Stability in cyclic epidemic models
type: Item
instance of: scholarly article
title: Stability in cyclic epidemic models
zbMATH Open document ID: 0571.92021
DOI: 10.1007/BF00276488
author: M. G. Roberts
published in: Journal of Mathematical Biology
publication date: 1985-01-01T00:00:00Z
review text: A general formulation for a family of cyclic epidemic models with density-dependent feedback mechanisms and removed classes is presented. A parameter, \(\lambda\), related to the basic reproductive rate determines the asymptotic behaviour of solutions of the model. It is shown that if \(\lambda <1\) the trivial solution is globally stable, and if \(\lambda >1\) it is conditionally stable. The results are applied to a set of differential equations that has been used to model the life cycle of a parasite that has two hosts.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 3912176
zbMATH Keywords: cyclic epidemic models
zbMATH Keywords: density-dependent feedback
zbMATH Keywords: removed classes
zbMATH Keywords: globally stable
zbMATH Keywords: conditionally stable
MaRDI profile type: Publication
Wikidata QID: Q52679329
cites work: Q4101645
cites work: The structural simplification of an epidemiological compartment model
cites work: Qualitative analyses of communicable disease models
cites work: Q3894443
cites work: Stability in a two host epidemic model
cites work: Asymptotic behavior and stability in four models of venereal disease
full work available at URL: https://doi.org/10.1007/bf00276488
OpenAlex ID: W2062061392
description: scientific article; zbMATH DE number 3912176