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

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 \(\mathcal{R}\)₀. That is, if \(\mathcal{R}\)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 \(\mathcal{R}\)₀ > 1.  Moreover, we investigate the case when \(\mathcal{R}\)₀ = 1.  Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.