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

作　　者：王来全[1] 夏米西努尔·阿布都热合曼[2] WANG Lai-quan;Xamxinur Abdurahman(Department of Basic Courses,Changji Vocational and Technical College,Changji 831100,China;College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]昌吉职业技术学院基础部,新疆昌吉831100 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2019年第18期285-291,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861063)

摘　　要：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.

关 键 词：随机模型 饱和发生率 基本再生数 微分算子和伊藤公式 P-阶指数稳定 

分 类 号：O175[理学—数学] R181[理学—基础数学]