一类甲型H1N1病毒人体内非线性发展模型及其稳定性分析  

Analysis on the Stability of a Non-Linear Development Model about H1N1 Influenza Virus in Human Body

作　　者：顾恩国[1] 张兴起[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2009年第4期106-110,共5页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(10871209);中南民族大学自然科学基金资助项目(YZZ06027)

摘　　要：在充分考虑H1N1病毒具有感染活性和人体免疫力不同的基础上,建立了H1N1病毒体内发展的非线性微分方程.利用Routh-Hurwitz判定特征方程有负实部根,并利用中心流形定理研究了自治微分系统在平衡点处双曲和非双曲情况下的稳定性,由此产生系统趋于不同稳定点时病毒分裂的临界值,同时利用数值模拟验证了分析的合理性.This paper builds a nonlinear differential equation about the development of H1N1 in human body,based on the potential infection of H1N1 and the fact that different people have different level of immunity.Routh-Hurwitz is used to determine that the characteristic equation has negative real root,and Center-Manifold theorem is used to study the stability of autonomous differential system in the case of hyperbolic and non-hyperbolic at the equilibrium point.Finally the critical point of virus division when the system tends towards different stable points is calculated and the rationality of the analysis above is verified by numerical simulation.

关 键 词：数学模型 Routh-Hurwitz定理 中心流形定理 稳定性分析 临界值 数值模拟 

分 类 号：O192[理学—数学]