Analytical Mechanics

Preprint: Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling

Author: Paul Steinmann

Link to Preprint: arXiv

Abstract: 

This contribution aims to shed light on mathematical epidemic dynamics
modelling from the viewpoint of analytical mechanics. To set the stage, it
recasts the basic SIR model of mathematical epidemic dynamics in an analytical
mechanics setting. Thereby, it considers two possible re-parameterizations of
the basic SIR model. On the one hand, it is proposed to re-scale time, while on
the other hand, to transform the coordinates, i.e.\ the independent variables.
In both cases, Hamilton’s equations in terms of a suited Hamiltonian as well as
Hamilton’s principle in terms of a suited Lagrangian are considered in minimal
and extended phase and state space coordinates, respectively. The corresponding
Legendre transformations relating the various options for the Hamiltonians and
Lagrangians are detailed. Ultimately, this contribution expands on a multitude
of novel vistas on mathematical epidemic dynamics modelling that emerge from
the analytical mechanics viewpoint. As result, it is believed that interesting
and relevant new research avenues open up when exploiting in depth the
analogies between analytical mechanics and mathematical epidemic dynamics
modelling.