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Mathematical Biosciences and Engineering

2009, Volume 6, Issue 2: 363-376. doi: 10.3934/mbe.2009.6.363
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Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic

  • 1.
    Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3
  • Received: 01 August 2007 Accepted: 29 June 2018 Published: 01 March 2009

  • MSC : 92D30.

  • Since the discovery of HIV/AIDS there have been numerous mathematical models proposed to explain the epidemic of the disease and to evaluate possible control measures. In particular, several recent studies have looked at the potential impact of condom usage on the epidemic [1, 2, 3, 4]. We develop a simple model for HIV/AIDS, and investigate the effectiveness of condoms as a possible control strategy. We show that condoms can greatly reduce the number of outbreaks and the size of the epidemic. However, the necessary condom usage levels are much higher than the current estimates. We conclude that condoms alone will not be sufficient to halt the epidemic in most populations unless current estimates of the transmission probabilities are high. Our model has only five independent parameters, which allows for a complete analysis. We show that the assumptions of mass action and standard incidence provide similar results, which implies that the results of the simpler mass action model can be used as a good first approximation to the peak of the epidemic.

    Citation: Jeff Musgrave, James Watmough. Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic[J]. Mathematical Biosciences and Engineering, 2009, 6(2): 363-376. doi: 10.3934/mbe.2009.6.363

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  • Since the discovery of HIV/AIDS there have been numerous mathematical models proposed to explain the epidemic of the disease and to evaluate possible control measures. In particular, several recent studies have looked at the potential impact of condom usage on the epidemic [1, 2, 3, 4]. We develop a simple model for HIV/AIDS, and investigate the effectiveness of condoms as a possible control strategy. We show that condoms can greatly reduce the number of outbreaks and the size of the epidemic. However, the necessary condom usage levels are much higher than the current estimates. We conclude that condoms alone will not be sufficient to halt the epidemic in most populations unless current estimates of the transmission probabilities are high. Our model has only five independent parameters, which allows for a complete analysis. We show that the assumptions of mass action and standard incidence provide similar results, which implies that the results of the simpler mass action model can be used as a good first approximation to the peak of the epidemic.


  • This article has been cited by:

    1. S.A. Pedro, J.M. Tchuenche, HIV/AIDS dynamics: Impact of economic classes with transmission from poor clinical settings, 2010, 267, 00225193, 471, 10.1016/j.jtbi.2010.09.019
    2. C. P. Bhunu, S. Mushayabasa, H. Kojouharov, J. M. Tchuenche, Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa, 2011, 10, 1570-1166, 31, 10.1007/s10852-010-9134-0
    3. Sarada S. Panchanathan, Diana B. Petitti, Douglas B. Fridsma, The development and validation of a simulation tool for health policy decision making, 2010, 43, 15320464, 602, 10.1016/j.jbi.2010.03.013
    4. Cristiana J. Silva, Delfim F.M. Torres, A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde, 2017, 30, 1476945X, 70, 10.1016/j.ecocom.2016.12.001
    5. S. D. Hove-Musekwa, F. Nyabadza, H. Mambili-Mamboundou, Modelling Hospitalization, Home-Based Care, and Individual Withdrawal for People Living with HIV/AIDS in High Prevalence Settings, 2011, 73, 0092-8240, 2888, 10.1007/s11538-011-9651-7
    6. Emmanuelina L. Kateme, Jean M. Tchuenche, Senelani D. Hove-Musekwa, HIV/AIDS Dynamics with Three Control Strategies: The Role of Incidence Function, 2012, 2012, 2090-5572, 1, 10.5402/2012/864795
    7. F. Nyabadza, Z. Mukandavire, S.D. Hove-Musekwa, Modelling the HIV/AIDS epidemic trends in South Africa: Insights from a simple mathematical model, 2011, 12, 14681218, 2091, 10.1016/j.nonrwa.2010.12.024
    8. Xiaodong Wang, Chunxia Wang, Kai Wang, Extinction and persistence of a stochastic SICA epidemic model with standard incidence rate for HIV transmission, 2021, 2021, 1687-1847, 10.1186/s13662-021-03392-y
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