Advancing Mathematical Epidemic Modeling via synergies with Chemical Reaction Network Theory and Lagrange-Hamilton Geometry

TL;DR

This paper explores how integrating chemical reaction network theory and Lagrange-Hamilton geometry can enhance the complexity and robustness of mathematical epidemic models, emphasizing interdisciplinary collaboration.

Contribution

It highlights the importance of complex non-negative kinetic systems and advocates for interdisciplinary approaches to advance epidemiological modeling.

Findings

Emphasizes the role of non-negative kinetic systems in epidemiology

Suggests interdisciplinary collaboration for complex model development

Reviews the intersection of epidemiology with chemical and geometric theories

Abstract

This essay reviews some key concepts in mathematical epidemiology and examines the intersection of this field with related scientific disciplines, such as chemical reaction network theory and Lagrange-Hamilton geometry. Through a synthesis of theoretical insights and practical perspectives, we underscore the significance of essentially non-negative kinetic systems in the development and implementation of robust epidemiological models. Our purpose is to make the case that currently mathematical modeling of epidemiology is focusing too much on simple particular cases, and maybe not enough on more complex models, whose challenges would require cooperation with scientific computing experts and with researchers in the "sister disciplines" involving essentially nonnegative kinetic systems (like virology, ecology, chemical reaction networks, population dynamics, etc).