非线性发病率随机流行病模型的动力学行为  

Dynamical Behavior for a Stochastic Epidemic Model with Nonlinear Incidence

作　　者：魏凤英[1] 林青腾 

机构地区：[1]福州大学数学与计算机科学学院

出　　处：《数学学报（中文版）》2018年第1期155-166,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11201075);福建省自然科学基金资助项目(2016J01015)

摘　　要：研究了一类具有非线性发病率的随机SEIR传染病模型的绝灭性及平稳分布问题，通过构造合适的Lyapunov函数及控制噪声强度，在适当的条件下，得到模型的全局解存在唯一、指数稳定，且解具有平稳分布及遍历性．利用线性化及Fourier变换，证明了解渐近服从四维正态分布，并给出均值及方差矩阵的表达式．数值模拟验证了我们所得的主要结果．The extinction and the stationary distribution to a stochastic SEIR epidemic model with nonlinear incidence rate in a population of varying size are discussed. Under moderate conditions, the existence-and-uniqueness of the global solution, ex- ponential stability and the stationary distribution with ergodicity are obtained. By means of linearization and Fourier transform, we prove that the solution obeys a fourdimensional normal distribution, and the mean and the variance matrix are followed. Then numerical simulations are carried out to illustrate our results.

关 键 词：传染病模型 绝灭性 平稳分布 ITO公式 

分 类 号：O211.63[理学—概率论与数理统计]