摘要
利用Lasalle不变集原理探讨系统的渐近性态,研究了一类具有双线性发生率且染病期传染的SEIR流行病传播数学模型的动力学性质.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全局渐近稳定性,揭示了潜伏期传染的影响.
Dynamical behavior of a kind of SEIR model of epidemic spreads with the bilinear rate,which has infective force in infected period,is studied.The system s asymptotic property is discussed by Lasalle invariant set principle.The threshold,Basic Reproductive Number,which determines whether the disease is extinct or not is gotten.Global asymptotically stabilities of the disease-free equilibrium and the endemic equilibrium are proved.The influence of infectivity in latent period is exposed.
出处
《山西大同大学学报（自然科学版）》
2007年第4期18-20,共3页
Journal of Shanxi Datong University(Natural Science Edition)
关键词
流行病
数学模型
动力学
基本再生数
局部渐近稳定性
全局渐近稳定性
epidemic
mathematic model
dynamics
basic reproductive number
local asymptotically stability
global asymptotically stability
