具有接种免疫的离散腮腺炎模型的动力学性态

The Dynamics of Discrete SEIR Model of Mumps with Immunization

根据腮腺炎的流行传播特点,建立了具有标准发生率的离散SEIR腮腺炎模型,并研究了其全局动力学性态。首先,介绍了离散传染病模型的研究意义、腮腺炎的传播发病机理以及国内外研究进展。其次,通过数学归纳法证明了模型解的非负性和有界性,定义了模型的基本再生数R_0,证明了当R_0<1时,模型存在唯一的无病平衡点并且是全局渐近稳定的。当R_0>1时,无病平衡点不稳定,模型存在地方病平衡点,通过构造合理的Lyapunov函数证明了地方病平衡点是全局渐近稳定的。最后,利用数值模拟验证了理论结果的正确性。

According to the epidemic characteristics of mumps, the SEIR model with standard incidence is constructed. First, the research significance of discrete epidemic model, the spread pathogenesis of mumps and research progress at home and abroad are introduced. Secondly, the nonnegativity and boundless of solutions are analyzed by inductive method, and the basic reproduction number R0 of SIR epidemic model is defined.When R01, the disease free equilibrium is globally stable. When R01, the disease free equilibrium is unstable and there exists an endemic equilibrium. The endemic equilibrium is globally asymptotically stable by constructing reasonable Lyapunov function. Finally, numerical simulation to replenish the theoretical results of the model is proved.