一类具有媒体报道和潜伏期的手足口病模型的分析

Analysis of a Kind of Hand-Foot-Mouth Disease Model with Media Coverage and Incubation Period

摘要: 本文研究了一类受媒体报道影响和潜伏期的手足口病模型，计算手足口病模型的基本再生数。利用Hurwitz判据、Laypunov函数讨论无病平衡点的稳定性，当基本再生数小于1时，无病平衡点是全局渐近稳定的；当基本再生数大于1时，无病平衡点是不稳定的。同时利用Hurwitz判据讨论了地方病平衡点的稳定性，得到地方病平衡点是局部渐近稳定的。

Abstract: A hand-foot-mouth disease model with media coverage and the incubation period has been considered in this article. The basic reproduction number of the hand-foot-mouth disease model is calculated. By using the Hurwitz criterion and Laypunov function, the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is under one. When the basic reproduction number is above one, the disease-free equilibrium is unstable. Meanwhile, the stabil-ity of the endemic equilibrium is discussed by using the Hurwitz criterion, which is locally asymptotically stable.