social distancing policiesHow intervention strategies are modelled
R0 multiplied by a factorAdditional Assumptions
1) the parameters that can be controlled by policy directives are independent of the ones that cannot be affected by the measures (e.g. the incubation period or death rate of the disease) 2) there exists a population dynamic that can be controlled 3) there exists a “policy goal”Problem Formulation
numerical scheme; inference on SIER model to infer which policies are more likely to be effective given explicit constraintsSolving Method
1) ODE to simulate the spreading 2) approximate Bayesian computation to compute the conditional probability of infected population conditionally to intervention and importance sampling from the prior 3) nested Monte Carlo to condition on the policy leading to a desired outcome with a given probabilityEpidemiological parameters
classic parametersOther parameters
reduction rate of social contactHow parameters are estimated
literatureComment/issues
1) well-written article that offers a comparison of intrinsic properties between compartmental model and agent-based models; 2) simple form of planning as inference to perform inference task in pre-existing stochastic epidemiological models 3) very useful tool to inform policy-makersCode available : https://github.com/plai-group/covid
Deterministic or stochastic model : stochastic
Model category : individual-level
Model sub-category
individual-based; FREDData used for the model
simulated dataGlobal approach
evolution forecast; modeling of various intervention strategies; optimisation of intervention strategiesDetails of approach
using existing epidemiological dynamics models to infere the policies that are more likely to be effective, given explicit constraints (such as threshold of infected population)Outputs
number of people infected wrt the impact of social distancing policiesHow intervention strategies are modelled
social distancing measure integrated in the structure of the model by control parametersAdditional Assumptions
1) the parameters that can be controlled by policy directives are independent of the ones that cannot be affected by the measures (e.g. the incubation period or death rate of the disease) 2) there exists a population dynamic that can be controlled 3) there exists a “policy goal”Problem Formulation
inference on individual-based model to infer which policies are more likely to be effective given explicit constraintsSolving Method
1) simulation the spreading 2) approximate Bayesian computation to compute the conditional probability and importance sampling from the prior 3) rejection sampling with nested Monte Carlo to condition on the policy leading to a desired outcome with a given probabilityEpidemiological parameters
classic parametersOther parameters
reduction rate of social contactHow parameters are estimated
literatureComment/issues
1) well-written article that offers a comparison of intrinsic properties between compartmental model and agent-based models; 2) simple form of planning as inference to perform inference task in pre-existing stochastic epidemiological models 3) very useful tool to inform policy-makersAuthors : Villalobos Arias, Mario Alberto
Publication date : 04/06
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : phenomenological
Model sub-category
logistic curve; Gompertz curveData used for the model
China, South Korea, Spain, Costa Rica, Italy, USA - from European Centre for Disease Prevention and ControlGlobal approach
evolution forecastDetails of approach
estimate and predict the dynamics by generalized logistic regression and Gompertz function curve-fittingOutputs
prediction of the infected population dynamicProblem Formulation
generalized logistic model and Gompertz model predictionOther parameters
parameters of the GLR functionHow parameters are estimated
data-drivenDetails on parameters estimation
fitted by a nonlinear optimisation algorithmComment/issues
1) simple and robust growth modelAuthors : Arkaprava Roy and Sayar Karmakar
Publication date : 04/05
Paper : Available here
Code available : Yes but link broken
Deterministic or stochastic model : stochastic
Model category : phenomenological
Model sub-category
Poisson auto-regressive modelData used for the model
3 most affected regions in China, South Korea, Singapore (for aggressive testing strategy), USA, European countries - 01/23 to 03/26Global approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
predict the spread of the epidemic; estimate the impact of the interventions on the time-varying coefficients through the change in the length of the period from infection to symptomatic per regionOutputs
daily count of newly infected; mean/intercept functionHow intervention strategies are modelled
consequence of lockdown measured through the time delay between infection and the onset of the symptoms; comparison of its impact on the time-dependent parameters processes; comparison of different strategies implemented in each regionAdditional Assumptions
daily infected countProblem Formulation
time-varying version of the linear Poisson autoregressive model; posterior error via square-loss minimisation;Solving Method
gradient-based HMCEpidemiological parameters
classic parametersOther parameters
prior distribution of the unknwon count; decomposition coefficients on the B-splin expansion basis of the parameters (mean and intercepts) prior distributionsHow parameters are estimated
data-drivenDetails on parameters estimation
1) MCMC to sample the prior distribution of the coefficients of the parameters B-spline decomposition from the likelihood function, using HMC algorithm; 2) for sensitivity analysis: coefficients of the parameters priors decompositionComment/issues
1) time-varying parameter for count-series modeled by Poisson regression; 2) interesting, good predictions and future work promising; 3) sensitivity analysisAuthors : Omer Karin, Yinon M. Bar-On, Tomer Milo, Itay Katzir, Avi Mayo, Yael Korem, Boaz Dudovich, Amos J. Zehavi, Nadav Davidovich, Ron Milo, Uri Alon
Publication date : 04/04
Paper : Available here
Code available : Use of https://github.com/ryansmcgee/seirsplus
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR; SEIR-Erlang; (R: recovered, quarantined or dead)Data used for the model
simulated dataGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
analyse the efficiency on reducing the infected population by cyclic lockdown strategy through three models of the spread of the virusOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
strong or weak cyclic lockdown modeled through cycle-dependent constant R0; analysis of the impact of various length of periods for the cycles, on the effectiviness of the lockdownSolving Method
unspecifiedEpidemiological parameters
classic parametersHow parameters are estimated
literatureDetails on parameters estimation
1) literature: Bar-On et al. 2020; rates of E and IComment/issues
1) original lockdown policy to maintain low R: 4days work-10days lockdown; 2) economic analysis but not modeledCode available : Use of https://github.com/ryansmcgee/seirsplus
Deterministic or stochastic model : stochastic
Model category : individual-level
Model sub-category
network-based; SEIR on social contact network; (R: recovered, quarantined or dead)Data used for the model
simulated dataGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
analyse the efficiency on reducing the infected population by cyclic lockdown strategy through three models of the spread of the virusOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
strong or weak cyclic lockdown modeled through cycle-dependent constant R0; analysis of the impact of various length of periods for the cycles, on the effectiviness of the lockdown; for the NN model, a proportion of the links are inactivatedProblem Formulation
for the NN: each node represents an individual that can be in one of the ODE states, includes Erdos-Reyi and small world networksSolving Method
unspecifiedEpidemiological parameters
classic parametersHow parameters are estimated
literatureDetails on parameters estimation
Bar-On et al. 2020; rates of E and IComment/issues
1) original lockdown policy to maintain low R: 4days work-10days lockdown; 2) economic analysis but not modeledAuthors : Elena Loli Piccolomini, Fabiana Zama
Publication date : 04/03
Paper : Available here
Code available : https://github.com/pcm-dpc/COVID-19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRDData used for the model
Italian regions: Lombardia and ER - 02/24 to 03/27Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) estimation of the epidemic model and prediction of its dynamic; 2) various modelings of intervention scenariosOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
piecewise (constant, rational and exponential) time-dependent infectious rateProblem Formulation
non-linear LSE minimisation with positive constraintsSolving Method
Runge-Kutta - Matlab, precision of the data estimation process by relative error computation of the modeled vector wrt the measured data per compartmentEpidemiological parameters
classic parameters; initial state conditions of the systemHow parameters are estimated
data-drivenDetails on parameters estimation
data-driven (on either 18 days or 31 days period); two model calibrations considering: 1) constant parameters, 2) time-dependent transmission rate (piecewise constant, rational and exponential)Comment/issues
1) low relative error on the modeled data; 2) exponential decay of the transmission rate too fast wrt Italian data; 3) sensitivity analysisAuthors : R. Djidjou-Demassea, Y. Michalakisa, M. Choisya, M. T. Sofoneaa, S. Alizona
Publication date : 04/02
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEAIR; symptoms/severity structured; optimal controlData used for the model
simulated dataGlobal approach
evolution forecast; modeling of various intervention strategies; model introducing economic components; optimisation of intervention strategies; epidemiological parameter estimationDetails of approach
1) forcast of the epidemic model with various public health interventions; 2) propose the optimal strategy to implement until the creation of a vaccine by minimizing the cumulative number of deaths and total economic costsOutputs
optimal intervention strategyHow intervention strategies are modelled
time-dependent control function modeling the decrease of R0 as consequence of the (non-pharmaceutical) intervetion strategy; control function optimized wrt both cumulative deaths and costs; comparison with cyclic intervention (but shown to be less efficient)Additional Assumptions
1) transmission rate different if symptomatic of asymptomatic; 2) recovered are supposed to be life-immuned; 3) mortality rate of severe cases and of natural deaths assumed piecewise-constant depending on the capacity of the health care system; 4) immigration; 5) squared cost functionProblem Formulation
minimisation of cumulative deaths (direct COVID and indirect due to the saturation of hospital system) and cumulative weighted costs implied by policy interventionSolving Method
Optimal control algorithm by Hamiltonian formulation of the system and using Pontraying's maximum principle for the theoritical optimal solution but due to limit conditions, interative forward-backward sweep algorithmEpidemiological parameters
classic parameters; initial state conditions of the system; step functions mortalitiy rate and natural mortality rate, dependent of the hospital saturationOther parameters
immigration rate; weight of the intervention cost policy; health care capacity (ICU)How parameters are estimated
data-driven; literatureDetails on parameters estimation
1) literature: case-fatality ratio and R0; 2) mortality rate of severe cases and of natural deaths assumed piecewise-constant depending on the capacity of the health care system; 3) disease-induced mortality and transmission rate computed by closed forms deterministic equationsComment/issues
1) very interesting modeling of the intervention policies that includes non-linear cost impliciations; 2) model optimized also wrt the health care system capacity; 3) reproductible; 4) subpopulation modeling wrt the intensity of the symptomsAuthors : Nikolay M. Yanev, Vessela K. Stoimenova, Dimitar V. Atanasov
Publication date : 04/02
Paper : Available here
Code available : No but daily reports per country http://ir-statistics.net/covid-19/
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
