具有垂直传染和脉冲接种的SIRS传染病模型的周期解  

Periodic solutions of an SIRS epidemic model with vertical transmission and pulse vaccination

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：《东北师大学报（自然科学版）》2013年第3期35-40,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11162004);广西自然科学基金资助项目(2012GXNSFAA053006);广西研究生教育创新计划项目(YCSZ2012072)

摘　　要：研究了一个具有脉冲生育、脉冲接种和垂直传染的SIRS传染病模型周期解的存在性和稳定性,通过利用分岔理论,给出了超临界分岔发生的条件,得到了决定疾病流行与否的阈值,并且数值结果较好验证了理论分析.In this paper,the existence and stability of the periodic solutions of an SIRS epidemic model with birth pulse,vertical transmission and pulse vaccination are studied.By using 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 diagrams,which are illustrated with an example,are in good agreement with the theoretical analysis.

关 键 词：传染病模型 脉冲 垂直传染 周期解 分岔 阈值 

分 类 号：O175.1[理学—数学]