一类具有饱和发生率的确定和随机SIRS模型的稳定性

Stability of a Deterministic and Stochastic SIRS Epidemic Model with Saturated Incidence Rate

考虑了一类具有饱和发生率的确定和随机SIRS模型,计算出基本再生数,得到随机模型正解的全局存在性及唯一性,在一定的噪声扰动条件下,应用微分算子和伊藤公式证明了无病平衡点的p-阶指数稳定,同时,讨论了随机模型的解围绕确定性模型平衡点的渐近行为,最后分析了噪声干扰对随机模型稳定性的影响.

We considered a deterministic and stochastic SIRS epidemic model with saturated incidence rate.We calculated the basic reproduction number R0 for the stochastic model and obtained the global existence and positivity of the unique solution.Under suitable conditions on the intensity of the noise perturbation,we proved the p-th exponential stablity of the disease free equilibrium by using the differential operator and Ito’s formula.We also discussed the asymptotic behavior of the solution of stocastic model around the equilibrium of the deterministic model.Finally,we analyzed the effect of the noise perturbation to the stability of stocastic model.