Uniform persistence and permanence for non-autonomous semiflows in population biology
type: Item
instance of: scholarly article
title: Uniform persistence and permanence for non-autonomous semiflows in population biology
zbMATH Open document ID: 0970.37061
DOI: 10.1016/S0025-5564(00)00018-3
author: Horst R. Thieme
published in: Mathematical Biosciences
publication date: 2001-02-06T00:00:00Z
review text: The author proves that under certain additional conditions uniform weak persistence implies uniform strong persistence. Then he shows how persistence theory can be turned around to demonstrate ultimate boundedness (or point dissipativity) for non-autonomous semiflows. Finally, these results are applied to establish threshold criteria for disease extinction and disease persistence in time heterogeneous SIRS epidemic models and to establish permanence for a one species model consisting of a scalar retarded functional-differential equation.
Mathematics Subject Classification ID: 37L15
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1525718
zbMATH Keywords: persistence
zbMATH Keywords: permanence
zbMATH Keywords: semiflow
zbMATH Keywords: dissipativity
zbMATH Keywords: SIRS epidemic models
zbMATH Keywords: functional differential equations
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
Wikidata QID: Q52075814
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full work available at URL: s0025-5564(00)00018-3
OpenAlex ID: W2161876659
description: scientific article; zbMATH DE number 1525718