A multiple-strain pathogen model with diffusion on the space of Radon measures

Abstract

We formulate a multiple strain Susceptible–Infectious–Susceptible (SIS) pathogen model withdiffusion on the space of Radon measures which has the advantage of unifying discrete andcontinuous strain spaces under one framework. We first establish the well-posedness of thismodel. Then we study the long-time behavior for the case of discrete strain spaces. We definethe basic reproduction number for each strain. We establish the existence of a disease-freeequilibrium and a strain-specific endemic equilibrium which defines a competitive exclusionequilibrium where the density of individuals at one strain is positive and the density at theremaining strains is zero. We study the stability of these equilibria under the assumption thatthe disease transmission and recovery rates are spatially homogeneous or under the assumptionthat the diffusion rate of the susceptible individuals is equal to the diffusion rate of the infectedindividuals. We then extend some of these long-time behavior results from the discrete strainspace case to the continuous strain space case.