关于传染病 compartmental 模型的李雅普诺夫函数的一项调查。

A survey on Lyapunov functions for epidemic compartmental models.

作者信息

Cangiotti Nicolò, Capolli Marco, Sensi Mattia, Sottile Sara

机构信息

Department of Mathematics, Politecnico di Milano, via Bonardi 9, 20133 Milan, Italy.

Institute of Mathematics, Polish Academy of Sciences, Jana i Jedrzeja Sniadeckich 8, 00-656 Warsaw, Poland.

出版信息

Boll Unione Mat Ital (2008). 2023 Jun 6:1-17. doi: 10.1007/s40574-023-00368-6.

DOI:10.1007/s40574-023-00368-6

PMID:37360758

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10242238/

Abstract

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, and provide 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.

摘要

在本次调查中，我们对流行病学中各种房室模型的李雅普诺夫函数进行了概述。我们展示了使用最广泛的函数，并对其使用情况进行了评论。我们的目的是为试图证明常微分方程系统全局稳定性的读者提供一个全面的起点。重点是数学流行病学，然而本文中提出的一些函数和策略可以适用于更广泛的模型，如捕食者 - 猎物模型或谣言传播模型。