Threshold dynamics of SAIRS epidemic model with semi‐Markov switching

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