具有非线性发生率的 SI 传染病模型中的状态相关脉冲接种和治疗策略。
State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate.
机构信息
College of Mathematics and Information Science, Anshan Normal University, Anshan 114016, China.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
出版信息
Comput Math Methods Med. 2019 Feb 6;2019:3859815. doi: 10.1155/2019/3859815. eCollection 2019.
In this paper, the state-dependent pulse vaccination and therapeutic strategy are considered in the control of the disease. A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. Then for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a unique order-1 homoclinic cycle, and by choosing as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.
在本文中，考虑了状态相关的脉冲接种和治疗策略来控制疾病。基于 SI 常微分方程模型，构建了一个脉冲系统来模拟这个过程。首先，对于忽略脉冲效应的系统，我们给出了奇点的分类。然后，对于脉冲系统，通过使用半连续动力系统理论，分析了其动力学。我们的分析表明，脉冲系统表现出丰富的动力学，系统具有唯一的一阶同宿环，并且通过选择作为控制参数，当变化时，一阶同宿环消失，并分支出一个轨道渐近稳定的一阶周期解。通过 Maple 18 进行数值模拟，验证了理论结果。
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