COVID

Programs to visualize data on covid-19, and some results.

It includes the following in directory files

all.pl

Script to run all the required programs and plot information related to covid-19 in the world with emphasis in Mexico.

To run you require a PERL compiler/interpreter and the packages Getopt::Long and List::Util, besides satisfying the requisites of the other programs.

Run it without arguments or with the argument --help to get (criptic) instructions: perl all.pl --help
extractCases.pl

Program to download (if necessary) a European CDC database listing the worldwide distribution of covid-19 cases and deceases, choose some countries and prepare some files for easy plotting of the results.

To run the program you need a perl compiler/interpreter and the perl packages Spreadsheet::Read, Spreadsheet::XLSX, Getopt::Long and List::Util. You might also need the programs wget, libreoffice and gnuplot.

Run it without arguments or with the argument --help to get instruccions: perl extractCases.pl --help.

The result is a list of files that can be fed to gnuplot for plotting
extractMX.pl

Program to extract the cases for different regions of México from clones of the github repository DataScienceResearchPeru/covid-19_latinoamerica

To run the program you need a perl compiler/interpreter and the perl package Getopt::Long.

Run it without arguments or with the argument --help to get instruccions: perl extractMX.pl --help.

The result is sent to STDOUT but it may be redirected to a file that may be fed to gnuplot for plotting.
mortandad.pl

Program to extract data from an INEGI database on monthly deceases and prepare a file for gnuplot. Requires the package Text::CSV_XS. Before running it you must configure the path to the csv database. The program not polished and is not robust. I was happy it did work once.
plotcases.g, plotdec.g, plotcasesN.g, plotdecN.g, plotcasesMX...

Gnuplot scripts that may be loaded by the gnuplot program to plot the number of new cases and new deseased as a function of the total number of cases. load 'plotcases.g' and load 'plotdec.g'. May need editing according to your choice of countries and the positioning of labels and arrows. The names with an N plot the same information, but normalized to the total population of the country. The names with an MX are for the regions of Mexico.
mx.txt, us.txt, cn.txt...

Extracted data files for some countries. They consist of space separated columns (appropriate for using as gnuplot's input) with

1- the accumulated number of confirmed cases 2- the daily number of confirmed cases 3- daily number of deceased 4- the daily number of confirmed cases divided by population 5- daily number of deceased divided by population 6- the total population (2018) 7- the total number of deceased 8- the estimate of sick people 9- total cases averaged 10- total deaths averaged

The order is an historical accident.
states.txt

Extracted data for the states of Mexico. They consist of newline separated blocks of data, one for each state, preceeded by the name of the state and followed by space separated columns (apprropirate for using as gnuplot's input). 1- the accumulated number of confirmed cases 2- the averaged daily number of confirmed cases 3- the accumulated number of deceases 4- the daily number of deceases
gompertzK.txt

Data with the gompertz prediction for Mexico. The first column is the last number of daily record used to make the prediction. Substracting 62 gives the number of days since the first decease. The second column is the saturation parameter of the Gompertz extrapolation fitted up to the corresponding date, i.e., the K in the formula K exp(-b exp(-a t)). The third column is the parameter a and the fourth the parameter b.
mortandad2018.txt

Total monthly deceases vs. date, extracted from INEGI's databases. It consists of two space separated columns of the form
1. Date (YYYY-MM)
2. Total monthly deceases.
cases.png

Plot: Daily cases vs. total cases Rolling 7 day average.

Comment: 2020-07-16. The last three months have seen an almost straight line for Mexico with a slope of 0.61. The fitted slope has been decreasing, but with an extreme slowness. A straight line means a power law. As daily cases are a power of total cases, the total cases are a power of time, with exponent 1/(1-m). Currently this means the number of cases has an accelerated growth, as t^{5/2}. As with any power law, the relative growth (daily/total cases) does diminish, but this doesn't mean there is any kind of deceleration. Mexico is now above most countries in total number of cases. (See below for normalized plots and for extrapolations).
detail.png

Plot: Detail of cases.png
dec.png

Plot: Daily deceased vs. total cases.

Comment: 2020-07-16. The behavior of this plot of daily deceases as a function of total cases is strange. It started as a straight line with a slope significantly larger than 1. This seems to mean that the initial growth was faster than exponential! It doesn't though, as the axes correspond to different quantities. Nevertheless, I would hve expected a result proportional to the number of daily cases, maybe with a delay, not a muh faster behavior. I don't know the reason. Speculating, maybe it shows that the health system improved in its identification capacity and the percentage of correctly identified causes of death increased with time, or maybe there was some advantage of stating that unrelated deaths were covid-19 related (I read that there were benefits for families of covid-19 deceased patients, and I was told long ago that hospitals asked permission of families to include covid-19 in unrelated death certificates for unknown reasons). Nevertheless, after a month, the slope evolved rapidly. Curiously, it is now smaller than the slope for new confirmed cases, and for the last month there seems to be an decrease in the number of covid-19 related deceases. I find it strange that the deceases diminish while the total cases accelerate. Again, I can only speculate. Maybe the hospitals are becoming better at dealing with covid-19, or there is some incentive to state other causes of death in the certificates. The pressure the government put on itself by their untimely and confusing announcement of the end of the pandemic and the return to (new) normal times may be distorting the reports; I don't know.
casesN.png

plot: daily cases vs. total cases normalized to population

Comment: 2020-07-16. The shape of these curves is the same as those of cases.png above. In the log scale, they are simply shifted. Mexico, being a relatively large country, doesn't seem as bad when the number of cases is normalized, though it doesn't look too good either.
decN.png

