A Central Limit Theorem for a Discrete-Time SIS Model with Individual Variation

Abstract

A discrete-time SIS model is presented that allows individuals in the population to vary in terms of their susceptibility to infection and their rate of recovery. This model is a generalisation of the metapopulation model presented in McVinish and Pollett (2010). The main result of the paper is a central limit theorem showing that fluctuations in the proportion of infected individuals around the limiting proportion converges to a Gaussian random variable when appropriately rescaled. In contrast to the case where there is no variation amongst individuals, the limiting Gaussian distribution has a nonzero mean.

Interaction between habitat quality and an Allee-like effect in metapopulations

“…A central limit theorem for an extended version of our metapopulation model is given in McVinish and Pollett [16]. It may be fruitful to investigate the effects of habitat destruction and degradation on the metapopulation using the more precise limit theory described in that paper.…”