LYAPUNOV FUNCTIONS AND GLOBAL STABILITY FOR AGE-STRUCTURED HIV INFECTION MODEL

We study the basic age-structured population model describing the HIV infection process, which is defined by PDEs. The model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age. By using the direct Lyapunov method an...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2012-01, Vol.72 (1), p.25-38
Main Authors: HUANG, GANG, LIU, XIANNING, TAKEUCHI, YASUHIRO
Format: Article
Language:English
Subjects:
Age
Applied mathematics
HIV
HIV infections
Human immunodeficiency virus
Infections
Liapunov functions
Lymphocytes
Mathematical analysis
Mathematical functions
Mortality
Ordinary differential equations
Production increases
Viral infections
Virions
Viruses
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Summary:We study the basic age-structured population model describing the HIV infection process, which is defined by PDEs. The model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age. By using the direct Lyapunov method and constructing suitable Lyapunov functions, dynamical properties of the agestructured model without (or with) drug treatment are established. The results show that the global asymptotic stability of the infection-free steady state and the infected steady state depends only on the basic reproductive number determined by the burst size. Further, we establish mathematically that the typical ODE and DDE (delay differential equation) models of HIV infection are equivalent to two special cases of the above PDE models.
ISSN:0036-1399
1095-712X
DOI:10.1137/110826588