Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment |
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Authors: | C P Bhunu W Garira G Magombedze |
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Institution: | (1) Department of Applied Mathematics, Modelling Biomedical Systems Research Group, National University of Science and Technology, P. O. Box AC 939 Ascot, Bulawayo, Zimbabwe;(2) Department of Mathematics and Applied Mathematics, University of Venda, Thohoyandou, South Africa |
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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. |
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Keywords: | |
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