摘要
本文根据人类感染禽流感的两种可能途径,一是被带有禽流感病毒的禽感染;二是被感染禽流感病毒的人群感染,通过考虑人类易感者和禽类感染者以及人类易感者和人类感染者之间的传播关系,利用微分方程建立两类SI-SIR禽流感传染病模型.通过对模型的分析,得到疾病是否流行的阈值,即基本再生数,并利用Lyapunov函数以及La Salle不变原理证明两类模型平衡点的局部与全局渐近稳定性.
Based on the two ways of human infection with avian influenza, one is by the infected birds, the other is by the infected humans, this paper establishs two SI-SIR avian flu epidemic models considering the two transmission relationships, susceptible humans and infected birds, susceptible humans and infected humans. Through the analysis of the model, we get a threshold whether the disease will epidemic, that is the basic reproductive number. Further, using the Lyapunov function and LaSalle invariance principle we show the global asymptotic stability of disease-free equilibrium and the endemic equilibrium in the two models.
出处
《应用数学》
CSCD
北大核心
2015年第3期481-489,共9页
Mathematica Applicata
基金
国家自然科学基金(11071275)
中央高校专项基金(CCNU10B01005)
湖北省自然科学基金(2013CFB013)
