一类潜伏期和染病期均具有传染性的手足口病模型

根据手足口病的病理特性及传播特点,建立一类描述其传播的数学模型并对模型的动力学性态进行分析.首先利用再生矩阵的方法定义了模型的基本再生数R_0,同时通过构造Lyapunov函数和Routh-Hurwitz判据证明了当R_0≤1时无病平衡点E_0的金局渐近稳定性,R_0>1时地方病平衡点E_*的局部渐近稳定性,并进一步证明了在一定条件下地方病平衡点的全局渐近稳定性.

A Hand-Foot-and-Mouth Epidemic Model with the Infectivity in the Latent and the Infected Period

In this paper,we formulated one kind of epidemic models for hand-foot-and-mouth disease based on the pathological mechanism and the spread characteristics of the disease.The basic reproductive number R_0 is defined the next generation matrix.It is proved that when the basic reproductive number R_0 ≤ 1,the disease-free equilibrium E_0 is globally stable by the Lyapunov function,while if R_0 > 1,the Routh-Hurwitz criterion indicated that the endemic equilibrium E_* is locally stable.Lyapunov functions also show E_* is globally stable under certain conditions.