Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate

Abstract A stochastic susceptible-infected-vaccinated model with a general incidence rate and varying population size is considered in this paper. By means of constructing a suitable Lyapunov function, the sufficient conditions for the extinction are derived. Further, some conditions that guarantee the existence of a unique stationary distribution is obtained. The main results are illustrated by computer simulations.