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Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment

Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment

Acta Biotheoretica , Volume 64 (1) – Nov 13, 2015

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References (40)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Science+Business Media Dordrecht
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-015-9273-9
pmid
26566620
Publisher site
See Article on Publisher Site

Abstract

This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results.

Journal

Acta BiotheoreticaSpringer Journals

Published: Nov 13, 2015

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