Acta Biotheoretica

, Volume 57, Issue 3, pp 361–381 | Cite as

Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment

Regular Article
First Online:
Received:
Accepted:

Abstract

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use.

Keywords

HIV/AIDS model Two strains Treatment with amelioration Center manifold theory Stability 
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Notes

Acknowledgements

C. P. Bhunu would like to acknowledge the financial support given to him by International Clinical Operational Health Services Research Training Award (ICOHRTA) through the Biomedical Research Training Institute (BRTI). The authors would like thank the anonymous referrees whose commends and suggestions really improved our work.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Modelling Biomedical Systems Research GroupNational University of Science and TechnologyBulawayoZimbabwe
  2. 2.Department of Mathematics and Applied MathematicsUniversity of VendaThohoyandouSouth Africa

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