Previous studies have shown that Gompertz model4 correctly describes the Covid-19 epidemic in all analysed countries. It is an empirical model that starts with an exponential growth but that gradually decreases its specific growth rate. Therefore, it is adequate for describing an epidemic that is characterized by an initial exponential growth but a progressive decrease in spreading velocity provided that appropriate control measures are applied. Gompertz model is described by the equation:
where X(t) is the cumulated number of confirmed cases at t (in days), and X0 is the number of cumulated cases the day at day t0. The model has two parameters: alpha is the velocity at which specific spreading rate is slowing down; K is the expected final number of cumulated cases at the end of the epidemic.
Chayu Yang, Jin Wang, «A mathematical model for the novel coronavirus epidemic in Wuhan, China,» Mathematical Biosciences and Engineering 17: 2708-2724 (11 Mar 2020), doi: https://doi.org/10.3934/mbe.2020148.
Here, we want to present a differnt approach of the simulation. The Gompertz model assumes the exponential behavior.
But just try to simulate the spead of the virus and the infection :
Patient 0 is infected, he can infect 1 or 3 people randomly
This hypothesis can be right for 30 days, after we can change the spread, an infected patient can infect only 0 or 1 people.
So a very basic program to understand the exponential growth and analyse after the decrease.
So with a basic algoritm, we can find the sophisticated Gompertz formula.