Harris, Lotka-Nagaev and Crump-Hove statistical estimatorsData used for the model
Bulgaria, Italy, France, Germany, Spain - 03/08 to 03/28 - from WHOGlobal approach
epidemiological parameter estimationDetails of approach
estimation of R0Outputs
estimation of R0How intervention strategies are modelled
confirmed infected population is fully quarantined (infection rate equal to zero) and the final size of the infected population used to estimate R0Additional Assumptions
1) symptomatic are quarantined; 2) fixed probability that newly infected heal and leave the reproduction processEpidemiological parameters
recovery probability for newly infected; mean values of the predicted non-observed population; probability of positive infectedHow parameters are estimated
data-drivenDetails on parameters estimation
statistical estimation of R0 by Harris, Lotka-Nagaev and Crump-Hove type estimators using the prediction of the final number of the infected populationComment/issues
1) daily optimisation 2) extensive theory 3) comparison of three estimators 4) statistical guarantees for all three estimators, sensitivity analysisCode available : No but daily reports per country http://ir-statistics.net/covid-19/
Deterministic or stochastic model : stochastic
Model category : individual-level
Model sub-category
branching process; two-type branching process; (type 1: non-discovered infected, type 2: discovered infected)Data used for the model
Bulgaria, Italy, France, Germany, Spain - 03/08 to 03/28 - from WHOGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
1) daily estimation of model parameters; 2) prediction of the non-observed infected populationOutputs
daily prediction of non-observed infected and infected populationHow intervention strategies are modelled
confirmed infected population is fully quarantined (infection rate equal to zero)Additional Assumptions
1) symptomatic are quarantined; 2) fixed probability that newly infected heal and leave the reproduction processProblem Formulation
prediction of the two-types branching processes: (1) contaminated but still healthy individuals, (2) positive individuals; every individual (1) produces a random number of (1) or is transformed to (2); (2) are then isolated (quarantine)Solving Method
the final number of each process directly used for the three estimators of R0Epidemiological parameters
recovery probability for newly infected; mean values of the predicted non-observed population; probability of positive infectedHow parameters are estimated
data-drivenDetails on parameters estimation
initial state of the system based of lab-confirmed casesComment/issues
1) daily optimisation 2) extensive theory 3) comparison of three estimators 4) statistical guarantees for all three estimators, sensitivity analysisEvolving epidemiology and transmission dynamics of coronavirus disease 2019 outside Hubei province, China: a descriptive and modelling study
Authors : Juanjuan Zhang, Maria Litvinova, Wei Wang, Yan Wang, Xiaowei Deng, Xinghui Chen, Mei Li, Wen Zheng, Lan Yi, Xinhua Chen, Qianhui Wu, Yuxia Liang, Xiling Wang, Juan Yang, Kaiyuan Sun, Ira M Longini Jr, M Elizabeth Halloran, Peng Wu, Benjamin J Cowling, Stefano Merler, Cecile Viboud, Alessandro Vespignani, Marco Ajelli, Hongjie Yu
Publication date : 04/02
Paper : Available here
Code available : for the calculation of the Re dynamics, https://github.com/majelli/Rt
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
parametric distribution estimationData used for the model
China at the provincial (outside Hubei) - 01/19 to 02/17 - individual information (demographic characteristics, exposure and travel history, and key timelines) of laboratory-confirmed cases from official public sourcesGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
estimate per region the changes in epidemiology and transmission dynamics between two periods through changes in key variables; assess whether the strict control measures put in place in China have been successful in slowing the transmissionOutputs
for the two periods 01/24 to 01/27 and 01/28 to 02/27, estimation per region of 1) the incubation period distribution, the sequence of epidemic intervals, the time delays from symptom onset to hospital admission, from first healthcare consultation to hospital admission and from symptom onset to official reporting 2) the dynamics of the ReProblem Formulation
1) Find the best fit of the key time-to-event data between weibull, gamma, and lognormal distributions 2) the number of casesEpidemiological parameters
generation time distribution; incubation period distributionHow parameters are estimated
data-drivenDetails on parameters estimation
1) estimation of key time-to-event intervals distributions via parametric distribution fitting: gamma, weibull and lognormal distributions are fitted to the incubation period, the generation time, the time from symptoms onset to hospital admission, the time from first healthcare consultation to hospital admission, the time from symptom onset to official reporting; AIC are computed to determine the best fit; 2) MH-MCMC sampling to estimate the posterior distribution of Re over time, assuming that the daily number of new cases (by date of symptom onset) is approximated by a Poisson distribution whose mean depends on the Re; non-informative prior distributions of Re(t) (flat distribution in the range [0-1000])Comment/issues
1) lot of information on the data 2) exploits information on individual exposure to estimate the generation time 3) investigates robustness in the estimation of Re wrt the changes in the detection of cases inducted by the new definition of suspected cases 3) the modelisation of the Re could be used as a propagation modelPredicting the Spread of the COVID-19 Across Cities in China with Population Migration and Policy Intervention
Authors : Jiang Zhang, Lei Dong, Yanbo Zhang, Xinyue Chen, Guiqing, Yao, Zhangang Han
Publication date : 04/01
Paper : Available here
Code available : https://github.com/jakezj/SICRD_model_COVID19_in_China
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SICRD; (I: unconfirmed, C: confirmed)Data used for the model
China - 01/01 to 02/07 - R package nCov2019 and Population Migration dataset from Baidu Migration ProjectGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
estimate the epidemic model during public lockdown in China using population migrationOutputs
reported/unreported casesHow intervention strategies are modelled
multiplicative term (time and effect sensibility dependence) for the infectious state; comparison with the base case scenario (without intervention)Additional Assumptions
1) same parameters for all regions; 2) China isolated system (no in/outflows)Problem Formulation
numerical schemeSolving Method
forward scheme - ODE solver in PytorchEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
mobility rateHow parameters are estimated
data-drivenDetails on parameters estimation
Wolfram database (National Health Comission and Chinese Centers for Disease Control and Prevention)Comment/issues
1) model with various scenarios of intervention; 2) sensitivity of parameters in supplementary doc; 3) use of population mobility/migration dataAuthors : Wenjie Zheng
Publication date : 04/01
Paper : Available here
Code available : https://github.com/WenjieZ/2019-nCoV
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIR; SIRQ; isolated/non-isolated structured; (R: death/recovered, Q: hospitalized or quarantined); state-space frameworkData used for the model
simulated data: virulence data, surveillance data, serological dataGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
estimate and predict the dynamics by modeling the discontinuities induced by changes of policies with total variation regularisation, modeling of a state-space framework using non MC methods to infere the nonparametric compartmental models; total variation regularisation replaces the prior in the log-posterior estimationOutputs
estimation of the compartments rates and its dynamics for: 1) constant SIRQ with no regularisation, 2) time-varying transmission rate, SIR with regularisation, 3) time-varying transmission and quarantine rates SIRQ with regularisationHow intervention strategies are modelled
interventions modelled by the addition of compartment Q; discontinuities of interventions modelled by time-dependent transmission rate and quarantined rate, regulated by total variation regularization; quarantined considered as non-infectiousProblem Formulation
numerical schemeSolving Method
Euler-Maruyama schemeEpidemiological parameters
classic parameters; initial state conditions of the systemHow parameters are estimated
simulatedDetails on parameters estimation
estimation of the vector of compartments rates for 1) MAP of MLE; 2) and 3) if total variation regularisation, dubbed iterative Nelder-Mead to compute the regularized posterior modeComment/issues
1) models the discontinuous policy implied by lockdowns; 2) state-space framework so possibility to use data from multiple sources; 3) can find a global optimum by MAP thanks to regularisation; 4) evaluates the a posteriori mode (not mean); 5) need to choose prior distributions for SIRQ's parameters (two proposed)Authors : Giuseppe C. Calafiore, Carlo Novara and Corrado Possieri
Publication date : 03/31
Paper : Available here
Code available : https://github.com/pcm-dpc/COVID-19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
reported/unreported structured; SIRDData used for the model
Italian regions - Civil Protection Department - 02/24 to 03/30Global approach
epidemiological parameter estimation; evolution forecastDetails of approach
estimation of the epidemic model by quantifying the rate of non-reported infected populationOutputs
1) estimation of the classic parameters, the fraction of undetected cases, the initial proportion of susceptible in the population; 2) prediction of compartments dynamicsAdditional Assumptions
the initial proportion of susceptible individuals in the population is learnedProblem Formulation
numerical schemeSolving Method
forward scheme - ODE; initial proportion of susceptibles in the population and proportion of undetected infected are estimated conjointly with compartments rates via grid searchEpidemiological parameters
initial proportion of susceptibles in the population, classic parameters and proportion of undocumented infectedOther parameters
exponential decay weighting parameter (used to give more relevance to most recent data)How parameters are estimated
data-drivenDetails on parameters estimation
classic parameters (transmission, recovery and mortality rates) estimated via the minimisation of a weighted MSE between observed and predicted I, R, D sequences, where errors weights decay exponentially with time to give more weight to most recent errors, and with a grid search over other parameters (initial proportion of susceptibles in the population and proportion of undetected infected)Comment/issues
1) unrecorded infected cases are considered in the dynamics of the model which seems more than relevant; 2) no intervention policy modeled but partially balanced by the weighting approach that gives more importance to most recent data 3) no need to initialize the model (because considered as a parameter)Authors : Harshad Khadilkar, Tanuja Ganu, Deva P Seetharam
Publication date : 03/31
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SEIRD; NNData used for the model
simulated dataGlobal approach
modeling of various intervention strategies; optimisation of intervention strategiesDetails of approach
learn the optimal intervention strategy in a complexe modeling of the epidemic dynamics via reinforcement learning algorithmOutputs
optimal intervention strategyHow intervention strategies are modelled
optimisation variable: the method computes the optimal lockdown/release policy for each node of the network; weights on health and economic impact to defineAdditional Assumptions
connection strength between each pair of nodes: proportional to the product of each node's population and inversely proportional to the square root of the distance between the nodesProblem Formulation
1) reward function defined by the weighted duration of lockdown, number of infected and dead; 2) loss defined by MSESolving Method
Reinforcement Learning: Deep Q Learning + SGD in keras + full Monte-Carlo reward at the endEpidemiological parameters
total population per node; symptomatic rate per node; recovered rate per node; evolution of symptomatic for the last days per node; potential external infectors per nodeOther parameters
