Modeling Detection of HIV in Cuba

  • Héctor de Arazoza
  • Rachid Lounes
  • Andres Sánchez
  • Jorge Barrios
  • Ying-Hen Hsieh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6692)


A nonlinear compartmental model is developed for the HIV detection system in Cuba with different types of detections, some random and others non-random. We analyze the dynamics of this system, compute the reproduction numbers, and use the data from the Cuban HIV/AIDS epidemic between 1986-2008 to fit the model. We obtain estimates for the detection-related parameters during two separate time periods to reflect the timeline of the implementation of various types of searches. The reproduction numbers for each time period are also computed from the sets of values of the parameters. We found that random screening is most important as a mean of surveillance. Moreover, local asymptotic stability for the Disease Free Equilibrium can be achieved if (i) random screening is sufficiently effective and (ii) infection by detected HIV-positive individuals is minimal. Our results highlight the importance of education for the known infectious for the purpose of preventing further infection. Fitting the 1986-2008 HIV data to obtain the model parameter estimates indicates that the HIV epidemic in Cuba is currently approaching an endemic equilibrium. A Genetic Algorithm is used.


Reproduction Number Family Doctor Modeling Detection Endemic Equilibrium Disease Free Equilibrium 
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  1. 1.
    Anderson, R.M., Gupta, S., May, R.M.: Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 350, 356–359 (1991)CrossRefGoogle Scholar
  2. 2.
    de Arazoza, H., Lounes, R.: A non linear model for a sexually transmitted disease with contact tracing. IMA. J. Math. Appl. Med. Biol. 19, 221–234 (2002)CrossRefzbMATHGoogle Scholar
  3. 3.
    de Arazoza, H., Joanes, J., Lounes, R., Legeai, C., Clémençon, S., Pérez, J., Auvert, B.: The HIV/AIDS epidemic in Cuba: Description and tentative explanation of its low HIV prevalence. BMC Infectious Diseases 7:130, 1–6 (2007)CrossRefGoogle Scholar
  4. 4.
    Granich, R.M., Gilks, C.F., Dye, C., De Cock, K.M., Williams, B.G.: Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 373, 48–57 (2009)CrossRefGoogle Scholar
  5. 5.
    Hsieh, Y.H., Cooke, K.: Behavior Change and Treatment of Core Group and Bridge Population: Its Effect on the Spread of HIV/AIDS. IMA J. of Math. Appl. Biol. Med. 17(3), 213–241 (2000)CrossRefGoogle Scholar
  6. 6.
    Hsieh, Y.H., de Arazoza, H., Lounes, R., Joanes, J.: A Class of Models for HIV Contact Tracing in Cuba: Implications for Intervention and Treatment. In: Tan, W.Y. (ed.) Deterministic and Stochastic Models for AIDS Epidemics and HIV Infection with Interventions. World Scientific, Singapore (2005)Google Scholar
  7. 7.
    Hsieh, Y.H., de Arazoza, H.: Correspondence to ”Universal voluntary HIV testing and immediate antiretroviral therapy”. Lancet 373, 1079–1080 (2009)CrossRefGoogle Scholar
  8. 8.
    Hsieh, Y.H., Wang, Y.S., de Arazoza, H., Lounes, R.: HIV Model with Secondary Contact Tracing: Impact of the Partner Notification Program in Cuba. BMC Infectious Diseases 10:194, 1–9 (2010)Google Scholar
  9. 9.
    Hsu, S.B., Hsieh, Y.H.: Modeling intervention measures and public response during SARS outbreak. SIAM J. Appl Math. 66(2), 627–647 (2006)CrossRefzbMATHGoogle Scholar
  10. 10.
    Inciardi, J.A., Syvertsen, J.L., Surratt, H.L.: HIV/AIDS in the Caribbean Basin. AIDS Care 17(suppl. 1), S9–S25 (2005)Google Scholar
  11. 11.
    WHO. World Health Organisation: Cuba, (accessed June 20, 2006)
  12. 12.
    MINSAP. CUBA:PLAN ESTRATEGICO NACIONAL ITS/VIH/SIDA 2007-2011 (2006),,_plan_estrategico__2007-2011.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Héctor de Arazoza
    • 1
    • 2
    • 4
  • Rachid Lounes
    • 2
  • Andres Sánchez
    • 1
  • Jorge Barrios
    • 1
  • Ying-Hen Hsieh
    • 3
  1. 1.Facultad de Matemática y ComputaciónUniversidad de la HabanaCuba
  2. 2.LaboratoireMAP5, UMR-CNRS 8145University Paris DescartesParis CEDEX 06France
  3. 3.Department of Public Health and Center for Infectious Disease Education and ResearchChina Medical University TaichungTaichungTaiwan
  4. 4.Laboratoire Paul PainlevéU. Lille 1Villeneuve d’Ascq CedexFrance

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