Competitive exclusion in a multi-strain SIS epidemic model on complex networks

Abstract

In this article, we propose an infection age-structured multi-strain SIS epidemic model on complex networks. We obtain the reproduction numbers for each strain by using the classical theory of renewal equations, and we define the basic reproduction number $\mathcal{R}_0$ for the whole system by the maximum of them. We prove that if $\mathcal{R}_0 1$, then there exists an endemic equilibrium in which only one strain with the largest reproduction number survives. Moreover, under an additional assumption that the recovery rate is homogeneous, we prove that such an endemic equilibrium is globally asymptotically stable. Interestingly, our theoretical results imply that the competitive exclusion can occur in a sense that only one strain with the largest reproduction number survives.

Keywords

• Multi-strain SIS epidemic model
• complex network
• infection age
• basic reproduction number
• global stability
• competitive exclusion