I haven't studied differential equations for a long time, but I have just started looking at material on the SIR model of epidemics. My problem is that the resources that I've looked at haven't given a formal definition of epidemic. A couple of the resources seem to use the following definition (although it's not explicitly stated): Let I(t) denote the infecteds function. Then the disease is an epidemic if there exists a time t such that I'(t)=0. Is this the technical definition of epidemic? Or there is a another definition? Thanks.
2026-03-29 10:15:19.1774779319
Definition of "epidemic" when using SIR models
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This "definition" is necessary to reconcile the deterministic theory with stochastic counterpart. So, yes, you can take it as a technical definition of an epidemic. Probably better to use an equivalent one: if $I'(t)|_{t=t_0}>0$ then there is an epidemic. But to actually get to the heart of it, start reading about the stochastic models of epidemics.