Journal of Mathematical Biology

, Volume 67, Issue 5, pp 1111–1139

The role of backward mutations on the within-host dynamics of HIV-1

  • John M. Kitayimbwa
  • Joseph Y. T. Mugisha
  • Roberto A. Saenz

DOI: 10.1007/s00285-012-0581-2

Cite this article as:
Kitayimbwa, J.M., Mugisha, J.Y.T. & Saenz, R.A. J. Math. Biol. (2013) 67: 1111. doi:10.1007/s00285-012-0581-2


The quality of life for patients infected with human immunodeficiency virus (HIV-1) has been positively impacted by the use of antiretroviral therapy (ART). However, the benefits of ART are usually halted by the emergence of drug resistance. Drug-resistant strains arise from virus mutations, as HIV-1 reverse transcription is prone to errors, with mutations normally carrying fitness costs to the virus. When ART is interrupted, the wild-type drug-sensitive strain rapidly out-competes the resistant strain, as the former strain is fitter than the latter in the absence of ART. One mechanism for sustaining the sensitive strain during ART is given by the virus mutating from resistant to sensitive strains, which is referred to as backward mutation. This is important during periods of treatment interruptions as prior existence of the sensitive strain would lead to replacement of the resistant strain. In order to assess the role of backward mutations in the dynamics of HIV-1 within an infected host, we analyze a mathematical model of two interacting virus strains in either absence or presence of ART. We study the effect of backward mutations on the definition of the basic reproductive number, and the value and stability of equilibrium points. The analysis of the model shows that, thanks to both forward and backward mutations, sensitive and resistant strains co-exist. In addition, conditions for the dominance of a viral strain with or without ART are provided. For this model, backward mutations are shown to be necessary for the persistence of the sensitive strain during ART.


Within-host modelHIV-1Drug resistanceVirus mutations

Mathematics Subject Classification


Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • John M. Kitayimbwa
    • 1
  • Joseph Y. T. Mugisha
    • 1
  • Roberto A. Saenz
    • 2
    • 3
  1. 1.Department of MathematicsMakerere UniversityKampalaUganda
  2. 2.Institute of Integrative BiologyETH Zürich, ETH-Zentrum CHNZurichSwitzerland
  3. 3.CUICBAS, Facultad de CienciasUniversidad de ColimaColimaMexico