Simply saying, this is a simulator using a model of probabilistic state transition of individuals on infection, disease, quarantine, recovery, and death. It starts with a randomly placed 3,000 individuals including one infected person, then progresses assuming five steps corresponds to one day. You can change the parameters on infection probability, distribution of incubation periods, distribution of symptom progress, distribution of turning period toward recovery, and distribution of effective immunity duration. It is also allowed to set up the rate and delay of quarantine for the infected individuals of each of asymptomatic and symptomatic, strength of social distancing and the rate of obedience, and the frequency and distance of individual mobility. Sorry, but more detail on the mathematical and algorithmic explanation is not ready yet.
Project Web site is here.