Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation

In this paper, we investigated a stochastic SIRS epidemic infectious disease model that accounted for environmentally driven infection and incorporated multiparameter perturbations. In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. The results indicated that high-intensity noise perturbation can inhibit the spread of the disease, and the dynamic behavior of the disease transitioned from persistence to extinction as noise intensity increased. Our study also demonstrated that, compared to perturbations in the indirect infection rate, changes in noise intensity that affect the direct infection rate will have a more significant impact on disease transmission.