Time delay and nonlinear incidence effects on the stochastic SIRC epidemic model

Abstract

This paper presents theoretical and numerical study of a stochastic SIRC epidemic model with time delay and nonlinear incidence. The existence and uniqueness of a global positive solution is proved. The Lyapunov analysis method is used to obtain sufficient conditions for the existence of a stationary distribution and the disease extinction under certain assumptions. Numerical simulations are also elaborated for the considered stochastic model in order to corroborate the theoretical findings.