Threshold dynamics for compartmental epidemic models in periodic environments
type: Item
instance of: scholarly article
title: Threshold dynamics for compartmental epidemic models in periodic environments
zbMATH Open document ID: 1157.34041
author: Wendi Wang
author: Xiao-Qiang Zhao
published in: Journal of Dynamics and Differential Equations
publication date: 2008-08-20T00:00:00Z
review text: The basic reproduction ratio and its computation formulae are established for a large class of compartmental epidemic models in periodic environments. It is proved that a disease cannot invade the disease-free state if the ratio is less than unity and can invade if it is greater than unity. It is also shown that the basic reproduction number of the time-averaged autonomous system is applicable in the case where both the matrix of new infection rate and the matrix of transition and dissipation within infectious compartments are diagonal, but it may underestimate and overestimate infection risks in other cases. The global dynamics of a periodic epidemic model with patch structure is analyzed in order to study the impact of periodic contacts or periodic migrations on the disease transmission.
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5314313
zbMATH Keywords: Compartmental models
zbMATH Keywords: Reproduction ratio
zbMATH Keywords: Periodicity
zbMATH Keywords: Threshold dynamics
MaRDI profile type: Publication
full work available at URL: s10884-008-9111-8
OpenAlex ID: W2050299562
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DOI: 10.1007/S10884-008-9111-8
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description: scientific article; zbMATH DE number 5314313