population mobility; contact parametersHow parameters are estimated
literatureComment/issues
1) interesting modeling and lockdown policies: basic idea: each node is locked down if the amount of symptomatic patients crosses a threshold + can be opened/closed once a week; 2) economic impact encompassed in the modelReport 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries
Authors : Seth Flaxman, Swapnil Mishra, Axel Gandy, H Juliette T Unwin, Helen Coupland, Thomas A Mellan, Harrison
Zhu, Tresnia Berah, Jeffrey W Eaton, Pablo N P Guzman, Nora Schmit, Lucia Cilloni, Kylie E C Ainslie, Marc
Baguelin, Isobel Blake, Adhiratha Boonyasiri, Olivia Boyd, Lorenzo Cattarino, Constanze Ciavarella, Laura Cooper,
Zulma Cucunubá, Gina Cuomo-Dannenburg, Amy Dighe, Bimandra Djaafara, Ilaria Dorigatti, Sabine van Elsland,
Rich FitzJohn, Han Fu, Katy Gaythorpe, Lily Geidelberg, Nicholas Grassly, Will Green, Timothy Hallett, Arran
Hamlet, Wes Hinsley, Ben Jeffrey, David Jorgensen, Edward Knock, Daniel Laydon, Gemma Nedjati-Gilani, Pierre Nouvellet, Kris Parag, Igor Siveroni, Hayley Thompson, Robert Verity, Erik Volz, Caroline Walters, Haowei Wang, Yuanrong Wang, Oliver Watson, Peter Winskill, Xiaoyue Xi, Charles Whittaker, Patrick GT Walker, Azra Ghani, Christl A. Donnelly, Steven Riley, Lucy C Okell, Michaela A C Vollmer, Neil M. Ferguson, Samir Bhatt
Publication date : 03/30
Paper : Available here
Code available : https://github.com/ImperialCollegeLondon/covid19model/releases/tag/v1.0; https://github.com/mrc-ide/covid-sim
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
ID; time-delayedData used for the model
11 European countries - observed deaths from the European Centre of Disease ControlGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) estimation of R0 dynamic due to different interventions; 2) comparison between the model prediction of deaths and a counterfactual model prediction considered without interventionOutputs
prediction of the compartments dynamics; estimation of the time varying R0How intervention strategies are modelled
piecewise constant R0 driven by interventions with shared effects for all countriesProblem Formulation
numerical schemeSolving Method
stochastic schemeEpidemiological parameters
classic parameters; generation time distribution; symptoms to death rate distribution; infection to symptoms rate distributionOther parameters
intervention dates per countryHow parameters are estimated
data-drivenDetails on parameters estimation
1) normal prior for R0 where varianceComment/issues
1) joint estimation of hierarchical model for all countries with estimation of the influence of policies; 2) validation and sensibility analysisAuthors : Robert Verity, Lucy C Okell, Ilaria Dorigatti, Peter Winskill, Charles Whittaker, Natsuko Imai, Gina Cuomo-Dannenburg, Hayley Thompson, Patrick G T Walker, Han Fu, Amy Dighe, Jamie T Griffin, Marc Baguelin, Sangeeta Bhatia, Adhiratha Boonyasiri, Anne Cori, Zulma Cucunubá, Rich FitzJohn, Katy Gaythorpe, Will Green, Arran Hamlet, Wes Hinsley, Daniel Laydon, Gemma Nedjati-Gilani, Steven Riley, Sabine van Elsland, Erik Volz, Haowei Wang, Yuanrong Wang, Xiaoyue Xi, Christl A Donnelly, Azra C Ghani, Neil M Ferguson
Publication date : 03/30
Paper : Available here
Code available : https://github.com/mrc-ide/COVID19_CFR_submission
Deterministic or stochastic model : deterministic
Model category : phenomenological
Model sub-category
age-structured; logistic curveData used for the model
various data from China including WHO-China until 03/03, Diamond Princess and demographic dataGlobal approach
epidemiological parameter estimation; evolution forecastDetails of approach
1) estimation of the age-dependent death rate and infected population requiring hospitalisation; 2) bias correction due to the different testing policies across ChinaOutputs
estimation of the age-dependant infection rate, death rate and required hospitalisation rateAdditional Assumptions
uniform infection rate for all age groupsProblem Formulation
logistic growth curveEpidemiological parameters
age-dependent death, infected and required hospitalisation ratesOther parameters
growth function parametersHow parameters are estimated
data-drivenDetails on parameters estimation
1) prior of growth rate estimated by a log-linear model; 2) onset-to-death timeComment/issues
1) forecast of the very useful proportion of infected individuals requiring hospitalisation 2) epidemiological parameters learned on different databases 3) correction of testing and delay bias 4) rigorous statistical analysisAuthors : Ashutosh Simha, R. Venkatesha Prasad, Sujay Narayana
Publication date : 03/29
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIR; with diffusionData used for the model
Europe and India - from 02/24Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
forward projection of the parametric epidemic model of a stochastic SIR model with diffusion, under various levels of lockdown percentageOutputs
prediction of the compartments dynamics for various levels of lockdownHow intervention strategies are modelled
exposure factor in the transmission between susceptible and infected which reflects the level of lockdownProblem Formulation
numerical schemeSolving Method
Euler-Maruyama numerical integration methodEpidemiological parameters
classic parametersOther parameters
diffusion coefficientHow parameters are estimated
data-drivenDetails on parameters estimation
simultaneous ISE minimisation, terminal error and terminal rate error between the data and the modelComment/issues
1) embeds volatility in SIR equationsAuthors : Alexis Akira Toda
Publication date : 03/27
Paper : Available here
Code available : https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRData used for the model
countries with at least 1000 cases - 03/13 to 03/27 - from JHUGlobal approach
evolution forecast; model introducing economic components; epidemiological parameter estimation; optimisation of intervention strategiesDetails of approach
1) forward projection of the impact of lockdown; 2) prediction of the optimal percentage of lockdown and the optimal start time to minimize the infected populationOutputs
prediction of the compartments dynamics; prediction of the optimal policy to minimize the infected population at the peak (optimal infection rate and optimal threshold of cases when measures should be applied)How intervention strategies are modelled
modified transmission rateProblem Formulation
minimisation of the infected population at the peakSolving Method
analytic solutionEpidemiological parameters
classic parametersHow parameters are estimated
data-drivenDetails on parameters estimation
1) nonlinear LSE if S,I,R timeseries are available, else from literature; 2) numerical minimisation of the sum of squared logarithmic errors (SSE) if only I is availableComment/issues
comparison of SIR parameters estimation for many countries, addresses the question of the optimal policy to minimize the peak and the optimal time to start the policyAuthors : Facundo Piguillem, Liyan Shi
Publication date : 03/27
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR; optimal control; symptom/gravity stratifiedData used for the model
Italy, early dataGlobal approach
epidemiological parameter estimation; evolution forecast; model introducing economic components; optimisation of intervention strategiesDetails of approach
1) prediction the trajectory of the optimal level of economic activity; 2) analysis of the impact of testingOutputs
trajectory of the optimal level of the economic activity; prediction of the compartments dynamics under different scenariosHow intervention strategies are modelled
multiplicative term in infection rate in function of variable level of working interactions in time; if tests are available, isolation of symptomatic infected and asymptomatic testedAdditional Assumptions
1) recovered and death rates depend on the number of infectious and health care capacity (ICU); 2) Some economic-based hypothesis (e.g. production equals consumption)Problem Formulation
maximisation of a welfare functionSolving Method
optimal control algorithm with hamiltonian formulationEpidemiological parameters
classic parameters; death rate if treated; death rate if untreated; critical massOther parameters
health care capacity (ICU); rate at which the society discounts the future; proportion of individuals tested at randomHow parameters are estimated
literature; data-drivenDetails on parameters estimation
literature of simple calibrationComment/issues
1) model formulated in terms of economic loss, gives the optimal trajectory of the intensity of lockdown 2) demands lot of exogenously fixed or calibrated parameters.The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study
Authors : Kiesha Prem, Yang Liu, Timothy W Russell, Adam J Kucharski, Rosalind M Eggo, Nicholas Davies
Publication date : 03/25
Paper : Available here
Code available : Code in R https://github.com/kieshaprem/covid19-agestructureSEIR-wuhan-social-distancing
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR; age-structured; symptoms/severity structured; (I: divided into clinical and subclinical)Data used for the model
simulated - synthetic contact mixing matrices for China scaled to Wuhan population sizeGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
simulations under different scenarios of intervention, modeled through the location-age contact matrixOutputs
prediction of the compartments dynamics per scenario and ageHow intervention strategies are modelled
social distancing measures modeled via changes in contact matricesProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
R0; average incubation period; average duration of infection; initial number of infected; probability that an infected case is clinical; probability that an infected case is subclinical; probability that an infection resulted from a subclinical individual; daily hospitalized and ICU recovered rate; daily hospitalized and ICU death rate; initial state conditions of the systemOther parameters
location-specific contact matrices per scenarioHow parameters are estimated
literatureComment/issues
1) simulates the impact of lockdown of different durations and exit strategies; 2) exploits the structure of contacts in function of age, and location; 3) investigates the effects of strategies in function of age categoriesModèle SIR mécanistico-statistique pour l'estimation du nombre d'infectés et du taux de mortalité par COVID-19
Authors : Lionel Roques, Etienne Klein, Julien Papaix et Samuel Soubeyrand
Publication date : 03/25
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIR; inferential statisticsData used for the model
France, South Korea - 02/22 to 03/17Global approach
evolution forecastDetails of approach
estimate the epidemic model and statistically infere the total unreported number of infected casesOutputs
prediction of the compartments dynamicsAdditional Assumptions
1) number of positive confirmedProblem Formulation
1) MLE wrt start time of the epidemic, relative probability to be tested if susceptible vs. infected independent of the time, average number of contacts per person and time; 2) MAP with uniform a priori distributions of the later parameters; 3) number of positive confirmedSolving Method
1) optimisation under constraints; 2) MCMC - MatlabEpidemiological parameters
classic parameters; a priori distributionsOther parameters
initial date of the epidemic, relative probability to be tested for a susceptible vs an infectedHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) uniform prior for transmission rate and initial time; 2) transmission rate, initial date of the epidemic, relative probability to be tested for a susceptible vs an infected; MLE of the increments of the daily new casesComment/issues
1) interesting statistical inference method to estimate the total number of unreported cases; 2) uniform a priori distribution chosen; 3) correlation of the estimated parameters analysis; 4) sensitivity analysisAuthors : Moritz U. G. Kraemer, Chia-Hung Yang, Bernardo Gutierrez, Chieh-Hsi Wu, Brennan Klein, David M. Pigott, Louis du Plessis, Nuno R. Faria, Ruoran Li, William P. Hanage, John S. Brownstein, Maylis Layan, Alessandro Vespignani, Huaiyu Tian, Christopher Dye, Oliver G. Pybus, Samuel V. Scarpino
Publication date : 03/25
Paper : Available here
Code available : null
Deterministic or stochastic model : stochastic
Model category : phenomenological
Model sub-category
