Extinction and stationary distribution of a stochastic SIRS epidemic model with standard incidence rate and partial immunity

In this paper, a stochastic SIRS model with standard incidence rate and partial temporary immunity is proposed. The sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established. Our results reveal that random perturbations in the environment can restrain the spread of disease. That is, the deterministic model neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are carried out to demonstrate the analytical results. (C) 2019 Elsevier B.V. All rights reserved.