Vol. 8, No. 4, 2020

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Analytical mechanics allows novel vistas on mathematical epidemic dynamics modeling

Paul Steinmann

Vol. 8 (2020), No. 4, 321–343
DOI: 10.2140/memocs.2020.8.321
Abstract

This contribution aims to shed light on mathematical epidemic dynamics modeling 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 reparametrizations of the basic SIR model: one rescales time, while the other transforms 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 modeling that emerge from the analytical mechanics viewpoint. As a 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 modeling.

Keywords
epidemics modeling, analytical mechanics
Mathematical Subject Classification
Primary: 70K99
Milestones
Received: 7 June 2020
Revised: 9 July 2020
Accepted: 11 August 2020
Published: 9 November 2020

Communicated by Francesco dell'Isola
Authors
Paul Steinmann
Institute of Applied Mechanics
Friedrich-Alexander Universität Erlangen-Nürnberg
Erlangen
Germany
Glasgow Computational Engineering Centre
University of Glasgow
Glasgow
United Kingdom