Hamiltonian structure of compartmental epidemiological models

Abstract

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.

Minor misprints corrected

References in corpus (4)

• Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan
• Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
• Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach
• Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations

Cited by in corpus (1)

• Geometry and solutions of an epidemic SIS model permitting fluctuations and quantization