# American Institute of Mathematical Sciences

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

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

 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.
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
 [1] Jisang Yoo. Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states. Journal of Modern Dynamics, 2018, 13: 271-284. doi: 10.3934/jmd.2018021 [2] Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229 [3] Gesham Magombedze, Winston Garira, Eddie Mwenje. Modelling the immunopathogenesis of HIV-1 infection and the effect of multidrug therapy: The role of fusion inhibitors in HAART. Mathematical Biosciences & Engineering, 2008, 5 (3) : 485-504. doi: 10.3934/mbe.2008.5.485 [4] Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105 [5] Noriaki Kawaguchi. Maximal chain continuous factor. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5915-5942. doi: 10.3934/dcds.2021101 [6] Andrejs Reinfelds, Klara Janglajew. Reduction principle in the theory of stability of difference equations. Conference Publications, 2007, 2007 (Special) : 864-874. doi: 10.3934/proc.2007.2007.864 [7] Mostafa Adimy, Fabien Crauste. Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 19-38. doi: 10.3934/dcdsb.2007.8.19 [8] Qingguo Bai, Fanwen Meng. Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1943-1965. doi: 10.3934/jimo.2019037 [9] Alain Chenciner. The angular momentum of a relative equilibrium. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1033-1047. doi: 10.3934/dcds.2013.33.1033 [10] Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135 [11] Ryusuke Kon. Dynamics of competitive systems with a single common limiting factor. Mathematical Biosciences & Engineering, 2015, 12 (1) : 71-81. doi: 10.3934/mbe.2015.12.71 [12] Ke Ruan, Masao Fukushima. Robust portfolio selection with a combined WCVaR and factor model. Journal of Industrial & Management Optimization, 2012, 8 (2) : 343-362. doi: 10.3934/jimo.2012.8.343 [13] Yanming Ge. Analysis of airline seat control with region factor. Journal of Industrial & Management Optimization, 2012, 8 (2) : 363-378. doi: 10.3934/jimo.2012.8.363 [14] Wu Chanti, Qiu Youzhen. A nonlinear empirical analysis on influence factor of circulation efficiency. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 929-940. doi: 10.3934/dcdss.2019062 [15] Brandon Seward. Every action of a nonamenable group is the factor of a small action. Journal of Modern Dynamics, 2014, 8 (2) : 251-270. doi: 10.3934/jmd.2014.8.251 [16] Shaoyong Lai, Yulan Zhou. A stochastic optimal growth model with a depreciation factor. Journal of Industrial & Management Optimization, 2010, 6 (2) : 283-297. doi: 10.3934/jimo.2010.6.283 [17] Mostafa Mbekhta. Representation and approximation of the polar factor of an operator on a Hilbert space. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 3043-3054. doi: 10.3934/dcdss.2020463 [18] Hiroaki Yoshimura, Jerrold E. Marsden. Dirac cotangent bundle reduction. Journal of Geometric Mechanics, 2009, 1 (1) : 87-158. doi: 10.3934/jgm.2009.1.87 [19] Katarzyna Grabowska, Paweƚ Urbański. Geometry of Routh reduction. Journal of Geometric Mechanics, 2019, 11 (1) : 23-44. doi: 10.3934/jgm.2019002 [20] Inês Cruz, M. Esmeralda Sousa-Dias. Reduction of cluster iteration maps. Journal of Geometric Mechanics, 2014, 6 (3) : 297-318. doi: 10.3934/jgm.2014.6.297

2018 Impact Factor: 1.313