带有治疗函数与双线性接触率的SIRS传染病模型的全局分析

Global Analysis of an SIRS Epidemic Model with Treatment Function and Bilinear Incidence Rate

对带有治疗函数与双线性接触率的SIRS传染病模型的全局动力学进行了分析,通过数学分析得到系统不存在极限环的充分性判据。当系统不存在极限环时,通过治疗和控制就能够消除传染病,此时传染病不会成为地方性流行病;当系统存在极限环时,则这是一个不稳定的极限环,即亚临界Hopf分支,此时通过治疗仍能消除传染病。

The global dynamics of SIRS infectious disease model with treatment function and bilinear contact rate are analyzed,and the adequacy criterion of the system without limit cycle is obtained through mathematical analysis.When there is no limit cycle in the system,the infectious disease can be eliminated through treatment and control,and the infectious disease will not become endemic;When there is a limit cycle in the system,it is an unstable limit cycle,that is,a subcritical Hopf branch,and the infectious disease can still be eliminated by treatment.