带有周期传染率的手足口病模型的稳定性分析

Stability Analysis of a Hand-foot-and-mouth Disease Model with Periodic Transmission Rates

文中建立了带有周期传染率的SEIQRS模型,在引入基本再生数R0后,利用构造适当的Lyapunov函数的方法,讨论了系统平衡点的稳定性.这一研究成果主要体现在:得出HFMD动力系统的全局稳定性由它的基本再生数R0决定,当R0<1时,该动力系统的无病平衡点全局渐进稳定,意味着该HFMD会在一定时期后消亡;当R0>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疾病.

In this paper, it established a SEIQRS model with periodic transmission rates, a{ter the in- troduction of the basic reproductive number, by using the method of constructing suitable Liapunov func- tion, 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 its basic reproductive number R0 , as R0 〈1, the dis- ease-free equilibrium of the dynamic system is globally asymptotically stable, the HFMD will die after a period of time; WhenR0 〉1 , the power system has at least one positive periodic solution, the HFMD will evolve into a kind of epidemic disease.