Backward bifurcation and global stability inan epidemic model with treatment and vaccination
Backward bifurcation and global stability inan epidemic model with treatment and vaccination
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DOI：
10.3934/dcdsb.2014.19.999
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发表时间：
2014-04
影响因子：
1.2
通讯作者：
Xiaomei Feng;Z. Teng;Kai Wang;Fengqin Zhang
中科院分区：
文献类型：
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作者：
Xiaomei Feng;Z. Teng;Kai Wang;Fengqin Zhang
本文考虑了一类由五个非线性常微分方程描述的传染病模型。人群分为易感、接种、暴露、感染和恢复亚类。这类模型的一个主要特点是引入治疗和疫苗接种来控制和预防传染病。研究了地方病平衡点的存在性和局部稳定性。利用中心流形理论证明了后向分岔的发生。移动，全球动力学研究应用几何方法。在双稳态情形下，由于不存在紧吸收集，因此很难得到全局结果。这是第一次讨论更高（大于或等于4）维系统。通过推广Arino等人[2]的方法，给出了系统参数的充分条件。数值模拟也提供了支持我们的理论结果。通过对基本再生数对某些参数的敏感性分析，分析了控制传染病的有效措施。
In this paper, we consider a class of epidemic models described by five nonlinear ordinary differential equations. The population is divided into susceptible, vaccinated, exposed, infectious, and recovered subclasses. One main feature of this kind of models is that treatment and vaccination are introduced to control and prevent infectious diseases. The existence and local stability of the endemic equilibria are studied. The occurrence of backward bifurcation is established by using center manifold theory. Moveover, global dynamics are studied by applying the geometric approach. We would like to mention that in the case of bistability, global results are difficult to obtain since there is no compact absorbing set. It is the first time that higher (greater than or equal to four) dimensional systems are discussed. We give sufficient conditions in terms of the system parameters by extending the method in Arino et al. [2]. Numerical simulations are also provided to support our theoretical results. By carrying out sensitivity analysis of the basic reproduction number in terms of some parameters, some effective measures to control infectious diseases are analyzed.