spatially-structured; Poisson auto-regressive model; negative binomial auto-regressive model; log-linear auto-regressive model; time-varying covariates; mixed-effects modelData used for the model
China from 12/01 to 02/10 - human mobility data with age and gender data from the Baidu Qianxi web platformGlobal approach
evolution forecast; modeling of various intervention strategies; epidemiological parameter estimationDetails of approach
1) measure the impact of various human mobility policy controls; 2) 3 models used and compared with BIC indexOutputs
prediction of the size of the infected population, and the time for doubling size for the 3 models consideredHow intervention strategies are modelled
comparison before and after travel shutdownProblem Formulation
GLM predictionSolving Method
BIC for model evaluation; AIC for model selection; elastic-net regression and n-fold cross validation for model validationEpidemiological parameters
incubation timeOther parameters
growth parameters; human mobility parameters depending on age and before/after travel shutdownHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) parameters fitted from province-level data; 2) incubation periodComment/issues
1) vast approach of the effect of travel shutdown with more than significant results 2) intersting differenciation of gender but with limited results due to high bias in data 3) rigorous comparison of 3 GLM modelsComposite Monte Carlo Decision Making under High Uncertainty of Novel Coronavirus Epidemic Using Hybridized Deep Learning and Fuzzy Rule Induction
Authors : Simon James Fong, Gloria Li, Nilanjan Dey, Ruben Gonzalez Crespo, Enrique Herrera-Viedma
Publication date : 03/22
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
composite MC (CMC)Data used for the model
China - 01/25 to 02/25 - from Chinese Center for Disease Control and PreventionGlobal approach
model introducing economic components; epidemiological parameter estimation; evolution forecastDetails of approach
1) estimate the direct cost of an urgent part of the national budget planning to control the epidemic; 2) modeling by a composite MC method and neural networksOutputs
total cost needed to control the epidemicAdditional Assumptions
growth of the daily medical costsProblem Formulation
1) deep learning network BFGS-PNN; 2) fuzzy rule induction (FRI)Solving Method
compartements dynamics forecast by BFGS-PNN to feed the composite MC model; BGFS-PNN algorithm (found with GROOM) with Broyden-Fletcher-Goldfarb-Shanno algorithm (Quasi-Newton method and secant method);Epidemiological parameters
classic parametersOther parameters
daily direct costsHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) growth of the daily medical costsComment/issues
1) composite MC model that enables non-deterministic data distributions along with future predictions from a deterministic model; 2) original approach to solve the very specific problem of estimating the total cost of the pandemic; 3) based on very strong assumptions (all details are in supplementary materials)Authors : Anthony Zhenhuan Zhang, Eva A. Enns
Publication date : 03/21
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR; symptoms/severity structured; (I: divided into symptomatic and asymptomatic populations); age-structured; spatially-structured; 1) for the Wuhan model: non subpopulation considered; 2) for the other cities: the initial subpopulation for individuals arrived from Wuhan, isolated subpopulations wrt to the day of arrival from Wuhan during the infectious period of 14 days (14 classes), and an independent subpopulation for the local city populationData used for the model
Major Chinese cities (Chongqing, Beijing, Shanghai) - 12/01/19 to 03/31 - from CDC, WHO, Diamond Princess CruiseGlobal approach
epidemiological parameter estimation; evolution forecast;modeling of various intervention strategies; model introducing economic componentsDetails of approach
evaluation of the impact on the compartments dynamics and the economy of various intervention scenariosOutputs
compartments dynamics for each intervention scenarioHow intervention strategies are modelled
1) three types of measures: social distancing (for all population or by age) modeled through reducting the contact matrix, lockdown for travellers from Wuhan and city-wide lockdown in Wuhan modeled by the subpopulations modeled by a quasi-total reduction of the travel volume; 2) variation of the measures duration and onset dates and comparison to the doing nothing scenario; 3) another analysis including workplace and school lockdowns in the cities except WuhanAdditional Assumptions
inter-individuals contact matrix to estimate the age-dependent mixing effectsProblem Formulation
model calibration of the obesrved morbidity and mortality statisticsSolving Method
unspecifiedEpidemiological parameters
classic parameters per age category; contact matrix per age category and for symptomatic/asymptomatic groupsOther parameters
local economic variables: multiple costs implied by the quarantine; travel volumes; reduction of travellers; recover cost; death costHow parameters are estimated
data-driven; literatureDetails on parameters estimation
1) data-driven (on mortality and morbidity dynamics per age category - CDC and WHO, rates for symptomatics and asymptomatics using the Cruise data); 2) data-driven: contact matrix estimation on an age-mixing study in Southern China; 3) Incremental Mixture Importance Sampling (bayesian algorithm) to estimate the a posteriori distribution of daily transmission rate given the ratio between asymptomatic and symptomatic per age (Russell et al.); 4) literature for the economic parametersComment/issues
1) complete report after the lockdown in China, with interesting policy strategies, cost estimation, sensitivity analysis; 2) parameter calibration depending on the three categories of ages; 3) age-mixing modeled by the contact matrix estimationAuthors : Vitaly Volpert, Malay Banerjee, Sergei Petrovskii
Publication date : 03/20
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; (I: latently infected); time-delayedData used for the model
China, Korea and Italy - infected cases from from https://www.worldometers.info/coronavirus/Global approach
evolution forecast;modeling of various intervention strategiesDetails of approach
analysis of R0 fluctuations by the estimation of a modified SIR model where the latently infected are put in quarantine after the incubation periodOutputs
estimation of R0, constant or piecewise constantHow intervention strategies are modelled
the latently infected are put in quarantine after the incubation period; therefore in the ODE system, at time t, contacts between susceptible and infected at time t minus the incubation time are substractedSolving Method
unspecifiedEpidemiological parameters
incubation time; R0How parameters are estimated
literature; data-drivenDetails on parameters estimation
literature for the incubation time; exponential curve fitting for the R0Comment/issues
1) not a lot of explanations on how parameters are fitted 2) simplifying assumptions of a constant susceptible population and a common model of quarantine for countries that applied different strategies 3) the intervention strategy is entirely parameterized by the incubation period 4) interesting suggestions of developments to integrate spatial considerationsPredicting the number of reported and unreported cases for the COVID-19 epidemic in South Korea, Italy, France and Germany
Authors : P. Magal, G. Webb
Publication date : 03/20
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRU; reported/unreported structured; (I: asymptomatic infectious, R: reported symptomatic, U: unreported symptomatic)Data used for the model
Korean Center for Disease Control 01/20 - 03/09, Italian Ministry of Health 01/31 - 03/03, French Public Agency of Health 02/25 - 03/09 and Robert Koch Institute of Germany 02/24 - 03/09Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) learn the epidemiological parameters 2) forecast of reported populationsOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
time-dependent transmission rate: constant before lockdown and exponential decrease once it beginsAdditional Assumptions
1) unreported cases are a constant fraction of the total reported infectious ones; 2) the positive-confirmed (R) are reported and isolated; 3) cumulative reported infectious cases have exponential increase; 4) isolated systemProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
parameters of the exponential growth of the cumulative reported infectious casesHow parameters are estimated
literature; data-drivenDetails on parameters estimation
using methods of the previous article (https://www.preprints.org/manuscript/202002.0079/v1)Comment/issues
1) similar analysis as for China (https://arxiv.org/pdf/2002.12298.pdf) applied to South Korea, Italy, France and GermanyAuthors : Joseph T. Wu, Kathy Leung, Mary Bushman, Nishant Kishore, Rene Niehus, Pablo M. de Salazar, Benjamin J. Cowling, Marc Lipsitch and Gabriel M. Leung
Publication date : 03/19
Paper : Available here
Code available : upon request to the corresponding author
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIR; age-structuredData used for the model
infected, death cases per age and data on human mobility in Wuhan from various sources from 12/10 to 02/25Global approach
epidemiological parameter estimation; modeling of various intervention strategiesDetails of approach
estimation of the clinical severity by age categoriesOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
transmission rate multiplied by a parameter representing the social distancing measured after 01/23 (lockdown in Wuhan)Additional Assumptions
1) observed proportion (ratio between recorded and actual infected population) is constant over time; 2) Gamma distribution for the incubation period, the generation time process and the time between onset and death; 3) multinomial sampling process from the age-dependent distribution of true cases for the age-dependent distribution of confirmed cases;Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters per age categoryOther parameters
parameters of Gamma distributionsHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: mean and standard deviation of the incubation period, infection-symptomatic probability, probability of detecting symptomatic cases exported from mainland; data-driven: others; 2) incubation period, the generation time process and the time between onset and deathComment/issues
extension of a previous article with an extensive approach of age categorisation using 9 subgroups that highlights the wide variations of clinical severity by age groupAuthors : Victor Alexander Okhuese
Publication date : 03/19
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRUS; (R: infected population quarantined and expecting recovery at time t, U: recovered satisfying undetectable criteria)Data used for the model
Worldwide - 01/22 to 03/14 - WHO, JHUGlobal approach
epidemiological parameter estimation; modeling of various intervention strategiesDetails of approach
anaylsis of the disease-free equilibrium point wrt the asymptotic stabilityOutputs
disease-free equilibrium point of the systemHow intervention strategies are modelled
intervention modeled by the compartment R common for all the population: infected population divided in infected and infected quarantinedAdditional Assumptions
1) isolated system; 2) each compartment has a non zero rate of direct deathProblem Formulation
numerical schemeSolving Method
Runge-Kutta-Fehllberg 4-5th order method - MapleEpidemiological parameters
classic parameters; implicit constant death rates per compartment; time-dependent incidence rate; initial state conditions of the system; fixed maximum lifespan after infectionOther parameters
maximal death rate constant; efficiency of the interventionHow parameters are estimated
literature; data-drivenDetails on parameters estimation
R0 derived in closed form, from the next-generation method; maximum lifespan after infection fixed to 14 daysComment/issues
1) models the possible event of multi-infections; 2) analysis of the disease free equilibrium point; 3) effectiveness of the quarantine and observatory rate through the recovery rateAuthors : Sk Shahid Nadim, Indrajit Ghosh, Joydev Chattopadhyay
Publication date : 03/18
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRQAJ; (Q: quarantined, A: asymptomatic, I: infected symptomatic, J: isolated, R: recovered)Data used for the model
