Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators
type: Item
instance of: scholarly article
title: Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators
zbMATH Open document ID: 1215.37052
author: Horst R. Thieme
published in: Journal of Differential Equations
publication date: 2011-03-25T00:00:00Z
review text: Establishing the global stability of the endemic equilibrium in host-parasite models has made great progress. This progress is mainly due to the adaptation to epidemic models of the Lyapunov function \(V(x)=x-a\ln (\frac{x}{a})\). In most of the investigations graph-theoretic methods are used. The aim of the paper is to show that, while using the same Lyapunov function, sometimes graph theory can be replaced by positive operator theory. The global stability of the endemic equilibrium is shown for an endemic model with infinite-dimensional population structure using a Volterra-like Lyapunov function and the Krein-Rutman theorem.
reviewed by: Victor Sharapov
Mathematics Subject Classification ID: 37L45
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 5869874
zbMATH Keywords: Volterra Lyapunov function
zbMATH Keywords: global compact attractor
zbMATH Keywords: uniform persistence
zbMATH Keywords: extinction
zbMATH Keywords: threshold behavior
MaRDI profile type: Publication
full work available at URL: j.jde.2011.01.007
OpenAlex ID: W1963895250
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DOI: 10.1016/J.JDE.2011.01.007
description: scientific article; zbMATH DE number 5869874