Bifurcation analysis of an SIR epidemic model with the contact transmission function
type: Item
instance of: scholarly article
title: Bifurcation analysis of an SIR epidemic model with the contact transmission function
zbMATH Open document ID: 1406.92590
DOI: 10.1155/2014/930541
author: Guihua Li
author: Gaofeng Li
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider an SIR endemic model in which the contact transmission function is related to the number of infected population. By theoretical analysis, it is shown that the model exhibits the bistability and undergoes saddle-node bifurcation, the Hopf bifurcation, and the Bogdanov-Takens bifurcation. Furthermore, we find that the threshold value of disease spreading will be increased, when the half-saturation coefficient is more than zero, which means that it is an effective intervention policy adopted for disease spreading. However, when the endemic equilibria exist, we find that the disease can be controlled as long as we let the initial values lie in the certain range by intervention policy. This will provide a theoretical basis for the prevention and control of disease.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7023332
zbMATH Keywords: SIR epidemic model
zbMATH Keywords: Bogdanov-Takens bifurcation
zbMATH Keywords: contact transmission function
Wikidata QID: Q59042907
describes a project that uses: MATCONT
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/930541
OpenAlex ID: W1965912053
cites work: A generalization of the Kermack-McKendrick deterministic epidemic model
cites work: Dynamical behavior of an epidemic model with a nonlinear incidence rate
cites work: Coexistence of Limit Cycles and Homoclinic Loops in a SIRS Model with a Nonlinear Incidence Rate
cites work: Multiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response
cites work: Epidemic models with nonlinear infection forces
cites work: Global analysis of an epidemic model with nonmonotone incidence rate
cites work: A qualitative study of a vaccination model with non-linear incidence
cites work: Dynamical behavior of epidemiological models with nonlinear incidence rates
cites work: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
cites work: Bifurcation analysis of an epidemic model with nonlinear incidence
cites work: Q4715203
cites work: Q3667657
cites work: Forced oscillations and bifurcations
cites work: Computational Science - ICCS 2004
description: scientific article; zbMATH DE number 7023332