Abstract
In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive periodic solution. One of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous SIR epidemic model.
•A stochastic nonautonomous SIR epidemic model with logistic growth is studied.•For the system, we present sufficient conditions for persistence of the epidemic.•We show that there is at least one nontrivial positive periodic solution.•Random perturbations may be beneficial to formate the periodic solution to the model.