Analyzing a class of stochastic SIRS models under imperfect vaccination

This work is devoted to a class of stochastic infectious disease models, namely, stochastic SIRS models under imperfect vaccination. Because of the inclusion of the vaccination, the underlying models are more difficult to analyze than that of the previously considered in the literature. Our main effort is devoted to overcoming the difficulties and deriving a complete characterization of longtime behavior of systems. Numerical examples are provided to present computational evidence. These examples also provide insight that the discrete event process (the random switching) can reverse persistence to extinction, and vice versa.