Calculus of Variations and Geometric Measure Theory

N. Cangiotti - M. Capolli - M. Sensi - S. Sottile

A survey on Lyapunov functions for epidemic compartmental models

created by cangiotti on 05 Dec 2023
modified on 10 May 2024


Published Paper

Inserted: 5 dec 2023
Last Updated: 10 may 2024

Journal: Bollettino dell'Unione Matematica Italiana
Year: 2023
Doi: 10.1007/s40574-023-00368-6

ArXiv: 2301.11947 PDF


In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, together with a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey-predator or rumor spreading.

Keywords: Ordinary differential equations, Epidemic models, Lyapunov functions, Compartmental models, Global stability, Disease free and endemic equilibria