两类传染病模型的定性理论分析
发布时间：2018-08-04 12:59
【摘要】：传染病动力学是利用动力学方法去研究疾病的发展过程,预测其流行规律和发展趋势,分析疾病流行的原因和关键因素,寻求对其进行预防和控制的最优策略.基于此,本文将研究具有一般非线性发生率和多个并行感染阶段的时滞SIR模型的稳定性以及具有部分指数非拟单调性的时滞反应扩散系统行波解的存在性问题.对于具有一般非线性发生率和多个并行感染阶段的时滞SIR模型,首先得到了模型的平衡点和基本再生数?0,然后通过构造适当的Lyapunov函数,研究了平衡点的全局稳定性.当?0≤1时,无病平衡点是全局渐近稳定的;当?01时,地方病平衡点是全局渐近稳定的.对于具有部分指数非拟单调性的时滞反应扩散系统,通过建立一系列的引理,并利用Schauders不动点定理建立了系统行波解的存在性定理.通过一致持续生存理论的方法来确定模型的一致持续性和所有平衡态的稳定性准则,得到长时间的疾病传播的阈值动力学,并将此方法应用到更多的传染病传播模型,无论在稳定性理论还是在疾病的控制预防方面,都是有意义的工作.
[Abstract]:The dynamics of infectious diseases is to study the process of disease development, predict the epidemic law and development trend, analyze the causes and key factors of disease prevalence, and seek the best strategy to prevent and control the disease. Based on this, this paper will study the stability of delay SIR model with general nonlinear incidence and multiple parallel infection stages and the existence of traveling wave solutions for delayed reaction-diffusion systems with partial exponential nonmonotonicity. For the delayed SIR model with general nonlinear incidence and multiple parallel infection stages, the equilibrium point and the basic reproduction number of the model are first obtained. Then, the global stability of the equilibrium point is studied by constructing appropriate Lyapunov functions. When 0 鈮，
本文编号：2163958
[Abstract]:The dynamics of infectious diseases is to study the process of disease development, predict the epidemic law and development trend, analyze the causes and key factors of disease prevalence, and seek the best strategy to prevent and control the disease. Based on this, this paper will study the stability of delay SIR model with general nonlinear incidence and multiple parallel infection stages and the existence of traveling wave solutions for delayed reaction-diffusion systems with partial exponential nonmonotonicity. For the delayed SIR model with general nonlinear incidence and multiple parallel infection stages, the equilibrium point and the basic reproduction number of the model are first obtained. Then, the global stability of the equilibrium point is studied by constructing appropriate Lyapunov functions. When 0 鈮，
本文编号：2163958
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