流行性传染病传播系统的奇摄动解  

The Singularly Perturbed Solution for Epidemic Virus Contagion System

作　　者：莫嘉琪 陈怀军 MO Jia-qi;CHEN Huai-jun(School of Mathematics & Statistics,Anhui Normal University,Wuhu 241003,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《安徽师范大学学报（自然科学版）》2020年第3期205-211,共7页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11771005).

摘　　要：讨论了一类流行性病毒传染问题,提出了传染病传播生态系统动力学模型,利用奇异摄动方法,首先构造初值问题的外部解,然后引入伸长尺度变量构造了问题解初始层校正项,最后利用合成展开理论得到了生态系统初值问题的渐近解。并利用微分方程的比较定理证明了对应的生态系统的渐近解的一致有效性,同时举出了一个例子,说明了利用奇异摄动方法得到的生态系统的渐近解具有较好的近似度。A class of epidemic virus contagion problem was discussed.The transmission ecological contagion system dynamic model was raised.Firstly,outer solution to the initial value problem was obtained by using the singular perturbation method.Then,leading the variable of stretched scales the corrective term to initial value problem was structured.Finally,the asymptotic solution to the ecological contagion system initial value problem was got by using the composite expansion theory.And using the comparative theorem of differential inequality,the asymptotic solution of ecological contagion system was proved its uniform validity.Moreover an example was itemized that the singular perturbation method is a better approximation.

关 键 词：流行传染病 非线性方程 动力学系统 

分 类 号：O175.14[理学—数学]