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.