Threshold dynamics for an HIV model in periodic environments

In this paper, we investigate an HIV model incorporating the effect of an ARV regimen. Since drug concentration varies during dose intervals, which results in periodic variation of the drug efficacy, our model is then a periodic time-dependent system. We get a threshold value between the extinction...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 361; no. 1; pp. 59 - 68
Main Authors Yang, Youping, Xiao, Yanni
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 2010
Elsevier
Subjects
Drug efficacy
Exact sciences and technology
Global stability
HIV
Mathematical analysis
Mathematics
Persistent theory
Sciences and techniques of general use
Drug efficacy
HIV
Global stability
Persistent theory
Mathematical analysis
Positive solution
Periodic solution
Application
Numerical stability
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Summary:In this paper, we investigate an HIV model incorporating the effect of an ARV regimen. Since drug concentration varies during dose intervals, which results in periodic variation of the drug efficacy, our model is then a periodic time-dependent system. We get a threshold value between the extinction and the uniform persistence of the disease by applying the persistence theory. Our main results show that the disease goes to extinction if the threshold value is less than unity, whilst the disease persists if the threshold value is larger than unity. We also prove that there exists a positive periodic solution which is globally asymptotically stable. The threshold dynamics is in agreement with that for the system with constant coefficients, which extends the classic results for the corresponding autonomous model.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.09.012