Stability of an equilibrium state in a multiinfectious-type SIS model on a truncated network

Abstract

In a homogeneous constant population, the basic SIS model potentially has an epidemic equilibrium state with global asymptotic stability since it can be reduced to the logistic equation. On the basic SIS model with a nonhomogeneous constant population, viewed as a multitype SIS model, the global or local asymptotic stability of an epidemic equilibrium state has also been studied.1–4 However, this kind of analysis in other models with nonhomogeneous populations has rarely been developed, even though the corresponding models with homogeneous populations are well known. In addition, recent studies of complex networks have revealed that heterogeneity of the link number of vertices drastically changes the epidemic thresholds.5–9 For these reasons, figuring out the roles of heterogeneity is a major topic in epidemic modeling. Here, we consider a multiinfectious-type SIS model on a network, and show the (local or global) asymptotic stability of an epidemic equilibrium state whenever it exists.