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 Stockwell
The new home of Seismic Un*x
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