I send my good wishes to all of you and I hope that you, your families, and your friends are faring well in this difficult time.
For those who are interested in modeling populations, such as the current epidemic, there is a logistic equation solver called
“verhulst” in the SU package which you may find of interest.
For example for Covid-19 cases in the US, taking 22 January as day 0 of cases in the US and 29 February as day 0 for deaths. Respective
stepmax= values of 72 for cases and 34 for deaths are both 3 April
verhulst stepmax=72 h=1 a1=.176 y0=1 a2=1e7 mode=x > calculated_cases.bin
verhulst stepmax=35 h=1 a1=.268 y0=1 a2=1e6 mode=x > calculated_deaths.bin
xgraph < calculated_cases.bin n=72 nplot=1 d1=1 &
xgraph < calculated_deaths.bin n=34 nplot=1 d1=1 &
The growth rate a1 values are determined empirically from publicly available data, in this case from the CDC and from the Worldometer site. You will have to make your own estimate of a1 for the data that you are modeling.
Another parameter that is harder to get is an estimate of the carrying capacity of the system a2. Here I am assuming a maximum of 1 million cases in the US and 100 thousand deaths.
The number of new cases or deaths per day is measured by the derivative of the solutions to the verhulst equation
verhulst stepmax=72 h=1 a1=.176 y0=1 a2=1e7 mode=y > delta_cases.bin
verhulst stepmax=35 h=1 a1=.268 y0=1 a2=1e6 mode=y > delta_deaths.bin
xgraph < delta_cases.bin n=72 nplot=1 d1=1 &
xgraph < delta_deaths.bin n=34 nplot=1 d1=1 &
The peak in the change of the population per day occurs when the population reaches the exactly half of the carrying capacity of the system. Thus, raising the carrying capacity will increase the height of the peak and move it out later in time.
Take care, everyone and stay safe.
-John
John StockwellThe new home of Seismic Un*x