Viral dynamics model with CTL immune response incorporating antiretroviral therapy

Yan Wang, Yicang Zhou, Fred Brauer, Jane M. Heffernan

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.

Original languageEnglish (US)
Pages (from-to)901-934
Number of pages34
JournalJournal Of Mathematical Biology
Issue number4
StatePublished - Oct 1 2013
Externally publishedYes


  • Antiretroviral therapy
  • Asymptotic stability
  • CD4 T-cells
  • Cytotoxic T lymphocytes
  • HIV

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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