Node-RED flows to implement compartmental models for contagious disease. The compartments used are:

• S = susceptible
• E = exposed
• I = infectious
• R= recovered
• D = deceased

The models implemented are SIR, SIRD, SEIR, and SEIRD. The rate equations (ordinary differential equations) representing transitions between the compartments are solved by the finite difference method, with a step size of 0.01 days. The populations of the compartments are represented by the time-dependent variables s,e,i,r,d, which are the fractions of the total population in each compartment. The system is initialized at t = 0 with i = 0.001 and s = 0.999.

The models assume that the population is uniform and homogeneously mixed and that recovered individuals (compartment R) are immune to re-infection. The time period simulated is assumed to be brief enough that births and deaths (other than from the disease being modeled) can be neglected.

SIR

• rate(S -> I) = beta * i * s
• rate(I -> R) = gamma * i

SIRD

• rate(S -> I) = beta * i * s
• rate(I -> R) = (1 - alpha) * gamma * i
• rate(I -> D) = alpha * rho * i

SEIR

• rate(S -> E) = beta * i * s
• rate(E -> I) = delta * e
• rate(I -> R) = gamma * i

SEIRD

• rate(S -> E) = beta * i * s
• rate(E -> I) = delta * e
• rate(I -> R) = (1 - alpha) * gamma * i
• rate(I -> D) = alpha * rho * i

where

• R0 = basic reproduction number
• I = incubation period (days)
• delta = 1/I
• D = contagious period (days)
• gamma = 1/D
• beta = R0 * gamma
• H = treatment period (days)
• rho = 1/H
• alpha = fatality rate

Consensus values in the COVID-19 literature seem to be approximately: R0 = 2.5, D = 6 days, I = 2 days, H = 14 days, alpha = 0.05 - 0.1

Note: alpha is not equal to the conventional infection fatality rate, IFR. The two are related by

If IFR << 1, then to a good approximation,

Contagion Models: allows the user to compare the results of two models, with the type and parameters selected independently.

Interventions: shows the result of imposing or modifying interventions (lockdown or social distancing), defined by changes in R0 at a specified times.