Abstract
A stochastic SIRS model with logistic growth and nonlinear incidence rate is probed in this paper. We exemplify that the proposed stochastic SIRS model reveals a global and positive solution. By applying suitable Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic SIRS model are derived. Furthermore, we acquire the sufficient conditions for extinction of the infectious disease.
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