Hamiltonian structure of compartmental epidemiological models

PHYSICA D-NONLINEAR PHENOMENA

卷:413

Article

Ballesteros, Angel¹  Blasco, Alfonso¹  Gutierrez-Sagredo, Ivan^1,2 

[1] Univ Burgos, Dept Fis, Burgos 09001, Spain

[2] Univ Burgos, Dept Matemat & Comp, Burgos 09001, Spain

关键词: Epidemics;    Compartmental models;    Dynamical systems;    Hamiltonian systems;    Poisson structures;    Casimir functions;   

DOI  :  10.1016/j.physd.2020.132656

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free