Number of infections suffered by a focal individual in a two-strain SIS-model with partial cross-immunity

Abstract

We study a stochastic model for the spread of two pathogen strains –termed type-1 and type-2 – amongst a homogeneously mixing community consisting of a finite number of individuals. In the model we assume partial cross-immunity,exogenous streams of infection, and that the degree of severity of a newly infective individual depends on who this infective individual was infected by. The aim is to characterize the joint probability distribution of the numbers M1 and M2 of type-1 and type-2 infections suffered by a focal individual during an outbreak of the disease. We present iterative procedures for computing the probability mass function of (M1, M2) under the assumption that the initial state of the focal individual is known, and a numerical study of the model is performed to investigate the influence of certain key parameters on the spread of resistant bacteria in hospitals.