China, five provinces - 01/22 to 02/22Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) predict the compartments dynamics and estimate the rates; 2) analysis of the characteristic points of the differential system; 3) estimate R0 with and without lockdownOutputs
prediction of the compartments dynamics per region; prediction of the effective transmission rate variations per regionHow intervention strategies are modelled
modeling of quarantine and isolation population as compartment and quantified by analysis of the disease transmission dynamics; comparison with base case scenarioAdditional Assumptions
all quarantined are exposedProblem Formulation
numerical schemeSolving Method
forward scheme, ODE; Matlab; accuracy of the predictions measured with MAE and RMSEEpidemiological parameters
classic parametersOther parameters
natural death rate equal for all compartments; net inflow of susceptible individuals per region (im/emmigratio, births)How parameters are estimated
data-drivenDetails on parameters estimation
1) estimation of the threshold rates of exposed and the isolated that are infected through the computation of the partial derivatives of R0 if lockdown, in order to measure the ranges for the interventions scenarios; 2) rates estimated on data with non-linear LSE minimisation on MatlabComment/issues
1) indepth theoritical analysis; 2) comparison if control policy and if not; 3) predictive model + estimation of R0 et if control, RC; 4) good numerical analysis (RMSE +MAE); 5) long and short term prediction (quick numerical analysis of possible outbreak); 6) interesting heat maps for parameters correlations and impact on RCAuthors : Eunha Shim, Amna Tariq , Wongyeong Choi , Yiseul Lee, Gerardo Chowell
Publication date : 03/17
Paper : Available here
Code available : null
Deterministic or stochastic model : stochastic
Model category : phenomenological
Model sub-category
generalized growth curve; Poisson error structureData used for the model
South Korea (CDC) - from 01/20 to 02/26Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
estimation of Re and comparison of death rate by age and genderOutputs
prediction of Re and of infected populationHow intervention strategies are modelled
time-varying scaling of growth parameterAdditional Assumptions
generation intervalProblem Formulation
renewal equationEpidemiological parameters
Re; generation intervalOther parameters
growth parameterHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: parameters of the generation time; 2) data-driven using MC: others; 3) generation intervalComment/issues
1) cluster study and articles based on the trajectory of the epidemic 2) fluctuations of Re are given by age and gender 3) short efficient articles, with limited details of the algorithmic partAuthors : Clement Massonnaud, Jonathan Roux, Pascal Crépey
Publication date : 03/16
Paper : Available here
Code available : upon request (R package and application developed)
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIR; age-structuredData used for the model
French regions - 01/22 to 03/14 - from INSEE, SAEGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
prediction of the epidemic model at fixed horizon wrt different values of R0, the age category and the impact on the healthcare resources (ICU constraints for each region)Outputs
prediction of the compartments dynamics; estimation of the overrun date of the ICU capacity and the healthcare resources for each regionHow intervention strategies are modelled
three scenarios with different R0 considered constant; no mobility between the regionsAdditional Assumptions
1) same hospitalisation period for all ages; 2) each region considered an isolated systemProblem Formulation
numerical schemeSolving Method
ODE - C++Epidemiological parameters
classic parameters per age category; initial state conditions of the system; contact matrix, severity, ICU and death risks per age categoryOther parameters
repartition of hospitals; health care capacity (ICU)How parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature for incubation and contagion periods; 2) data-driven for the age sensors based on Chinese datasets but for age-dependent death risk on the Italian National Institute of Health; 3) geographical repartition of hospitals estimated by Voronoi polygons; 4) inter-individuals contact matrix using Chinese data that is standardized to the French population to estimate the expected age distribution of cases; 5) age-dependent age deaths risks estimated on Italian datasetsComment/issues
1) introduction of 17 age groups with estimation of age-dependent mixing ; 2) mortality rate per age estimated with Chinese data but different in Europe cf recent data; 3) estimation of ICU beds and date of capacity limits / region; 4) no transmissions between regions; 5) age-mixing modeling by the contact matrix estimationReport 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand
Authors : Neil M Ferguson, Daniel Laydon, Gemma Nedjati-Gilani, Natsuko Imai, Kylie Ainslie, Marc Baguelin, Sangeeta Bhatia, Adhiratha Boonyasiri, Zulma Cucunubá, Gina Cuomo-Dannenburg, Amy Dighe, Ilaria Dorigatti, Han Fu, Katy Gaythorpe, Will Green, Arran Hamlet, Wes Hinsley, Lucy C Okell, Sabine van Elsland, Hayley Thompson, Robert Verity, Erik Volz, Haowei Wang, Yuanrong Wang, Patrick GT Walker, Caroline Walters, Peter Winskill, Charles Whittaker, Christl A Donnelly, Steven Riley, Azra C Ghani
Publication date : 03/16
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : individual-level
Model sub-category
individual-based; spatially-structuredData used for the model
1) GB - data on spatial and social repartition (age and household distributions size, average class sizes and staff-student ratios, distribution number of workers in workplaces); 2) to 03/14 - GB and US - cumulative number of deathsGlobal approach
evolution forecast; modeling of various intervention strategiesDetails of approach
from a simulated population which reproduces a realistic repartition on geographical space and realistic contact patterns, forcast the epidemic evolution of the populationOutputs
prediction of the compartments dynamics (chosen time-step)How intervention strategies are modelled
5 possible scenarios (school lockdown, social distancing, quarantine, ...) explicitely parameterized in the model via changes in the contact structure (using assumptions about the impact of each intervention and compensatory changes in contacts (e.g. in the home) associated with reduced contact rates in specific settings outside the household)Additional Assumptions
1) transmission events occur through contacts made between susceptible and infectious individuals in either the household, workplace, school or randomly in the community, with the latter depending on spatial distance; 2) infectiousness vary among individuals and over time; 3) per-capita contacts within schools were assumed to be double those elsewhere in order to reproduce the attack rates in children observed in past influenza pandemicsProblem Formulation
1) simulation of a realistic population 2) simulation of a realistic epidemic propagationSolving Method
individual-based algorithmEpidemiological parameters
R0; transmission rates per location (household, school, workplace); incubation period; distribution of individual infectiousness; delay from infectiousness to symptoms onset; recovery period; ratio of symptomatic infectiousness wrt asymptomatic infectiousnessHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: all parameters except 2); 2) data-driven: the exponentially growing rate calibrated to give local epidemics which reproduced the observed cumulative number of deaths in GB or the US seen by 14th March 2020Comment/issues
1) a simulated population is generated to reproduce a realistic distribution across geographical space and realistic contact patterns; 2) realistic simulation which can embed a high level of details and structure and parameterize different strategies, but demands many geographical, social and health dataSubstantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2)
Authors : Ruiyun Li, Sen Pei, Bin Chen, Yimeng Song, Tao Zhang, Wan Yang, Jeffrey Shaman
Publication date : 03/16
Paper : Available here
Code available : https://github.com/SenPei-CU/COVID-19
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SEI; reported/unreported structured; region-mixing; spatially-structured; (two states of infected: documented and undocumented)Data used for the model
China - from 01/10 to 02/08 - daily confirmed cases; China - 2018 - daily numbers of travelers between 375 Chinese cities during the Spring Festival period from the Tencent location-based serviceGlobal approach
epidemiological parameter estimation; evolution forecastDetails of approach
simulate the spatiotemporal dynamics of infections before and after the shutdown of travel in and out of ChinaOutputs
prediction of the compartments dynamicsProblem Formulation
numerical schemeSolving Method
stochastic scheme with Poisson distributions; 4th order Runge Kutta schemeEpidemiological parameters
initial conditions of the system; transmission rate due to documented infected individuals; multiplicative factor reducing the transmission rate of unreported infected patients; fraction of infections that develop severe symptoms (and thus are documented); average latency period; average duration of infection; delay between infection and confirmation of that individual infection for documented infectedOther parameters
matrix of spatial-coupling (travel between cities); multiplicative factor to adjust mobility data estimates of human movement between citiesHow parameters are estimated
data-drivenDetails on parameters estimation
1) MLE for the parameters: transmission rate due to documented infected individuals; multiplicative factor reducing the transmission rate of unreported infected patients; multiplicative factor to adjust mobility data estimates of human movement between cities; fraction of infections that develop severe symptoms (and thus are documented); average latency period; average duration of infection; 2) delay between infection and confirmation of that individual infection for documented infected) via Bayesian inference (Ensemble Adjustment Kalman Filter)Comment/issues
stochastic model which incorporates heterogeneous contact mixing between citiesAuthors : Laura Di Domenico, Giulia Pullano, Pietro Coletti, Niel Hens, Vittoria Colizza
Publication date : 03/14
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SEIR; multistage; age-structured; spatially-structured; (two categories of infectious: pre-symptomatic infectious, symptomatic infectious)Data used for the model
Île-de-France, Hauts-de-France, Grand Est - serie of confirmed cases from Réseau SentinellesGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) comparison per region of the evolution under a scenario with no intervention and under various scenarios implementing school shutdown and telework; 2) estimation of the model's parametersOutputs
prediction of the compartments dynamics per region, under various intervention scenariosHow intervention strategies are modelled
schools lockdown expressed via changes in the location-age contact matricesAdditional Assumptions
1) current uncertainties in the relative susceptibility and transmissibility of children 2) infectiousness is equal for both symptomatics and pre-symptomatics infectious 3) symptomatic adults reduce their contacts, no change of behavior for the ill children as they experience mild or no symptoms 4) take into account of the large under-estimate of unreported casesProblem Formulation
numerical schemeSolving Method
forwards scheme, ODE, 100 stochastic runsEpidemiological parameters
classic parameters; incubation period; infectious period; children relative susceptibility to infection and infectivinessOther parameters
contact matrixHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) contact matrix from literature: when schools are opened, contact matrix computed during the regular school term, when schools are closed, contact matrix computed during holidays in France in a regular year, when telework is additionally considered, mixing accounts for the reduction of contacts that teleworkers would otherwise establish at workplaces; 2) incubation period, infectious period, children relative susceptibility and infectivity from literature; 3) transmission rate is calibrated on the exponential growth and estimated per regionComment/issues
