Homoclinic bifurcation in an SIQR model for childhood diseases
type: Item
instance of: scholarly article
title: Homoclinic bifurcation in an SIQR model for childhood diseases
zbMATH Open document ID: 0969.34042
author: Lin-Ing Wu
author: Zhilan Feng
published in: Journal of Differential Equations
publication date: 2001-01-25T00:00:00Z
review text: The authors study an SIQR model for childhood disease, where \(S, I, Q, R\) denote the number of susceptible, infected, isolated (quarantined) and recovered individuals, respectively. A center manifold reduction at a bifurcation point has the normal form for this model: \[ \dot x=y, \quad \dot y=axy+bx^2y+0(4), \] which indicate that there is a bifurcation of codimension greater than two for some critical parameter values. In particular, the authors find an unfolding which gives rise to a codimension two bifurcation and prove analytically the existence of limit cycles and homoclinic orbits. They also confirm that there exist Hopf and homoclinic bifurcations of the model by several numerical computations.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1556506
zbMATH Keywords: epidemic model
zbMATH Keywords: homoclinic bifurcations
zbMATH Keywords: limit cycles
describes a project that uses: AUTO
reviewed by: Lansun Chen
MaRDI profile type: Publication
OpenAlex ID: W2112827773
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DOI: 10.1006/JDEQ.2000.3882
description: scientific article; zbMATH DE number 1556506