一类具有常数移民和分布时滞的SIRS传染病模型分析  

Epidemic Models of SIRS Type with Constant Immigration and Distribution Delay

作　　者：朱春娟[1] 

机构地区：[1]广东韶关学院数学与信息科学学院,韶关512005

出　　处：《上海理工大学学报》2013年第3期261-264,共4页Journal of University of Shanghai For Science and Technology

摘　　要：通过恰当的Liapunov函数,研究了一类在易感者类和移出者类具有常数移民、通过媒介传播和含分布时滞的SIRS传染病模型.在不存在染病者移民时,得到了地方平衡点存在的阈值R0.当R0<1时,无病平衡点是全局渐近稳定的;当R0>1时,无病平衡点不稳定,地方平衡点全局渐近稳定.在染病者存在常数输入时,模型不存在无病平衡点,地方平衡点全局渐近稳定.An epidemic model of SIRS type with constant immigration of each class and distribution delay was dealt with by means of suitable Liapunov functions. In the absence of infectious individuals, the threshold of existence of endemic equilibrium was found. Below the threshold, the disease-free equilibrium is globally asympototically stable~ above the threshold, the disease-free equilibrium is unstable and the endemic quilibrium is globally asymptotically stable. In the existence of input of infectious individuals, the models have no disease-free equilibrium and the SIRS model is globally stable in the corresponding region.

关 键 词：传染病模型 分布时滞 平衡点 稳定性 

分 类 号：O175.1[理学—数学]