2006, 3(2): 297-312. doi: 10.3934/mbe.2006.3.297

The Effects of Vertical Transmission on the Spread of HIV/AIDS in the Presence of Treatment

1. 

Department of Basic Sciences, Botswana College of Agriculture, Private Bag 0027, Gaborone, Botswana

2. 

Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana

Received  September 2005 Revised  January 2006 Published  February 2006

In this study, we develop a model that incorporates treatment of both juveniles who were infected with HIV/AIDS through vertical transmission and HIV/AIDS-infected adults. We derive conditions under which the burden of HIV/AIDS can be reduced in the population both in the absence of and in the presence of vertical transmission. We have determined the critical threshold parameter ($R_v^*$), which represents the demographic replacement of infectives through vertical transmission, below which treated infected juveniles can reach adulthood without causing an epidemic. Five countries in sub-Saharan Africa are used to illustrate our results. We have concluded that $R_v^*$ is dependent on the current prevalence rate but that a significant proportion of infected juveniles receiving treatment can reach adulthood without causing an epidemic.
Citation: Moatlhodi Kgosimore, Edward M. Lungu. The Effects of Vertical Transmission on the Spread of HIV/AIDS in the Presence of Treatment. Mathematical Biosciences & Engineering, 2006, 3 (2) : 297-312. doi: 10.3934/mbe.2006.3.297
[1]

Cristiana J. Silva, Delfim F. M. Torres. A TB-HIV/AIDS coinfection model and optimal control treatment. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4639-4663. doi: 10.3934/dcds.2015.35.4639

[2]

Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song. Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. Mathematical Biosciences & Engineering, 2008, 5 (1) : 145-174. doi: 10.3934/mbe.2008.5.145

[3]

Praveen Kumar Gupta, Ajoy Dutta. Numerical solution with analysis of HIV/AIDS dynamics model with effect of fusion and cure rate. Numerical Algebra, Control & Optimization, 2019, 9 (4) : 393-399. doi: 10.3934/naco.2019038

[4]

Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311

[5]

Cristiana J. Silva, Delfim F. M. Torres. Modeling and optimal control of HIV/AIDS prevention through PrEP. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 119-141. doi: 10.3934/dcdss.2018008

[6]

Christopher M. Kribs-Zaleta, Melanie Lee, Christine Román, Shari Wiley, Carlos M. Hernández-Suárez. The Effect of the HIV/AIDS Epidemic on Africa's Truck Drivers. Mathematical Biosciences & Engineering, 2005, 2 (4) : 771-788. doi: 10.3934/mbe.2005.2.771

[7]

Brandy Rapatski, Petra Klepac, Stephen Dueck, Maoxing Liu, Leda Ivic Weiss. Mathematical epidemiology of HIV/AIDS in cuba during the period 1986-2000. Mathematical Biosciences & Engineering, 2006, 3 (3) : 545-556. doi: 10.3934/mbe.2006.3.545

[8]

Helen Moore, Weiqing Gu. A mathematical model for treatment-resistant mutations of HIV. Mathematical Biosciences & Engineering, 2005, 2 (2) : 363-380. doi: 10.3934/mbe.2005.2.363

[9]

Nara Bobko, Jorge P. Zubelli. A singularly perturbed HIV model with treatment and antigenic variation. Mathematical Biosciences & Engineering, 2015, 12 (1) : 1-21. doi: 10.3934/mbe.2015.12.1

[10]

Shohel Ahmed, Abdul Alim, Sumaiya Rahman. A controlled treatment strategy applied to HIV immunology model. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 299-314. doi: 10.3934/naco.2018019

[11]

Shujing Gao, Dehui Xie, Lansun Chen. Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 77-86. doi: 10.3934/dcdsb.2007.7.77

[12]

Chandrani Banerjee, Linda J. S. Allen, Jorge Salazar-Bravo. Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission. Mathematical Biosciences & Engineering, 2008, 5 (4) : 617-645. doi: 10.3934/mbe.2008.5.617

[13]

Arnaud Ducrot, Michel Langlais, Pierre Magal. Qualitative analysis and travelling wave solutions for the SI model with vertical transmission. Communications on Pure & Applied Analysis, 2012, 11 (1) : 97-113. doi: 10.3934/cpaa.2012.11.97

[14]

Hisashi Inaba. Mathematical analysis of an age-structured SIR epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 69-96. doi: 10.3934/dcdsb.2006.6.69

[15]

Stephen Tully, Monica-Gabriela Cojocaru, Chris T. Bauch. Multiplayer games and HIV transmission via casual encounters. Mathematical Biosciences & Engineering, 2017, 14 (2) : 359-376. doi: 10.3934/mbe.2017023

[16]

Arni S.R. Srinivasa Rao, Masayuki Kakehashi. Incubation-time distribution in back-calculation applied to HIV/AIDS data in India. Mathematical Biosciences & Engineering, 2005, 2 (2) : 263-277. doi: 10.3934/mbe.2005.2.263

[17]

Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595

[18]

Gigi Thomas, Edward M. Lungu. A two-sex model for the influence of heavy alcohol consumption on the spread of HIV/AIDS. Mathematical Biosciences & Engineering, 2010, 7 (4) : 871-904. doi: 10.3934/mbe.2010.7.871

[19]

Arni S. R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar, Philip K. Maini. HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis. Mathematical Biosciences & Engineering, 2009, 6 (4) : 779-813. doi: 10.3934/mbe.2009.6.779

[20]

Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli, Claudia Balotta. A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment. Mathematical Biosciences & Engineering, 2018, 15 (1) : 181-207. doi: 10.3934/mbe.2018008

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]