一类潜伏期有传染力的离散SEIR传染病模型的Neimark-Sacker分岔  

An analysis of Neimark-Sacker bifurcation for a discrete SEIR epidemic model with infectious force in latent period

作　　者：杜文举[1,2] 秦爽[2] 张建刚[2] 俞建宁[1] 

机构地区：[1]兰州交通大学交通运输学院,甘肃兰州730070 [2]兰州交通大学数理学院数学系,甘肃兰州730070

出　　处：《暨南大学学报（自然科学与医学版）》2016年第6期518-524,共7页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金项目(61364001)

摘　　要：目的:传染病模型的研究能更好地显示疾病发展过程,揭示其流行规律,寻求对其预防及控制的最优策略.方法:欧拉向前差分法、Neimark-Sacker分岔准则、Kuznetsov's理论和中心流形定理.结果:构造了1个新的离散的潜伏期具有传染力的SEIR传染病模型.主要研究离散SEIR传染病模型的动力学性质、讨论系统平衡点的存在性,并进一步分析系统无病平衡点的稳定性.结论:对g EIR传染模型在无病平衡点处Neimark-Sacker分岔的存在性、稳定性和方向进行详细的理论分析后,通过数值模拟验证了结论的正确性.Aim： The study of epidemic model can show better the development of the disease, revea-ling its popular rule, and seeking the optimal strategies for the prevention and control of the disease. Methods Forward Euler scheme, explicit Neimark- Sacker bifurcation criterion, Kuznetsov＇s method and center manifold theorem. Results ： A new discrete SEIR epidemic model with infectious force in latent period is proposed. The dynamics of this discrete SEIR epidemic model and the existence of its equilibri-ums are studied, and the stability of the disease-free equilibrium is further analyzed. Conclusion： The existence, stability and direction of the Neimark-Sacker bifurcation are analyzed. Finally, a numerical example is given to illuminate the validity of the theoretical analysis.

关 键 词：离散SEIR模型 稳定性 中心流形定理 NEIMARK-SACKER分岔 

分 类 号：O175.1[理学—数学]