具有非线性传染率和预防接种的SEIR传染病模型的全局稳定性

Global stability of a SEIR epidemic model with nonlinear incidence rate and vaccination

研究一类具有非线性传染率和预防接种的SEIR传染病模型动力学性质,综合利用LaSalle不变集原理、Lyapunov函数、Routh-Hurwitz判据、微分方程轨道稳定和复合矩阵的相关理论,获得保证无病平衡点和地方病平衡点全局渐近稳定的阀值条件,以及一些新结果.

In this paper, dynamic property about a SEIR epidemic model with nonlinear incidence rateand vaccination is studied. By using some methods, including LaSalle invariant set principle, Lya-punov function, Routh -Hurwitz bounded, the theory about asymptotically orbital in differential equa-tions and compound matrix, the threshold conditions which guarantee the global asymptotic stable dis-ease - free equilibrium and endemic equilibrium of the SEIR epidemic model are obtained. Some newresults are obtained.