具有饱和治愈率的SIS传染病模型的稳定性  

Stability of an SIS epidemic model with saturated cure rate

作　　者：谭宏武[1] 

机构地区：[1]陕西科技大学理学院,陕西西安710021

出　　处：《宝鸡文理学院学报（自然科学版）》2013年第4期3-6,10,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省教育厅科学研究项目(No.2013JK0599)

摘　　要：目的通过研究一类具有饱和治愈率的离散SIS传染病模型的稳定性,为疾控部门制定治疗传染病的方案提供了理论依据。方法利用动力系统知识对所建立的模型进行理论分析。结果定义了模型的基本再生数,讨论了无病平衡点和地方病平衡点的存在性和局部稳定性,以及R0<1时可能出现的后向分支。结论不充分的治疗可能会导致传染病的持久。Objective--To provide the theoretical basis for CDC（Centers for Disease Contral） developing the treatment program on the epidemics by formulating and studying the stability of the discrete SIS epidemic model with the saturated cure rate. Methods--The model was discussed theoretically with the knowledge of dynamics. Results--The basic reproductive number was defined and the existence and stability conditions of the disease-free equilibrium and endemic equilibrium were obtained. Moreover, the backward bifurcation might appear as R0 〈 1 was less than 1. Conclusion--The inadequate treatment of infectious diseases may lead to the persistence of the disease.

关 键 词：离散传染病模型 基本再生数 稳定性 后向分支 

分 类 号：O175[理学—数学]