Abstract
We reformulate a stochastic epidemic model consisting of four human classes. We show that there exists a unique positive solution to the proposed model. The stochastic basic reproduction number R0s is established. A stationary distribution (SD) under several conditions is obtained by incorporating stochastic Lyapunov function. The extinction for the proposed disease model is obtained by using the local martingale theorem. The first order stochastic Runge-Kutta method is taken into account to depict the numerical simulations.
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