Pieter Trapman: A SIR epidemic in a population with demographics and importation of infectives

Abstract: Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size n. A Markovian SIR  infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where the population size goes to infinity, keeping the basic reproduction number R0 as well as the importation rate of infectives fixed, but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than \(1/\log n\). It is shown that, 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, describing the limiting fraction of the population that are susceptible.

I will also discuss faster population dynamics (compared to the disease dynamics) and connect this to the so-called critical population size.

This talk is based on joint work with Frank Ball and Tom Britton.