American Institute of Mathematical Sciences

Advanced
2009, 6(3): 427-450. doi: 10.3934/mbe.2009.6.427

HIV model incorporating differential progression for treatment-naive and treatment-experienced infectives

Esther Chigidi 1, and  Edward M. Lungu 1,

1. 

University of Botswana, P B 0022, Gaborone, Botswana, Botswana

Received  February 2008 Revised  November 2008 Published  June 2009

We formulate an HIV/AIDS deterministic model which incorporates differential infectivity and disease progression for treatment-naive and treatment-experienced HIV/AIDS infectives. To illustrate our model, we have applied it to estimate adult HIV prevalence, the HIV population, the number of new infectives and the number of AIDS deaths for Botswana for the period 1984 to 2012. It is found that the prevalence peaked in the year 2000 and the HIV population is now decreasing. We have also found that under the current conditions, the reproduction number is $R_c\approx1.3$, which is less than the 2004 estimate of $R_c$ ≃ 4 by [11] and [13]. The results in this study suggest that the HAART program has yielded positive results for Botswana.
Keywords: HAART, stability, equilibrium, HAART susceptible, HIV prevalence., relative impact, progression reduction factor, infectivity reduction factor.
Mathematics Subject Classification: Primary: 92D30; Secondary: 92B05; 34D2.
Citation: Esther Chigidi, Edward M. Lungu. HIV model incorporating differential progression for treatment-naive and treatment-experienced infectives. Mathematical Biosciences & Engineering, 2009, 6 (3) : 427-450. doi: 10.3934/mbe.2009.6.427
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