一类非线性SEIRS流行病传播数学模型  

A kind of nonlinear SEIRS epidemic spread mathematic model

作　　者：徐文雄[1] 张太雷[1] 

机构地区：[1]西安交通大学理学院,陕西西安710049

出　　处：《西北大学学报（自然科学版）》2004年第6期627-630,共4页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(30170823)

摘　　要：目的　研究一类具有饱和接触率且潜伏期、染病期均传染的非线性SEIRS流行病传播数学模型动力学性质。方法　利用Lasalle不变集原理和Routh Hurwitz判据探讨系统的渐近性态。结果　得到了疾病绝灭与持续的阈值———基本再生数,证明了无病平衡点的全局渐近稳定性和地方病平衡点的局部渐近稳定性,揭示了潜伏期传染的影响。结论　潜伏期有传染的疾病,不但要注意控制染病期的病人,还要注意控制潜伏期的病人。只有这样,才能有效地控制疾病的蔓延。Aim Dynamical behavior of a kind of nonlinear SEIRS model of epidemic spread with the saturated rate, which has infective force in both latent period and infected period, is studied.Methods The system′s asymptotic property is discussed by Lasalle invariant set principle and Routh-Hurwitz criterion.Results The threshold, Basic Reproductive Number, which determines whether the disease is extinct or not is gotten. The stabilities of the disease-free equilibrium and the endemic equilibrium are proved. The influence of infectivity in latent period is exposed.Conclusion In order to remove the disease which has infective force in latent period, it is necessary to control the patients not only in the infected period but also in the latent period. Only in this way, can the (disease′s) spread be effectively restrained.

关 键 词：饱和接触率 潜伏期 数学模型 阈值 Lasalle不变集 Routh-Hurwitz判据 

分 类 号：O175[理学—数学]