1) various scenarios with precise assumptions 2) sensitivity analysis of the impact of assumptions on relative susceptibility and infectivity of children compared to adults on the effectiveness of school closure.Authors : Wuyue Yang , Dongyan Zhang , Liangrong Peng , Changjing Zhuge , Liu Hong
Publication date : 03/12
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : phenomenological
Model sub-category
Gompertz curve; Richards' curve; Hill's curve; linear curve; quadratic curve; cubic curve; exponential curve; logistic curveData used for the model
China, seven provinces/cities - 01/20 to 02/28 - confirmed infected cases from CDCGlobal approach
evolution forecastDetails of approach
model comparison on the evolution forecastsOutputs
prediction of the compartments dynamics with different methodsProblem Formulation
evaluate the performance of a method in terms of forecast abilitySolving Method
1) for each of the methods, data of the cumulated confirmed cases are separated in several train/test sets where the train sets consist in the data troncated at some different dates and the test sets are the data in the following days; 2) each curve is fitted on the train set and used to predict the dynamics of the test set; 3) the AIC, robustness index and RMSE are computed on the test setsOther parameters
parameters induced by the modelsHow parameters are estimated
data-drivenDetails on parameters estimation
unknown parameters in the models are fitted standard non-linear LSEComment/issues
1) systematical investigation on the forecast ability of 8 widely used empirical functions, 4 statistical inference methods and 5 dynamical models widely used in the literature; addresses the requierements on robustness, sensitivity and the trade-off between model complexity and accuracy; 2) not enough details on the different methodsCode available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; SEIR; SEIR-QD; SEIR-AHQ; SEIR-POData used for the model
China, seven provinces/cities - 01/20 to 02/28 - confirmed infected cases from CDCGlobal approach
evolution forecastDetails of approach
model comparison on the evolution forecastsOutputs
prediction of the compartments dynamics with different methodsProblem Formulation
evaluate the performance of a method in terms of forecast abilitySolving Method
1) for each of the methods, data of the cumulated confirmed cases are separated in several train/test sets where the train sets consist in the data troncated at some different dates and the test sets are the data in the following days; 2) each compartmental model is fitted on the train and used to predict the dynamics of the test set; 3) the AIC, robustness index and RMSE are computed on the test setsEpidemiological parameters
classic parametersHow parameters are estimated
data-drivenDetails on parameters estimation
unknown parameters in the models are fitted standard non-linear LSEComment/issues
1) systematical investigation on the forecast ability of 8 widely used empirical functions, 4 statistical inference methods and 5 dynamical models widely used in the literature; addresses the requierements on robustness, sensitivity and the trade-off between model complexity and accuracy; 2) not enough details on the different methodsCode available : Use of R0 package in R
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
four statistical inference methods; exponential growth; MLE; sequential Bayesian; time-dependent R0Data used for the model
China, seven provinces/cities - 01/20 to 02/28 - confirmed infected cases from CDCGlobal approach
epidemiological parameter estimationDetails of approach
model comparison on the estimation of R0Outputs
estimation of the R0 with different methodsProblem Formulation
evaluate the performance of a method in terms of estimation performanceSolving Method
1) for each of the methods, data of the cumulated confirmed cases are separated in several train/test sets where the train sets consist in the data troncated at some different dates and the test sets are the data in the following days; 2) for each estimate of the R0 a logistic curve where the exponent is derived from the estimated R0 is fitted on the train set and used to predict the dynamics of the test set; 3) the AIC, robustness index and RMSE are computed on the test setsOther parameters
R0How parameters are estimated
data-drivenDetails on parameters estimation
R0 is estimated via 4 different methods: 1) exponential growth, which assumes an exponential growth curve to the virus and estimates the R0 from the Lotka-Euler equation; 2) MLE method based on the assumption that the number of cases generated from a single case is Poisson distributed and depends on the R0; 3) sequential bayesian method, in which the posterior probability distribution of the R0 is estimated sequentially using the posterior at the previous time point as the new prior; 4) time-dependent R0 method: in which the basic reproduction number at any time point is estimated as an average of accumulated estimates at previous time pointsComment/issues
1) systematical investigation on the forecast ability of 8 widely used empirical functions, 4 statistical inference methods and 5 dynamical models widely used in the literature; addresses the requierements on robustness, sensitivity and the trade-off between model complexity and accuracy; 2) not enough details on the different methodsAuthors : Adam J Kucharski, Timothy W Russell, Charlie Diamond, Yang Liu, John Edmunds, Sebastian Funk, Rosalind M Eggo,
Publication date : 03/11
Paper : Available here
Code available : https://github.com/ adamkucharski/2020-ncov/
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SIERData used for the model
six datasets from China (mainly Wuhan) from Dec. to Feb.Global approach
epidemiological parameter estimation; evolution forecastDetails of approach
1) analysis of the risk of outbreak if infectious cases were introduced in cities out of Wuhan using branching processes; 2) measure the effect of large scale control measures; 3) estimation of early transmission dynamicsOutputs
prediction of the compartments dynamics; prediction of ReHow intervention strategies are modelled
time-varying R0Additional Assumptions
start of the outbreak the 11/22Problem Formulation
transmission modelized with a geometric random walk processEpidemiological parameters
classic parametersOther parameters
proportion of detectable cases; relative probability of reporting a confirmed case compared with an exported case; connectivity between countriesHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) from literature: connectivity between countries; 2) data-driven by sequential MC: epidemiological parameters; Erlang distribution for disease delays and exponential distribution for delay from onset to reportingComment/issues
1) intersting stochastic modelisation 2) sensititvity analysis 3) rigorous methodAuthors : Jia Jiwei, Ding Jian, Liu Siyu, Liao Guidong, Li Jingzhi, Duan Ben, Wang Guoqing, Zhang Ran
Publication date : 03/06
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SEIRDAQ; (Q: home quarantined, I: symptomatic infected, A: asymptomatic infected, D: diagnosed)Data used for the model
China, inside/outside of Hubei - 01/23 to 02/17Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategies; model introducing economic componentsDetails of approach
1) prediction of the compartments dynamics under various intervention scenarios; 2) estimation of the control repoduction number function and R0 per region; 3) computation of the accumulated medical resource during the period of time analysisOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
compartment Q with constant rate; analysis of the impact of the governemnental strategies on the R0 functionProblem Formulation
LSE to minimize the number of deathsSolving Method
unspecifiedEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
comprehensive meteorological index; accumulated medical resource needed until the study periodHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) LSE for suceptible to exposed rate and recovery rate; 2) empirical estimates otherwise from literature; 3) R0 when intervention estimated using the next generation matrix approach; 4) accumulated medical resource proportional to the integrate of compartment DComment/issues
1) data based parameter estimation; 2) strict lockdown scenarios with different durations; 3) data-driven estimation of R0 per region and the global dynamic wrt time; 4) supplementary analysis of the meteorogical impact; 5) supplementary prediction if vaccineAuthors : GLEAM Team
Publication date : 03/06
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SLIR; (L: Latent); metapopulation network; spatially-structuredData used for the model
for hubs International Air Transport Association (IATA) and OAG database - for human mobility the Offices of Statistics of 30 countries on five continentsGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) geographical globe's division using the Voronoi method, centered on the major transportation hubs 2) modeling of the transmission dynamics through agent-based epidemic model for the mobility layers and compartmental for the infection progression 3) individual dynamic where transitions are mathematically defined by chain binomial and multinomial processesOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
individual dynamics dependent on the level of disease status, modelisation of the ban by a deacrese of mobility flowProblem Formulation
1) numerical scheme; 2) transmission mechanism driven by chain binomial and multinomial processesSolving Method
Forward scheme, ODEEpidemiological parameters
classic parametersOther parameters
population features, mobility flowHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: range of latent period, infectious period, and generation time parameters; 2) data-driven: sensitivity analysis to select them with ABC and MAP with uniform prior for R0Comment/issues
1) an impressive number of parameters are considered to model the mobility in a very precise way 2) intersting model that combine an agent-based and a compartmental modelAuthors : Matteo Chinazzi, Jessica T. Davis, Marco Ajelli, Corrado Gioannini, Maria Litvinova, Stefano Merler, Ana Pastore y Piontti, Kunpeng Mu, Luca Rossi, Kaiyuan Sun, Cécile Viboud, Xinyue Xiong, Hongjie Yu, M. Elizabeth Halloran, Ira M. Longini Jr., Alessandro Vespignani
Publication date : 03/06
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SLIR; (L: Latent); metapopulation network; spatially-structuredData used for the model
the full dataset contains about 80,000 administrative regions on 5 continents and over 5 million commuting flow connections between them 1) population data from the high-resolution population database of the Gridded Population of the World project from the Socioeconomic Data and Application Center at Columbia University 2) airline transportation data: daily origin-destination traffic flows from the Official Aviation Guide (OAG) and IATA databases (updated 2019). 3) ground mobility/commuting flows are derived by the analysis and modeling of data collected from the Offices of Statistics for 30 countries on 5 continentsGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) geographical globe's division using the Voronoi method, centered on the major transportation hubs 2) modeling of the transmission dynamics through agent-based epidemic model for the mobility layers and compartmental for the infection progression 3) individual dynamic where transitions are mathematically defined by chain binomial and multinomial processes 4) estimate the number of case importations from China and simulate the impact of travel banOutputs
estimate the number of case importations from China and simulate the impact of travel banHow intervention strategies are modelled
individual dynamics dependent on the level of disease status, modelisation of the ban by a deacrese of mobility flowProblem Formulation
1) numerical scheme; 2) transmission mechanism driven by chain binomial and multinomial processesSolving Method
Forward scheme, ODEEpidemiological parameters
classic parametersOther parameters
population features, mobility flowHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: range of latent period, infectious period, and generation time parameters; 2) data-driven: sensitivity analysis to select them with ABC and MAP with uniform prior for R0Comment/issues
