一类改进的手足口病模型的稳定性分析

Stability Analysis of a Improved Hand-foot-and-mouth Disease Model

建立了一个改进的SEIQRS模型,在引入基本再生数R_0后,利用构造适当的Lyapunov函数的方法,讨论了平衡点的稳定性.这一研究成果主要体现在:得到HFMD动力系统的全局稳定性由它的基本再生数R_0决定,当R_0<1时,该动力系统的无病平衡点是全局渐进稳定的,意味着该HFMD会在一定时期后消亡;当R_0>1时,该动力系统至少有一个正的周期解,即该HFMD会演变成为一种流行性的疾病.

In this paper,it established a SEIQRS model, after the introduction of the basic reproductive number R0 , by using the method of constructing suitable Lyapunov function, the stability of the equilibrium point is discussed. The results of the study are mainly reflected in： the stability of the HFMD system is determined by the basic reproductive number R0, as Ro 〈 I, the disease - free equilibrium of the dynamic system is globally asymptotically stable,the HFMD will die after a period of time. When Ro 〉 1 ,the system has a positive equilibrium,the HFMD will evolve into a kind of epidemic disease.