A stochastic SIRS infectious disease model with Logistic growth and Ornstein-Uhlenbeck process and psychological effects
A stochastic SIRS infectious disease model with Logistic growth and Ornstein-Uhlenbeck process and psychological effects is established.By constructing Lyapunov function and applying Itô's formula,the global existence and uniqueness of positive solution are proved.It is analytically made out the stochastic epidemic threshold Rs0 which pilots the extinction and permanence in mean of the disease.It is given that the disease extinguishes when Rs0＜1.Othewise,if Rs0＞1,then disease is permanent in mean.For the critical case Rs0=1,it has shown that disease dies out by using an approach involving some appropriate stopping times.A series of numerical simulations is presented to confirm the correctness of the theoretical analysis results and the dependence of disease on psychological effects.
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