1) GLEAM is a powerful tool to simulate the effect of travel ban 2) remarkable visualisation of the import case risk between cities and countriesAuthors : Aniruddha Adiga, Srinivasan Venkatramanan, James Schlitt, Akhil Peddireddy, Allan Dickerman, Andrei Bura, Andrew Warren, Brian D Klahn, Chunhong Mao, Dawen Xie, Dustin Machi, Erin Raymond, Fanchao Meng, Golda Barrow, Henning Mortveit, Jiangzhuo Chen, Jim Walke, Joshua Goldstein, Mandy L Wilson, Mark Orr, Przemyslaw Porebski, Pyrros A Telionis, Richard Beckman, Stefan Hoops, Stephen Eubank, Young Yun Baek, Bryan Lewis, Madhav Marathe, Chris Barrett
Publication date : 03/02
Paper : Available here
Code available : https://nssac.github.io/covid-19/import_risk.html
Deterministic or stochastic model : deterministic
Model category : statistical estimation
Model sub-category
regressionData used for the model
WHO reports - global air traffic data from IATA for the month of February 2019Global approach
evolution forecastDetails of approach
1) prediction of the risk of disease emergence in various countries by combining an estimation of the country's vulnerability to disease outbreaks and the connectivity of the country to China by the concept of effective distance; 2) modeling the impact of flight suspensions to and from ChinaOutputs
estimation of the beginning date of the epidemic spread per countryHow intervention strategies are modelled
airline suspensions represented by a variation in the flow volumes of the air traffic networkProblem Formulation
univariate linear regression modelsSolving Method
Wald test with a t-distribution against a null hypothesis of a slope of 0Other parameters
Infectious Disease Vulnerability Index (IDVI); effective distanceDetails on parameters estimation
estimation of the beginning date of the epidemic spread per country, univariate linear regression models and Wald test with a t-distribution against a null hypothesis of a slope of 0Comment/issues
1) no model for the spread of the disease is proposed 2) highlight the role of air traffic in the spreading of the disease, modeling direct importation risk and the effect of its suspensionAuthors : Aniruddha Adiga, Srinivasan Venkatramanan, Akhil Peddireddy, Alex Telionis, Allan Dickerman, Amanda Wilson, Andrei Bura, Andrew Warren, Anil Vullikanti, Brian D Klahn, Chunhong Mao, Dawen Xie, Dustin Machi, Erin Raymond, Fanchao Meng, Golda Barrow, Hannah Baek, Henning Mortveit, James Schlitt, Jiangzhuo Chen, Jim Walke, Joshua Goldstein, Mark Orr, Przemyslaw Porebski, Richard Beckman, Ron Kenyon, Samarth Swarup, Stefan Hoops, Stephen Eubank, Bryan Lewis, Madhav Marathe, Chris Barrett
Publication date : 03/02
Paper : Available here
Code available : https://nssac.github.io/covid-19/import_risk.html
Deterministic or stochastic model : deterministic
Model category : statistical estimation
Model sub-category
regressionData used for the model
WHO reports - global air traffic data from IATA for the month of February 2019Global approach
evolution forecastDetails of approach
1) prediction of the risk of disease emergence per country, by combining an estimation of the country's vulnerability to disease outbreaks and the connectivity of the country to China by the concept of effective distance; 2) modeling of the impact of flight suspensions to and from ChinaOutputs
estimation of the beginning date of the epidemic spread per countryHow intervention strategies are modelled
airline suspensions represented by a variation in the flow volumes of the air traffic networkProblem Formulation
univariate linear regression modelsOther parameters
Infectious Disease Vulnerability Index (IDVI); effective distanceDetails on parameters estimation
estimation of the beginning date of the epidemic spread per country, univariate linear regression models and Wald test with a t-distribution against a null hypothesis of a slope of 0Comment/issues
1) no model for the spread of the disease is proposed 2) highlight the role of air traffic in the spreading of the disease, modeling direct importation risk and the effect of its suspensionAuthors : Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, Tzu-Hsuan Liu
Publication date : 02/28
Paper : Available here
Code available : https://github.com/PingEnLu/Time-dependent_SIR_COVID-19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIR; symptoms/severity structured; time-dependent; (I: divided into asymptomatic and symptomatic populations); cascade mechanismData used for the model
China and other countries, including Japan, Singapore, South Korea, Italy and Iran - 01/15 (China) and 01/22 (world) to 03/02 - from NHC (China) and JHU (World) and a network from Facebook for social distancing modelingGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) one-day model prediction; 2) estimation of R0, of the asymptomatic population's impact on the spread of the epidemic, herd immunity and effectiveness of social distancingOutputs
prediction of the compartments dynamics; estimation of R0 per country; prediction of the infected population on the prediction window, one-day predictionHow intervention strategies are modelled
time-dependent propagation parameters, SIR parameters depending on the control policiesAdditional Assumptions
order of FIR filters: 3Problem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parametersOther parameters
regularisation parameters; order of FIR filters; prediction windowHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: probability to be symptomatic if infected; 2) data-driven: transmission and recovering rates by ridge regression with regularized MSEComment/issues
1) extensive in theory and in terms of numerical experiments; 2) SIR model containing asymptomatic cases and discrete variations of SIR model parameters showing relevant results; 3) proposal for the modeling of social distancing via Independent Cascades, experimentations on a random network from FacebookAuthors : Z. Liu, P. Magal , O. Seydi, G. Webb
Publication date : 02/28
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRU; reported/unreported structured; (I: asymptomatic infectious, R: reported symptomatic, U: unreported symptomatic)Data used for the model
Wuhan and central region of China - Chinese CDC and NHC - 01/20 to 02/15Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) learn the epidemiological parameters 2) forecast of reported populationsOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
time-dependent transmission rate: constant before lockdown and exponential decrease once it beginsAdditional Assumptions
1) constant rate of unreported/reported cases of the total reported infectious ones; 2) the positive-confirmed (R) are reported and isolated; 3) cumulative reported infectious cases have exponential increase; 4) isolated systemProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
parameters of the exponential growth of the cumulative infected and reported casesHow parameters are estimated
literature; data-drivenDetails on parameters estimation
on the period 01/20 - 01/29 using the methods of the previous article (https://www.preprints.org/manuscript/202002.0079/v1)Comment/issues
1) illustrates the effect of China's policy; 2) based on previous work on parameter estimation from early-staged epidemic (https://www.preprints.org/manuscript/202002.0079/v1); 3) asymptomatic and symptomatic are modeledAuthors : Jinghua Li , Yijing Wang, Stuart Gilmour, Mengying Wang, Daisuke Yoneoka, Ying Wang M Med, Xinyi You, Jing Gu , Chun Hao, Liping Peng, Zhicheng Du, Dong Roman , Yuantao Hao
Publication date : 02/25
Paper : Available here
Code available : Use of R0 package in R
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
four statistical inference methods; exponential growth; MLE; sequential Bayesian; time-dependent R0 and SEIRData used for the model
Wuhan - before the lockdown (01/19 - 01/23) and post-closure (01/23 - 02/08) - from NHCGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) compare different methods of estimation of the R0; 2) model aggregation methodOutputs
R0 estimates for five different methods and overall R0 estimate combining all methods (with confidence intervals)Problem Formulation
estimation of the R0 by five different methods and comparison with a SEIR simulationEpidemiological parameters
R0; for the SEIR model: latent period; recovery period; for the MLE, exponential growth and time-dependent methods: generation time distributionHow parameters are estimated
literature; data-drivenDetails on parameters estimation
estimation of the R0 given historical data; methods: 1) exponential growth, which assumes an exponential growth curve to the virus and estimates the R0 from the Lotka-Euler equation; 2) MLE method based on the assumption that the number of cases generated from a single case is Poisson distributed and depends on the R0; 3) sequential bayesian method, in which the posterior probability distribution of the R0 is estimated sequentially using the posterior at the previous time point as the new prior; 4) time-dependent R0 method: in which the R0 at any time point is estimated as an average of accumulated estimates at previous time points; 5) estimation of the R0 from a SEIR model; with the use of a MH-MCMC algorithm 6) for the overall estimate of R0: weighted average (weights from a Poisson loss function) of the five previous R0Comment/issues
comparison of five estimation methods to estimate the R0, confidence intervals and credible intervals are givenAuthors : Milan Batista
Publication date : 02/25
Paper : Available here
Code available : https://www.mathworks.com/matlabcentral/fileexchange/74658-fitviruscovid19
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRData used for the model
01/16 to 02/25 - published table with the dataGlobal approach
evolution forecast; epidemiological parameter estimationDetails of approach
evolution forecast of the number of daily cases and estimation of the epidemic end dateOutputs
prediction of the daily number of infection dynamicProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemHow parameters are estimated
data-drivenDetails on parameters estimation
nonlinear LSE between the actual and predicted number of casesComment/issues
1) second of a serie of two articles with two methods compared 2) the method is explained in details and all the code is availablePreparedness and vulnerability of African countries against importations of COVID-19: a modelling study
Authors : Marius Gilbert, Giulia Pullano, Francesco Pinotti, Eugenio Valdano, Chiara Poletto, Pierre-Yves Boëlle, Eric D’Ortenzio, Yazdan Yazdanpanah, Serge Paul Eholie, Mathias Altmann, Bernardo Gutierrez, Moritz U G Kraemer, Vittoria Colizza
Publication date : 02/20
Paper : Available here
Code available : null
Deterministic or stochastic model : deterministic
Model category : statistical estimation
Model sub-category
point estimationData used for the model
Africa, China - 2016 to 2019 - SPAR database and Joint External Evaluation from WHO IHR MEF; Infectious Disease Vulnerability Index; INFORM Epidemic IndexGlobal approach
epidemiological parameter estimationDetails of approach
estimation of the virus importation risk from Chinese regions (except Wuhan) to Africa and its impact on two metric: preparedness and vulnerabilityOutputs
probability of exporting the virus; comparison between countriesProblem Formulation
1) risk of importation from a region to a country: mean of the travel flux multiplied by the cumulated incidence weighted by the probability of traveling; 2) exposure analysis: for each country, vector of the proportions of regional risk importationSolving Method
for 2) use of entropy-metric (Jensen-Shannon devergence) to compare similarities between countries; sensitivity estimated by considering the basin of attraction of the airports of Beijing and ShangaiHow parameters are estimated
data-driven; literatureDetails on parameters estimation
estimation of the preparedness and vulnerability metrics based on indicators and score multivariate analysis; 1) risk of importation from a region to a country: mean of the travel flow multiplied by the cumulated incidence weighted by the probability of traveling; 2) exposure analysis: for each country, vector of the proportions of regional risk importation, use of entropy-metric (Jensen-Shannon devergence) to compare similarities between countries; sensitivity estimated by considering the basin of attraction of the airports of Beijing and ShangaiComment/issues
