Tom Britton: An epidemic in a dynamic population with importation of infectives

In the talk we consider the long term behavior of an infectious disease spreading in dynamic community to which also infectious people enter from outside. More precisely, assuming that the mean community size n is large, we study a Markovian SIR infectious disease keeping basic reproduction number \(R_0\) as well as the importation rate of infectives is fixed, but assuming that the infectious period is short compared to life duration. It is shown that, as n tends to infinity, the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible, infective and recovered, is encapsulated in a 1-dimensional regenerative process S(t) describing the limiting fraction of the population that are susceptible.  This process grows deterministically, except at one random time point per regenerative cycle, where it jumps down by a size that is completely determined by the waiting time since the previous jump. (Joint work with Frank Ball and Pieter Trapman)