非线性发病率随机流行病模型的动力学行为

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.

Dynamical Behavior for a Stochastic Epidemic Model with Nonlinear Incidence

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, exponential 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.