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Hopf bifurcation and stability of periodic solutions for delay differential model of HIV infection of CD4+ T-cells

Balasubramaniam, P., Prakash, M., Rihan, F. A. and Lakshmanan, S. 2014, Hopf bifurcation and stability of periodic solutions for delay differential model of HIV infection of CD4+ T-cells, Abstract and applied analysis, vol. 2014, doi: 10.1155/2014/838396.

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Title Hopf bifurcation and stability of periodic solutions for delay differential model of HIV infection of CD4+ T-cells
Author(s) Balasubramaniam, P.
Prakash, M.
Rihan, F. A.
Lakshmanan, S.ORCID iD for Lakshmanan, S. orcid.org/0000-0002-4622-3782
Journal name Abstract and applied analysis
Volume number 2014
Article ID 838396
Total pages 18
Publisher Hindawi Publishing
Place of publication Cairo, Egypt
Publication date 2014-08-31
ISSN 1085-3375
1687-0409
Keyword(s) Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
DYNAMICS IN-VIVO
CTL IMMUNE-RESPONSE
VIRAL DYNAMICS
ANTIRETROVIRAL THERAPY
INTRACELLULAR DELAY
GLOBAL STABILITY
TIME
IMPACT
MEMORY
Summary This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD 4 + 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.
Language eng
DOI 10.1155/2014/838396
Field of Research 0101 Pure Mathematics
Copyright notice ©2014, P. Balasubramaniam et al.
Free to Read? Yes
Use Rights Creative Commons Attribution licence
Persistent URL http://hdl.handle.net/10536/DRO/DU:30077159

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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.