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

We study a stochastic model for the spread of two pathogen strains-termed type 1 and type 2-among 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 M-1 and M-2 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 (M-1,M-2) 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.