Plot: Daily deceased vs. total cases normalized to population

Comment: 2020-07-16. Similar comments as to dec.png and casesN.png apply here.
decvsdec.png

Plot: Daily deceased vs. total deceased.

Comment: 2020-07-16. Comments similar to those of dec.png apply, though, the initial slope here is below 1, which corresponds to a non-exponential, but accelerated power-law growth.
sick.png

Plot: Estimated currently sick people vs. total cases

Comment: 2020-07-17. This plot doesn't show the actual data, but rather, an estimate. I arbitrarily assume that the recovery (or death) is a probabilistic Poisson process with some given time scale tau. Thus, the number of active sick patients today is yesterday's number multiplied by their probability of not recovering (or dying), some fixed factor which I write as exp(1 day/tau), plus the newly arrived cases. I adjusted the time constant to the official data of 2020-05-04 and found tau=6. I have heard that the recovery time is 14 days but I don't know exactly how it is defined. Nevertheless, 6.08=14/log(10), so tau=6 corresponds to 90% of all cases recovered after 14 days, which I seems a reasonable definition of the recovery time. The number of actively sick patients using this approach has remained close to the official numbers which I have checked occasionally. This plot is similar to that in cases.png above, but with a slightly larger slope. This could be understood as it contains memory of previous data, from when the slope for new cases was also higher.
casesMX.png

Plot: Daily cases vs. total cases for regions of Mexico
decMX.png

Plot: Daily deceased vs. total deceased of México
decesosMensuales.png

Plot: Historical monthly total deceases in México vs. date
gompertz.png

Plot: Daily cases vs. total cases for Mexico and extrapolation using fitted Gompertz formula. Not averaged

Comment: 2020-07-17. Gompertz formula is a simple model which has been applied to study epidemics and many other systems with analogous dynamics. Instead of the differential equations of the SIR model and all its more or less sophisticated variants, it offers a simple formula C(t)=K exp(-b exp(-a t)), where C(t) is the number of accumulated total cases, and K, a and b are parameters to be fitted. As I'm plotting C' (daily cases) vs. C, I derive a simpler formula C'=a C log(K/C) which has only two parameters, making it slightly more robust. K is the maximum number of (confirmed) cases and is expected to reach values around 1,200,000. You might have to multiply by some factor to convert confirmed cases to total cases (I've read estimations that go from 8 to 30 or up to 80). The maximum corresponds to C=K/e (e=exp(1)) around 440,000, with a maximum value C'=aK/e around 6500. As the total number of cases is currently 324000, we should expect slightly more than two weeks for the peak and around four months for the end.
animateGompertz.gif

Plot: Daily cases vs. total cases for Mexico and animation of the extrapolation for different days fitted Gompertz formula. Not averaged.

Comment: 2020-07-17. See the comment for gompertz.png. This animation shows that the Gompertz extrapolation is not a good predictor during the initial phase of an epidemics, as there is only data on one of the tails of the distribution. This, a single new data point might strongly change the fit. Nevertheless, as more data is accumulated and we approach the peak, the fits somewhat stabilizes.
gompertzK.png

Plot: Estimated total number of cases as a function of the number of days since the first case when the estimation was made.

Comment: 2020-07-17. The estimations were done using the Gompertz formulae (see gompertz.png above). The very early estimates vary wildly and are not shown. After 50 days the expected total number of cases seems to increase systematically but with some large fluctuations. Currently the estimate lies around 1.2 million cases.
maximum.png

Plot: Estimated remaining days till the maximum number of daily infections as a function of the number of days since the first case when the estimation was made.

Comment: 2020-07-26. The estimations were done using the Gompertz formulae (see gompertz.png above) C(t)=K exp(-b exp(-a t)). The parameters K, a and b were estimated with the data up to a given moving date and from them the day corresponding to the maximum was estimated as t=log(b)/a. From it, the remaining time was obtained. This was repeated for different dates. For a good enough model one could expect that the remaining time decreases one day each day, but not so for the Gompertz estimate. Thus, a linear interpolation was done and its intersection with the x axis probably provides a better estimate. Currently the maximum would be expected by the end of August.
gompertzdec.png

Daily deceased vs. total deceased for Mexico and extrapolation using fitted Gompertz formula. Not averaged.