摘要
本文研究了两类具有种群密度制约接触率的SIR流行病模型,其生态学结构分别为常数输入和Logistic出生。可以证明两模型均存在在强阈值现象,阈值参数即模型的基本再生数,它决定了疾病的绝灭和流行也决定了模型的全局性态。为了证明地方病平衡点的全局稳定性,对具有常数输入的SIR模型,引入了一个变量代换将三维模型转化为具有极限方程的二维渐近自治系统;对具有Logistic出生的SIR模型,构造了Lyapunov函数。
Two SIR type epidemic models with population size dependent contact rate are analyzed. The demographic structures considered here are recruitment and logistic birth, respectively. The basic reproduction numbers of two SIR models are all the sharp thresholds which determine whether the diseases die out or remain endemic. To prove the global stability of endemic equilibria, the change of variable, which can reduce the SIR model with recruitment to a two-dimensional asymptotical autonomous system, is introduced when the population dynamics is immigration and the Liapunov function is constructed when the population dynamics is logistic birth.
出处
《工程数学学报》
CSCD
北大核心
2004年第2期259-267,共9页
Chinese Journal of Engineering Mathematics
基金
ThisresearchissupportedbyNationalNaturalScienceFoundationofChina
grantNo(199710 6 6 )
