Qualitative behavior of a SIRS epidemic model with vaccination on heterogeneous network

Abstract

This paper studies the dynamics of a SIRS epidemic model with varying population size and vaccination in a complex network. Using an analytical method, we mainly investigate the stability of the model according to the threshold $R_{0}$. That is, if $R_{0}$ is less than one, then the disease will die out. Alternatively, the system admits a unique endemic equilibrium which is globally asymptotically stable if $R_{0} > 1$. Moreover, we investigate the case when $R_{0} = 1$. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results