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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 427 - 450, Volume 6, Issue 3, July 2009      doi:10.3934/mbe.2009.6.427

 
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Esther Chigidi - University of Botswana, P B 0022, Gaborone, Botswana (email)
Edward M. Lungu - University of Botswana, P B 0022, Gaborone, Botswana (email)

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 $R_c\approx1.3$, 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, HAART susceptible, infectivity reduction factor, equilibrium, stability, progression reduction factor, relative impact, HIV prevalence.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 92B05; 34D23.

Received: February 2008;      Accepted: November 2008;      Available Online: June 2009.