Journal Article

Global asymptotic stability for HIV-1 dynamics with two distributed delays

Jinliang Wang, Gang Huang and Yasuhiro Takeuchi

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 3, pages 283-300
Published in print September 2012 | ISSN: 1477-8599
Published online July 2011 | e-ISSN: 1477-8602 | DOI:
Global asymptotic stability for HIV-1 dynamics with two distributed delays

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Based on the drugs treatment to control HIV-1 infection and viral replication, we express the intracellular eclipse phase of virions in host cell as distributed delays because of pharmacological actions. In present paper, we investigate a class of HIV-1 infection dynamical model with two distributed delays. One of them describes the period between the time that HIV virion enters (infects) target cell and the time that the infected cell starts to produce new viral particles. The other describes the time for the virion maturation process. They are both allowed to tend to be infinite because of drugs resistent strains. By the Lyapunov direct method of and utilizing the technology of constructing Lyapunov functionals, we identify the basic reproduction number R0 as a threshold quantity for the stability of equilibria. More precisely, if R0 ≤ 1, the infection-free equilibrium is globally asymptotically stable; on the contrary, if R0 > 1, then an infected equilibrium appears which is globally asymptotically stable. The dynamical results indicate that time delays have effect on the global stability of two equilibria through threshold value R0, which is a decreasing function of delays. The biological meanings imply that any drugs that can prolong the time of viral reproduction through slowing down the reverse transcription of HIV in host and virus maturation process may also help control the HIV-1 infection and virus loads. Another way to increase the efficacy of the protease inhibitor and the reverse transcriptase inhibitor (i.e. increasing np and nrt) is also desirable treatment strategies.

Keywords: HIV-1; intracellular delay; Lyapunov functional; global stability

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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