Analysis of a Kind of Stochastic Dynamics Model with Nonlinear Function (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we establish stochastic differential equations on thebasis of a nonlinear deterministic model and study the global dynamics. Forthe deterministic model, we show that the basic reproduction number $\mathfrak{R}_0$ determines whether there is an endemic outbreak or not: if $\mathfrak{R}_01,$ the disease persists. For the stochastic model, weprovide analytic results regarding the stochastic boundedness, perturbation,permanence and extinction. Finally, some numerical examples are carried outto confirm the analytical results. One of the most interesting findings is thatstochastic fluctuations introduced in our stochastic model can suppress disease outbreak, which can provide us some useful control strategies to regulatedisease dynamics.