具有接种疫苗和再次感染的媒介传染病模型的稳定性分析  

Global Stability of an Epidemic Model with Vaccination and Re-Infection

作　　者：白梦[1] 薛亚奎[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2016年第2期120-125,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11301491);山西省自然科学基金资助项目(2015011009)

摘　　要：建立和研究了一类具有接种疫苗和再次感染的媒介传染病模型.假设易感者接种疫苗后还被感染,得到了疾病流行与否的阈值,即基本再生数R0,并讨论了平衡点的存在性.进一步运用Lyapunov函数及Routh-Hurwitz判据证明了无病平衡点和地方病平衡点的全局稳定性.最后根据实际情况选取适当数据,进行数值模拟,验证了所得结论的正确性.The epidemic model with vaccination and re-infection is formulated and analysed.It is assumed that the susceptible individuals are infected after being vaccinated,the basic reproduction number R0 which determines the outcome of disease is identified and the existence of the equilibrium is discussed.Further application of Lyapunov function and Routh-Hurwitz criterion are used to prove that disease free equilibrium and endemic equilibrium is global stability.Then a series of numerical simulations are presented to illustrate the mathematical findings.

关 键 词：接种疫苗 再次感染 媒介传染病 无病平衡点 地方病平衡点 

分 类 号：O175[理学—数学]