Endemic behaviour of SIS epidemics with general infectious period distributions.

Neal, Peter (2014) Endemic behaviour of SIS epidemics with general infectious period distributions. Advances in Applied Probability, 46 (1). pp. 241-255. ISSN 1475-6064

Abstract

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through E[Q].