一类具有非线性传染率的SVEIR模型的定性分析

摘要

The global stability of a SVEIR epidemic model with nonlinear incidence rate is studied,and the threshold parameter R0 is obtained.The existence of equilibrium point is discussed by using char-acteristic line method.By means of Lasalle invariance principle and constructing appropriate Lyapunov function,it is proved that if R0<1 ,the disease free equilibrium is global asymptotically stable,and if R0>1 ,the endemic equilibrium is global asymptotically stable.%研究一类具有非线性传染率的SVEIR传染病模型的全局稳定性,得到决定此模型全局动力学性质的阈值R0.利用特征线的方法讨论模型平衡点的存在性,根据Lasalle不变原理及构造恰当的Lyapunov函数,证明当阈值R0<1时无病平衡点是全局渐进稳定的,R0>1时地方病平衡点是全局渐近稳定的.