一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

本文对一类具有非线性发生率的SEIR传染病模型进行了研究.确定了决定疾病灭绝或持续存在的阈值-基本再生数,并分析了模型的平衡点的存在性;通过构造恰当的Lyapunov函数,运用La Salle不变性原理证明了当基本再生数小于或等于1时,无病平衡点是全局渐进稳定的;利用Lyapunov直接方法证明了当基本再生数大于1时,地方病平衡点是全局渐进稳定的.最后,将发生率具体化用数值模拟验证了所得理论分析结果的正确性.

Global Stability of an SEIR Epidemic Model with Nonlinear Incidence

In this paper, an SEIR epidemic model with nonlinear incidence is investigated. By applying the next generation matrix, the basic reproduction number determining whether the disease dies is found, and the existence of the equilibria of the model is discussed;according to the suitable Lyapunov function and the LaSalle invariance principle, it is proved that the disease free equilibrium is globally asymptotically stable as the basic reproduction number is less than or equal to unity; by means of the Lyapunov direct method, it is testified that the endemic equilibrium is globally asymptotically stable as the basic reproduction number is greater than unity. Finally, the theoretical results obtained here are verified by numerical simulations for the SEIR model with a specific incidence.