# Analytical Mechanics

Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling

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

**Authors: **Paul Steinmann

**Links**: Preprint

**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.