  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.
