Abstract
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 Rc approximately 13, which is less than the 2004 estimate of Rc approximately equal 4 by [11] and [13]. The results in this study suggest that the HAART program has yielded positive results for Botswana.
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