论文标题
隔室流行病学模型的哈密顿结构
Hamiltonian structure of compartmental epidemiological models
论文作者
论文摘要
任何具有恒定种群的流行病学隔室模型被证明是哈密顿的动力系统，在该系统中，总人口在其中扮演了哈密顿功能的作用。此外，在这一大型模型中，某些特殊情况被证明是双汉米尔顿的。引入了不同人群之间的新相互作用的隔间模型，这些模型被引入了赋予哈密顿结构的赋予。明确提出了对所有这些动力学系统的哈密顿描述为基础的泊松结构，并显示其相关的CASIMIR功能提供了有效的工具，以便为流行病学模型找到确切的分析解决方案，例如描述COVID-19大流行的动力学。
Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class of models are shown to be bi-Hamiltonian. New interacting compartmental models among different populations, which are endowed with a Hamiltonian structure, are introduced. The Poisson structures underlying the Hamiltonian description of all these dynamical systems are explicitly presented, and their associated Casimir functions are shown to provide an efficient tool in order to find exact analytical solutions for epidemiological models, such as the ones describing the dynamics of the COVID-19 pandemic.
