具有饱和接触率的SIRS传染病模型的周期解  

Periodic solutions of an SIRS epidemic model with saturation incidence

作　　者：郝丽杰[1] 蒋贵荣[1] 鹿鹏[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2013年第1期61-65,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11162004;60964006);广西自然科学基金(0832244)

摘　　要：基于离散映射和分岔理论,研究了具有脉冲生育、脉冲接种和饱和接触率的SIRS传染病模型的动力学性质,通过分析模型平凡解和无病周期解的存在性和稳定性以及超临界分岔发生的条件,得到决定疾病流行与否的阈值,给出验证理论分析的数值结果。The dynamics of an SIRS epidemic model with birth pulse, pulse vaccination and saturation incidence is studied. The existence and stability of the trivial solution and infection-free periodic solution are analyzed. By using discrete mapping and bifurcation theory, the condition of occurrence for supercritical bifurcation is derived. The threshold for a disease to be extinct or endemic is established. Moreover, numerical results for phase portraits, periodic solutions and bifurcation dia- grams are illustrated with an example, which are in agreement with the theoretical analysis.

关 键 词：SIRS传染病模型 饱和接触率 脉冲接种 周期解 超临界分岔 

分 类 号：O175.1[理学—数学]