摘要
研究了各仓室均有常数输入且接触率为种群密度制约的SEI流行病模型.如果输入的新成员都是易感的,模型存在强阈值现象,阈值参数即其基本再生数,它决定了疾病的绝灭与流行也决定了模型的全局性态.如果输入的新成员中有被感染的,疾病不会绝灭.利用三维竞争系统的Poincar啨 Bendixson性质排除了周期解存在的可能性,从而证明了惟一的地方病平衡点是全局渐近稳定的.
An SEI epidemic model with the constant inflows of susceptible, exposed and infective compartments is constructed and analyzed,whose incidence is poplation size dependent. When new members of inflows are all susceptible, the model admits a sharp threshold phenomena. The threshold parameter is considered as the basic reproduction number, which determines the outcome of the disease and the global dynamics of the model. If three epidemic compartments are all with the constant inflow, there is no diseasefree equilibrium, but the model admits a unique endemic equilibium which is globally asymptotically stable. With the help of the PoincaréBendixson property of competitive system, this result is proved by ruling out periodic trajectories.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2003年第6期653-656,共4页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目 (1 9971 0 6 6 ).
关键词
SEI模型
常数输入
种群规模制约接触率
竞争系统
全局渐近稳定性
SEI model
constant inflow
population size dependent contact rate
competitive system
global asymptotical stability