1) estimation of the risk of importation of the virus without modeling the spread of the virus; 2) based on historical data and indicators available per country in Africa; 3) lack of data available wrt to passengers information to give precise impact for each country; 4) interesting indicators analysed to model the chosen metrics (preparedness, vulnarability of each country)Authors : Milan Batista
Publication date : 02/19
Paper : Available here
Code available : https://www.mathworks.com/matlabcentral/fileexchange/74411-fitvirus
Deterministic or stochastic model : deterministic
Model category : phenomenological
Model sub-category
logistic curveData used for the model
01/16 to 01/21 - published table with the data; 01/22 from 02/19 - data from worldmeterGlobal approach
evolution forecast; epidemiological parameter estimationDetails of approach
prediction of the number of cases and prediction of the peak of the epidemicOutputs
regression coefficients; estimation of the final size of the infected population; estimation of the date of peakProblem Formulation
prediction of a logistic regression modelSolving Method
logistic regression fitted on the number of the historical serie of infected casesOther parameters
logistic regression parametersHow parameters are estimated
data-drivenDetails on parameters estimation
parameters for the curve fittingComment/issues
1) first of a serie of two articles that develop and compare two methods 2) the method is explained in details and all the code is availableIncubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data
Authors : Natalie M. Linton, Tetsuro Kobayashi, Yichi Yang, Katsuma Hayashi, Andrei R. Akhmetzhanov, Sung-mok Jung, Baoyin Yuan, Ryo Kinoshita, Hiroshi Nishiura
Publication date : 02/17
Paper : Available here
Code available : https://github.com/aakhmetz/WuhanIncubationPeriod2020
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
bayesian estimationData used for the model
China - 01/01 to 01/31Global approach
epidemiological parameter estimationDetails of approach
estimation of the virus duration states (eg incubation period)Outputs
estimation of the incubation period including and excluding Wuhan residents, time to hospital admission, time to death and time to death if hospitalizedAdditional Assumptions
1) selection bias in the dataset modeled by right truncting the pdf of the incubation period; 2) exponential growth rate of infection spreadProblem Formulation
doubly interval-censored likelihood function with: 1) uniform law of the exposure time variable; 2) pdf of the incubation period chosen as lognormal, Weibull, gamma distributionsSolving Method
bayesian method with the widely applicable information criterion (WAIC) for model selection; comparison with point estimation outputs from MLEEpidemiological parameters
dates of the illness onset; date of hospital admission; date of death; exponential growth rate of the infection spreadHow parameters are estimated
literatureDetails on parameters estimation
doubly interval-censored likelihood function with: 1) uniform law of the exposure time variable; 2) pdf of the incubation period chosen as lognormal, Weibull, gamma distributions; bayesian method with the widely applicable information criterion (WAIC) for model selection; comparison with point estimation outputs from MLEComment/issues
1) sensitivity analysis; 2) results could be applied to subgroups wrt gender, age; 3) need of longitudinal datasetsAssessing the impact of reduced travel on exportation dynamics of novel coronavirus infection (COVID-19)
Authors : Asami Anzai, Tetsuro Kobayashi, Natalie M. Linton, Ryo Kinoshita, Katsuma Hayashi, Ayako Suzuki, Yichi Yang, Sung-mok Jung, Takeshi Miyama, Andrei R. Akhmetzhanov, Hiroshi Nishiura
Publication date : 02/13
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : statistical estimation
Model sub-category
point estimation; Poisson regression; hazard functionData used for the model
China - 01/13 to 02/06Global approach
evolution forecastDetails of approach
estimation of the impact on the epidemic's transmission by travel reduction outside of China with a counterfactual model and through: the number of reported cases, the probability of a major epidemic, the time delay to a major epidemicOutputs
estimation of the number of reported cases, the probability of a major epidemic and the time delay to a major epidemicHow intervention strategies are modelled
evaluation of the success of isolation strategy modelled though three different constant values of R0; three rates of contact tracing implied in the computation of the probability of a major epidemicAdditional Assumptions
number of secondary infected by a single primary caseProblem Formulation
1) number of exported cases: counterfactual model; 2) reduced probability of a major epidemic overseas: difference between the true cumulative number of reported cases and the estimated by the counterfactual modelSolving Method
confidence intervals estimated by profile likelihood method (SAS)Epidemiological parameters
R0; dispersion parameter; probability of extinction (function of R0 and dispersion parameter)Other parameters
proportion of true infected cases wrt to the reported onesHow parameters are estimated
literature; data-drivenDetails on parameters estimation
time delay of a major epidemic: hazard of exponential function of a major epidemic in the absence of travel volume changes, reduced hazard of exponential function by the relative reduced probability of a major epidemic, confidence intervals estimated by profile MLE method (SAS)Comment/issues
1) estimation using Japan data but can be extended to other countries if data is available; 2) simple assumptions on the parameters; 3) data-fiting; 4) sensitivity analysisAuthors : Tianyu Zeng, Yunong Zhang, Zhenyu Li, Xiao Liu, Binbin Qiu
Publication date : 02/12
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : phenomenological
Model sub-category
sigmoid curve; gaussian curve; Poisson curveData used for the model
China - 01/10 to 02/04 - from epidemic datasets, density and transportation data during the Spring FestivalGlobal approach
evolution forecastDetails of approach
estimate the end of the transmission by predicting the dynamic of the new confirmed population, for each province, model-free methods (3 functions: sigmoid, Gaussian, Poisson)Outputs
prediction of the dynamic of the number of confirmed population per provinceAdditional Assumptions
infectious can become susceptible againProblem Formulation
three model-free methods: sigmoid, gaussian and Poisson with Stirling approximationSolving Method
calibration using the error evaluation method MAE for each function on the confirmed datasetsOther parameters
parameters of the distributionsHow parameters are estimated
data-drivenDetails on parameters estimation
parameters of the distributions calibrated using the error evaluation method MAE for each function on the confirmed datasetsComment/issues
1) article with a lot of simulations and predictions; 2) test sample of 4 days; 3) model includes the possible multi-infection patientsCode available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
Model sub-category
SEIRSD; Multi-Model ODEs NN; NNData used for the model
China - 01/10 to 02/04 - from epidemic datasets, density and transportation data during the Spring FestivalGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) learn the epidemiological model parameters; 2) estimate the end of the transmission by predicting the dynamic of the new confirmed population, for the mainland, in order to include the modeling of the inner-transportations (by activation method)Outputs
prediction of the confirmed dynamicHow intervention strategies are modelled
different lockdown policy levels (including the base case scenario) encoded in the proposed network, that models can simulate transportation limitations between provinces; use of a time-dependent continuous restriction force functionAdditional Assumptions
infectious can become susceptible againProblem Formulation
each neuron has a SEIRSD model so that for each layer, the parameters are optimized - fully connected feedforward SEIRSD activated by the ODEs NN, links between layers controlled by the transportation data that simulates the interprovincial disease transmission in neuron wide propagation and population change according to the transportation dataSolving Method
conjugate gradient-based algorithm to learn the parameters of the networkEpidemiological parameters
classic parameters; virus-contact population function per province; time-dependent amount of moving-out population; time-dependent exposed patientsOther parameters
weights of the network; interprovincial transportation ratio: time-dependent restriction force function; exceed rate of the exposed patients; shrink rate of the transportation; population density per province; contact ratioHow parameters are estimated
data-driven; literatureDetails on parameters estimation
for the time-dependent functions: virus-contact population per province, amount of moving-out population, exposed patients and restriction force: closed-formed equations of fixed parameters from public dataComment/issues
1) article with a lot of simulations and predictions; 2) test sample of 4 days; 3) model includes the possible multi-infection patientsAuthors : Yu Chen, Jin Cheng, Yu Jiang, Keji Liu
Publication date : 02/07
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
IRGJ; time-delayed; isolated/non-isolated structured; (G: isolated infected, J: confirmed)Data used for the model
Chinese regions - NHC - 01/23 to 02/04Global approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) learn the epidemiological parameters model for the infectious source area; 2) forecast the compartments dynamics for this area; 3) learn the epidemiological parameters model for an other area taking account of outflow from source area; 4) forecast the compartments dynamics for this areaOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
parameter corresponding to the isolation rate of the populationAdditional Assumptions
outflows between regionsProblem Formulation
numerical schemeSolving Method
forward scheme, ODEEpidemiological parameters
classic parametersOther parameters
isolation rateHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) data-driven: R0 and isolation rate using Levenberg-Marquad method or MCMC with LSE; 2) literature: othersComment/issues
1) very intersting model that allows taking account the infectious process between differents area from a source area with local SIR models; 2) results showing two peaks of infectionsUnderstanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions
Authors : Z. Liu, P. Magal , O. Seydi, G. Webb
Publication date : 02/05
Paper : Available here
Code available : No
Deterministic or stochastic model : deterministic
Model category : compartmental
Model sub-category
SIRU; reported/unreported structured; (I: asymptomatic infectious, R: reported symptomatic, U: unreported symptomatic)Data used for the model
Wuhan - 01/23 to 01/31 - from Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission for Hubei ProvinceGlobal approach
epidemiological parameter estimation; evolution forecast; modeling of various intervention strategiesDetails of approach
1) learn the epidemiological parameters; 2) forecast of reported populationsOutputs
prediction of the compartments dynamicsHow intervention strategies are modelled
time-varying transmission rate: constant before lockdown and null once it beginsAdditional Assumptions
1) constant rate of unreported/reported cases of the total reported infectious ones; 2) cumulative reported infectious casesProblem Formulation
numerical scheme; cumulative reported infectious casesSolving Method
forward scheme, ODEEpidemiological parameters
classic parameters; initial state conditions of the systemOther parameters
parameters of the exponential growth of the cumulative reported infectious casesHow parameters are estimated
literature; data-drivenDetails on parameters estimation
1) literature: average time patients are asymptomatic or symptomatic, proportion of reported symptomatic patients, S0; 2) data-driven: othersComment/issues
1) first article of a series of three; 2) prediction of cumulative reported cases from which unreported can be directly deduced by computing a fractionNowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study
Authors : Joseph T Wu, Kathy Leung, Gabriel M Leung
Publication date : 02/04
Paper : Available here
Code available : No
Deterministic or stochastic model : stochastic
Model category : compartmental
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