One can produce a very simple model for a pandemic involving just infecteds and susceptibles, the haves and the have nots, with the infection rate being proportional to rate of interaction between individuals with complete mixing. It is almost trivial to show that the changes for the two compartments follow the Logistic Equation.
We might call this the SI Model since there is no removed compartment for those who have recovered and are no longer infectious and those who have died and no longer interact with others.
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