Global dynamics of an infinite dimensional epidemic model with nonlocal state structures
type: Item
instance of: scholarly article
title: Global dynamics of an infinite dimensional epidemic model with nonlocal state structures
zbMATH Open document ID: 1402.37090
author: Peng Zhang
published in: Journal of Differential Equations
publication date: 2018-09-04T00:00:00Z
review text: This paper studies the global dynamics of an infinite-dimensional epidemic model with nonlocal state structures. To describe a continuous state model, the population is partitioned into susceptible and recovered, and a state-structured SIR model is introduced. Under certain balance conditions and smooth conditions, a sharp threshold result characterizing the global dynamics in terms of basic reproduction number \(R_0\) is presented. The model is a general multi-stage one in which infected individuals are allowed to transfer among different stages and new infections are distributed into all stages with certain probability. The existence and local stability of stationary solutions such as the disease-free equilibrium and endemic equilibria are discussed. The authors establish the global stability of the disease-free equilibrium when \(R_0<1\) and uniform persistence when \(R_0>1\). Some examples are also provided to illustrate the theoretical results.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 37L45
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6931740
zbMATH Keywords: integro-differential equations
zbMATH Keywords: nonlocal structures
zbMATH Keywords: nonlinear semi-groups
zbMATH Keywords: principal spectral conditions
zbMATH Keywords: global stability
MaRDI profile type: Publication
full work available at URL: j.jde.2018.06.036
OpenAlex ID: W2886955493
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Wikidata QID: Q129402115
DOI: 10.1016/J.JDE.2018.06.036
description: scientific article; zbMATH DE number 6931740