基于NSFD法对离散型传染病模型的数值模拟与等量分析

摘要

通过NSFD方法研究了具有不同人口规模的离散型SI传染病模型.研究发现,模型的全局动力学行为是由基本的繁殖数量R0决定的.借助李雅普诺夫函数和相关稳定性,当R0≤1时,在样本空间Ω中对任意的h,无病平衡点E0是全局渐近稳定的.当R0＞1时,在样本空间Ω中对任意的h,地方病平衡点E’是全局渐近稳定的.最后,用数值模拟证明理论分析的有效性.%In this article,we study a discrete SI epidemic model with varying total population size by NSFD method.The global dynamics of the model is determined by the basic reproduction number R0.By Lyapunov function and correlation sta bility,when R0 ≤1,we have that the disease-free equilibrium E0 is globally asymptotically stable in Ω for all h.When R0 ＞1,the epidemic equilibrium E* is globally asymptotically stable in Ω for all h.Finally,numerical simulations demonstrate the validity of our theoretical analysis.