Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells
This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changin...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/838396 |
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| author | P. Balasubramaniam M. Prakash Fathalla A. Rihan S. Lakshmanan |
| author_facet | P. Balasubramaniam M. Prakash Fathalla A. Rihan S. Lakshmanan |
| author_sort | P. Balasubramaniam |
| collection | DOAJ |
| description | This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results. |
| format | Article |
| id | doaj-art-e7dde456ae6e4da193eea30043201afc |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e7dde456ae6e4da193eea30043201afc2025-08-20T03:21:02ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/838396838396Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cellsP. Balasubramaniam0M. Prakash1Fathalla A. Rihan2S. Lakshmanan3Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, IndiaDepartment of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, IndiaDepartment of Mathematical Sciences, College of Science, UAE University, P.O. Box 15551, Al-Ain, UAEDepartment of Mathematical Sciences, College of Science, UAE University, P.O. Box 15551, Al-Ain, UAEThis paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results.http://dx.doi.org/10.1155/2014/838396 |
| spellingShingle | P. Balasubramaniam M. Prakash Fathalla A. Rihan S. Lakshmanan Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells Abstract and Applied Analysis |
| title | Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells |
| title_full | Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells |
| title_fullStr | Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells |
| title_full_unstemmed | Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells |
| title_short | Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells |
| title_sort | hopf bifurcation and stability of periodic solutions for delay differential model of hiv infection of cd4 t cells |
| url | http://dx.doi.org/10.1155/2014/838396 |
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