具有扩散现象的非自治四维生态流行病模型的稳定性分析

Stability Analysis for Four-Dimensional Nonautonomous and Eco-Epidemiological Model with Diffusion

建立并分析了具有扩散现象的非自治四维生态流行病模型,得到了系统持久生存的充分条件;基于Brouwer不动点定理,证明了系统周期解的存在性,同时通过构造Lyapunov泛函得到该系统周期解的唯一性与全局渐近稳定性,并给出了合理的生态解释.最后,通过一个数值例子说明了结论的有效性.

A four-dimensional nonautonomous and eco-epidemiological model with diffusion is modified and analyzed.Sufficient conditions are obtained for the permanence of the eco-epidemiological model and the existence of the periodic solutions is proven by Brouwer Fixed Point Theorem.Moreover,some conditions for global asymptotic stability of the system are investigated by using Lyapunov function.Also,some rational explanations for the eco-epidemiological model from the point of ecology are given.A numerical example is given to illuminate the effectiveness of the results.