具周期性潜伏期的SEIR传染病模型的动力学

The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period

研究了一类具有周期性潜伏期的常微分SEIR传染病模型.首先借助于染病年龄分布函数导出了模型.紧接着定义了模型的基本再生数R_0并利用耗散动力系统的相关理论证明R_0是决定疾病是否继续流行的阈值.最后,利用数值方法进一步验证了结论,并分析了忽略潜伏期的周期性对估计疾病传播能力的影响.

A SEIR ordinary differential epidemic model with time-periodic latent period is studied.Firstly,the model is derived by means of the distribution function of infected ages.Next,the basic reproduction ratio R0 is introduced,and it is shown that R0 is a threshold index for determining whether the epidemic will go extinction or become endemic using the theory of dissipative dynamic systems.Finally,numerical methods are carried out to validate the analytical results and further to invetigate the effects on evaluating the propagation of disease owning to the neglect of the periodicity of the incubation period.