一类具有常数移民和分布时滞的SIR传染病模型分析

Analysis of an epidemic models of SIR type with constant immigration and distribution delay

通过极限理论和Liapunov函数,研究了易感者和移出者具有常数移民、通过媒介传播和含分布时滞的SIR传染病模型,得到了地方平衡点存在的阈值.在阈值之下,无病平衡点是全局渐进稳定的;在阈值之上,无病平衡点是不稳定的;地方平衡点在相应的区域内是全局渐进稳定的.

This paper deals with an epidemic models of SIR type with constant immigration of susceptible and recovery individuals and distribution delay by the means of theory of limit system and some suitable Liapunov functions. The threshold of existence of endemic equilibrium is found. Below the threshold, the disease-free equilibrium is globally asymptotically stable; above the threshold, the disease-free equilibrium is unstable and endemic equilibrium is globally asymptotically stable in the corresponding regions.