Threshold dynamics of SAIRS epidemic model with Semi-Markov switching

Abstract

We study the threshold dynamics of a stochastic SAIRS-type model with vaccination, where the role of asymptomatic and symptomatic infectious individuals are explicitly considered in the epidemic dynamics. In the model, the values of the disease transmission rate may switch between different levels under the effect of a semi-Markov process. We provide sufficient conditions ensuring the almost surely epidemic extinction and persistent in time mean. Moreover, we investigate the omega-limit set of the system.