一类具有饱和发生率的SIVS吸毒模型的动力学分析

Dynamic Behavior of a Class of SIVS Drugs Epidemic Model with Saturation Incidence Rate

本文研究一类具有饱和传染率的SIVS传染病模型.首先利用Routh-Hurwitz判据和特征根方法,得到平衡点的局部渐近稳定性,其次证明系统的持久性和无病平衡点的全局渐近稳定性,并利用极限系统理论得到地方病平衡点的全局渐近稳定性.最后用数值模拟验证理论结果的正确性.

In this paper,an SIVS epidemic model with saturated incidence rate was stud- ied. The locally asymptotically stable of equilibria were verified by Routh-Hurwitz criterion and eigenvalue method. We also discussed the globally asymptotically stable of disease-free e- quilibrium and the persistence of the system. Moreover, the globally stable of endemic equi- librium was proved by the limit system. In addition, numerical simulations are presented to support and complement the theoretical findings.