On a strain-structured epidemic model

TL;DR

This paper develops a strain-structured SIS epidemic model with nonlinear infection dynamics to study competition among different pathogen strains, analyzing the model's well-posedness and steady states.

Contribution

It introduces a nonlinear strain-structured epidemic model and proves global existence, positivity, and endemic steady states under certain conditions.

Findings

Global existence and positivity of solutions established.

Existence of endemic steady states demonstrated.

Model captures competition between different pathogen strains.

Abstract

We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities.