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Modeling the joint epidemics of TB and HIV in a South African township

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Abstract

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate.

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References

  1. Atun, R.A., Lebcir, R., Drobniewski, F., Coker, R.J.: Impact of an effective multidrug-resistant tuberculosis control programme in the setting of an immature HIV epidemic: system dynamics simulation model. Int. J. STD AIDS 16, 560–570 (2005)

    Article  Google Scholar 

  2. Atun, R.A., Lebcir, R.M., Drobniewski, F., McKee, M., Coker, R.J.: High coverage with HAART is required to substantially reduce the number of deaths from tuberculosis: system dynamics simulation. Int. J. STD AIDS 18, 267–273 (2007)

    Article  Google Scholar 

  3. Badri, M., Wilson, D., Wood, R.: Effect of highly active antiretroviral therapy on incidence of tuberculosis in South Africa: a cohort study. Lancet 359, 2059–2064 (2002)

    Article  Google Scholar 

  4. Bermejo, A., Veeken, H., Berra, A.: Tuberculosis incidence in developing countries with high prevalence of HIV infection. AIDS 6, 1203–1206 (1992)

    Article  Google Scholar 

  5. Blyuss, K.B., Kyrychko, Yu.N.: On a basic model of a two-disease epidemic. Appl. Math. Comput. 160, 177–187 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Borgdorff, M.W.: Annual risk of tuberculosis infection—time for an update?. Bull. WHO 80, 501–502 (2002)

    Google Scholar 

  7. Breban, R., Blower, S.: The reinfection threshold does not exist. J. Theor. Biol. 235, 151–152 (2005)

    Article  MathSciNet  Google Scholar 

  8. Brewer, T.F., Heymann, S.J., Colditz, G.A., Wilson, M.E., Auerbach, K., Kane, D., Fineberg, H.V.: Evaluation of tuberculosis control policies using computer simulation. J. Am. Med. Assoc. 276, 1898–1903 (1996)

    Article  Google Scholar 

  9. Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1, 361–404 (2004)

    MATH  MathSciNet  Google Scholar 

  10. Cohen, T., Lipsitch, M., Walensky, R.P., Murray, M.: Beneficial and perverse effects of isoniazid preventive therapy for latent tuberculosis infection in HIV-tuberculosis coinfected populations. Proc. Natl. Acad. Sci. USA 103, 7042–7047 (2006)

    Article  Google Scholar 

  11. Corbett, E.L., Charalambous, S., Fielding, K., Clayton, T., Hayes, R.J., De Cock, K.M., Churchyard, G.J.: Stable incidence rates of tuberculosis (TB) among human immunodeficiency virus (HIV)-negative South African gold miners during a decade of epidemic HIV-associated TB. J. Infect. Dis. 188, 1156–1163 (2003)

    Article  Google Scholar 

  12. Corbett, E.L., Charalambous, S., Moloi, V.M. et al.: Human immunodeficiency virus and the prevalence of undiagnosed tuberculosis in African gold miners. Am. J. Respir. Care Med. 170, 673–679 (2004)

    Article  Google Scholar 

  13. Corbett, E.L., Watt, C.J., Walker, N., Maher, D., Williams, B.G., Raviglione, M.C., Dye, C.: The growing burden of tuberculosis: global trends and interactions with the HIV epidemic. Arch. Intern. Med. 163, 1009–1021 (2003)

    Article  Google Scholar 

  14. Currie, C.S.M., Williams, B.G., Cheng, R.C.H., Dye, C.: Tuberculosis epidemics driven by HIV: is prevention better than cure?. AIDS 17, 2501–2508 (2003)

    Article  Google Scholar 

  15. Currie, C.S.M., Floyd, K., Williams, B.G., Dye, C.: Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence. BMC Public Health 5, 130 (2005). doi:10.1186/1471-2458-5-130

    Article  Google Scholar 

  16. Daley, C.L., Small, P.M., Schecter, G.F., Schoolnik, G.K., McAdam, R.A., Jacobs, W.R. Jr, Hopewell, P.C.: An outbreak of tuberculosis with accelerated progression among persons infected with the human immunodeficiency virus: An analysis using restriction-fragment-length polymorphisms. N. Engl. J. Med. 326(4), 231–235 (1992)

    Google Scholar 

  17. Debanne, A.M., Bielefeld, R.A., Cauthen, G.M., Daniel, T.M., Rowland, D.Y.: Multivariate markovian modeling of tuberculosis: forecasts for the United States. Emerg. Infect. Dis. 6, 148–157 (2000)

    Google Scholar 

  18. Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectious Diseases—Model Building, Analysis and Interpretation. Wiley, Chichester (2000)

    Google Scholar 

  19. Di Perri, G., Cruciani, M., Danzi, M.C., Luzzati, R., De Checchi, G., Malena, M. et al.: Nosocomial epidemic of active tuberculosis among HIV-infected patients. Lancet 2, 1502–1504 (1989)

    Google Scholar 

  20. Dowdy, D.W., Chaisson, R.E., Moulton, L.H., Dorman, S.E.: The potential impact of enhanced diagnostic techniques for tuberculosis driven by HIV: a mathematical model. AIDS 20, 751–762 (2006)

    Google Scholar 

  21. Dye, C., Garnett, G.P., Sleeman, K., Williams, B.G.: Prospects for worldwide tuberculosis control under the WHO DOTS strategy. Lancet 352, 1886–1891 (1998)

    Article  Google Scholar 

  22. Egwaga, S.M., Cobelens, F.G., Muwinge, H., Verhage, C., Kalisvaart, N., Borgdorff, M.W.: The impact of the HIV epidemic on tuberculosis transmission in Tanzania. AIDS 20, 915–921 (2006)

    Article  Google Scholar 

  23. Elliott, A.M., Halwiindi, B., Hayes, R.J., Luo, N., Mwinga, A.G., Tembo, G. et al.: The impact of human immunodeficiency virus on mortality of patients treated for tuberculosis in a cohort study in Zambia. Trans. R. Soc. Trop. Med. Hyg. 89, 78–82 (1995)

    Article  Google Scholar 

  24. Feng, Z., Castillo-Chavez, C., Capurro, A.F.: A model for tuberculosis with exogenous reinfection. Theor. Popul. Biol. 57, 235–247 (2000)

    Article  MATH  Google Scholar 

  25. Feng, Z., Huang, W., Castillo-Chavez, C.: On the role of variable latent periods in mathematical models for tuberculosis. J. Dyn. Differ. Equ. 13, 425–452 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  26. Gomes, M.G.M., Franco, A.O., Gomes, M.C., Medley, G.F.: The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy. Proc. R. Soc. Lond. B 271, 617–623 (2004)

    Article  Google Scholar 

  27. Gomes, M.G.M., White, L.J., Medley, G.F.: The reinfection threshold. J. Theor. Biol. 236, 111–113 (2005)

    Article  MathSciNet  Google Scholar 

  28. Gomes, M.G.M., Rodrigues, P., Hilker, F.M., Mantilla-Beniers, N.B., Muehlen, M., Paulo, A.C., Medley, G.F.: Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventions. J. Theor. Biol. 248, 608–617 (2007)

    Article  Google Scholar 

  29. Guwatudde, D., Debanne, S.M., Diaz, M., King, C., Whalen, C.C.: A re-examination of the potential impact of preventive therapy on the public health problem of tuberculosis in contemporary sub-Saharan Africa. Prev. Med. 39, 1036–1046 (2004)

    Article  Google Scholar 

  30. Hethcote, H.W., van den Driessche, P.: Some epidemiological models with nonlinear incidence. J. Math. Biol. 29, 271–287 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  31. Heymann, S.J.: Modelling the efficacy of prophylactic and curative therapies for preventing the spread of tuberculosis in Africa. Trans. R. Soc. Trop. Med. Hyg. 87, 406–411 (1993)

    Article  Google Scholar 

  32. Hughes, G.R., Currie, C.S.M., Corbett, E.L.: Modeling tuberculosis in areas of high HIV prevalence. In: Perrone, L.F., Wieland, F.P., Liu, J., Lawson, B.G., Nicol, D.M., Fujimoto, R.M. (eds.) Proceedings of the 2006 Winter Simulation Conference, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 459–465 (2006)

  33. Kline, S.E., Hedemark, L.L., Davies, S.F.: Outbreak of tuberculosis among regular patrons of a neighborhood bar. N. Engl. J. Med. 333, 222–227 (1995)

    Article  Google Scholar 

  34. Lawn, S.D., Badri, M., Wood, R.: Tuberculosis among HIV-infected patients receiving HAART: long term incidence and risk factors in a South African cohort. AIDS 19, 2109–2116 (2005)

    Google Scholar 

  35. Lawn, S.D., Bekker, L.-G., Middelkoop, K., Myer, L., Wood, R.: Impact of HIV infection on the epidemiology of tuberculosis in a peri-urban community in South Africa: The need for age-specific interventions. Clin. Infect. Dis. 42, 1040–1047 (2006)

    Article  Google Scholar 

  36. Lawn, S.D., Bekker, L.-G., Wood, R.: How effectively does HAART restore immune responses to Mycobacterium tuberculosis? Implications for tuberculosis control. AIDS 19, 1113–1124 (2005)

    Google Scholar 

  37. Lawn, S.D., Myer, L., Bekker, L.-G., Wood, R.: Burden of tuberculosis in an antiretroviral treatment programme in sub-Saharan Africa: impact on treatment outcomes and implications for tuberculosis control. AIDS 20, 1605–1612 (2006)

    Google Scholar 

  38. Lawn, S.D., Wood, R.: The epidemic of HIV-associated tuberculosis in sub-Saharan Africa: does this also impact non-HIV-infected individuals?. AIDS 20, 1787–1788 (2006)

    Article  Google Scholar 

  39. Lawn, S.D., Wood, R.: Tuberculosis control in South Africa—will HAART help?. S. Afr. Med. J. 96, 502–504 (2006)

    Google Scholar 

  40. Lawn, S.D., Wood, R.: When should antiretroviral treatment be started in patients with HIV-associated tuberculosis in South Africa?. S. Afr. Med. J. 97, 412–414 (2007)

    Google Scholar 

  41. Lawn, S.D., Wilkinson, R.J., Lipman, M.C.I., Wood, R.: Immune reconstitution and ‘unmasking’ of tuberculosis during antiretroviral therapy. Am. J. Respir. Crit. Care Med. (2008). doi:10.1164/rccm.200709-1311PP

    MATH  Google Scholar 

  42. Lipsitch, M., Murray, M.B.: Multiple equilibria: Tuberculosis transmission require unrealistic assumptions. Theor. Popul. Biol. 63, 169–170 (2003)

    Article  Google Scholar 

  43. Lungu, E.: Anti-tuberculosis resistance in patients co-infected with HIV and TB. Abstract presented at CMS-MITACS Joint Conference, Winnipeg, MB, Canada, May 31–June 3, 2007. http://www.math.ca/Reunions/ete07/abs/pdf/id-el.pdf

  44. Massad, E., Burattini, M.N., Coutinho, F.A.B., Yang, H.M., Raimundo, S.M.: Modeling the interaction between AIDS and tuberculosis. Math. Comput. Modell. 17, 7–21 (1993)

    Article  MATH  Google Scholar 

  45. Miranda, A., Morgan, M., Jamal, L. et al.: Impact of antiretroviral therapy on the incidence of tuberculosis: the Brazilian experience, 1995–2001. PLoS ONE 2, e826 (2007)

    Article  Google Scholar 

  46. Moghadas, S.M., Gumel, A.B.: Analysis of a model for transmission dynamics of TB. Can. Appl. Math. Q. 10, 411–428 (2002)

    MATH  MathSciNet  Google Scholar 

  47. Moghadas, S.M., Gumel, A.B.: An epidemic model for the transmission dynamics of HIV and another pathogen. ANZIAM J. 45, 1–13 (2003)

    Article  MathSciNet  Google Scholar 

  48. Moghadas, S.M., Alexander, M.E.: Exogenous reinfection and resurgence of tuberculosis: a theoretical framework. J. Biol. Syst. 12, 231–247 (2004)

    Article  MATH  Google Scholar 

  49. Murphy, B.M., Singer, B.H., Kirschner, D.: On the treatment of TB in heterogeneous populations. J. Theor. Biol. 223, 391–404 (2003)

    Article  Google Scholar 

  50. Murray, C.J.L., Styblo, K., Rouillon, A.: Tuberculosis in developing countries: burden, intervention, and cost. Bull. Int. Union Tuberc. Lung Dis. 65, 6–24 (1990)

    Google Scholar 

  51. Murray, C.J.L., Salomon, J.A.: Modeling the impact of global tuberculosis control strategies. Proc. Natl. Acad. Sci. USA 95, 13881–13886 (1998)

    Article  Google Scholar 

  52. Naresh, R., Tripathi, A.: Modelling and analysis of HIV–TB coinfection in a variable size population. Math. Model. Anal. 10, 275–286 (2005)

    MATH  MathSciNet  Google Scholar 

  53. Nunn, A.J., Mulder, D.W., Kamali, A., Ruberantwari, A., Kengeya-Kayondo, J.F., Whitworth, J.: Mortality associated with HIV-1 infection over five years in a rural Ugandan population: cohort study. Br. Med. J. 315(7111), 767–771 (1997)

    Google Scholar 

  54. Porco, T.C., Blower, S.M.: Quantifying the intrinsic transmission dynamics of tuberculosis. Theor. Popul. Biol. 54, 117–132 (1998)

    Article  MATH  Google Scholar 

  55. Porco, T.C., Small, P.M., Blower, S.M.: Amplification dynamics: predicting the effect of HIV on tuberculosis outbreaks. JAIDS 28, 437–444 (2001)

    Google Scholar 

  56. Raimundo, S.M., Yang, H.M., Bassanezi, R.C., Ferreira, M.A.C.: The attracting basins and the assessment of the transmission coefficients for HIV and M. Tuberculosis infections among women inmates. J. Biol. Syst. 10, 61–83 (2002)

    Article  MATH  Google Scholar 

  57. Raimundo, S.M., Engel, A.B., Yang, H.M., Bassanezi, R.C.: An approach to estimating the transmission coefficients for AIDS and for tuberculosis using mathematical models. Syst. Anal. Model. Simul. 43, 423–442 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  58. Schinazi, R.B.: Can HIV invade a population which is already sick?. Bull. Braz. Math. Soc. 34, 479–488 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  59. Schulzer, M., Fitzgerald, J.M., Enarson, D.A., Grzybowski, S.: An estimate of the future size of the tuberculosis problem in sub-Saharan Africa resulting from HIV infection. Tuber. Lung. Dis. 73, 52–58 (1992)

    Article  Google Scholar 

  60. Schulzer, M., Radhamani, M.P., Grzybowski, S., Mak, E., Fitzgerald, J.M.: A mathematical model for the prediction of the impact of HIV infection on tuberculosis. Int. J. Epidemiol. 23, 400–407 (1994)

    Article  Google Scholar 

  61. Selwyn, P.A., Hartel, D., Lewis, V.A., Schoenbaum, E.E., Vermund, S.H., Klein, R.S., Walker, A.T., Friedland, G.H.: A prospective study of the risk of tuberculosis among intravenous drug users with human immunodeficiency virus infection. N. Engl. J. Med. 320, 545–550 (1989)

    Google Scholar 

  62. Selwyn, P.A., Sckell, B.M., Alcabes, P., Friedland, G.H., Klein, R.S., Schoenbaum, E.E.: High risk of active tuberculosis in HIV-infected drug users with cutaneous anergy. JAMA 268, 504–509 (1992)

    Article  Google Scholar 

  63. Sharomi, O., Podder, C.N., Gumel, A.B.: Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. Math. Biosci. Eng. 5, 145–174 (2008)

    MATH  MathSciNet  Google Scholar 

  64. Singer, B.H., Kirschner, D.E.: Influence of backward bifurcation on interpretation of R 0 in a model of epidemic tuberculosis with reinfection. Math. Biosci. Eng. 1, 81–93 (2004)

    MATH  MathSciNet  Google Scholar 

  65. Sutherland, I., Svandova, E., Radhakrishna, S.: The development of clinical tuberculosis following infection with tubercle bacilli. Tubercle 63, 255–268 (1982)

    Article  Google Scholar 

  66. UNAIDS: 2006 Report on the global AIDS epidemic. UNAIDS, Geneva (2006)

  67. Veening, G.J.: Long term isoniazid prophylaxis: controlled trial on INH prophylaxis after recent tuberculin conversion in young adults. Bull. Int. Union Tuberc. 41, 169–171 (1968)

    Google Scholar 

  68. Vynnycky, E., Fine, P.E.M.: The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol. Infect. 119, 183–201 (1997)

    Article  Google Scholar 

  69. Wang, W.: Epidemic models with nonlinear infection forces. Math. Biosci. Eng. 3, 267–279 (2006)

    MATH  MathSciNet  Google Scholar 

  70. West, R.W., Thompson, J.R.: Modeling the impact of HIV on the spread of tuberculosis in the United States. Math. Biosci. 143, 35–60 (1997)

    Article  MATH  Google Scholar 

  71. Williams, B.G., Gouws, E.: The epidemiology of human immunodeficiency virus in South Africa. Philos. Trans. R. Soc. Lond. B Biol. Sci. 356, 1077–1086 (2001)

    Google Scholar 

  72. Williams, B.G., Granich, R., Chauhan, L.S., Dharmshaktu, N.S., Dye, C.: The impact of HIV/AIDS on the control of tuberculosis in India. Proc. Natl. Acad. Sci. USA 102, 9619–9624 (2005)

    Article  Google Scholar 

  73. Williams, B.G., Lloyd-Smith, J.O., Gouws, E., Hankins, C., Getz, W.M., Hargrove, J., de Zoysa, I., Dye, C., Auvert, B.: The potential impact of male circumcision on HIV in sub-Saharan Africa. PLoS Med. 3(7), e262 (2006)

    Article  Google Scholar 

  74. Williams, B.G., Maher, D.: Tuberculosis fueled by HIV: Putting out the flames. Am. J. Resp. Crit. Care 175, 6–7 (2007)

    Article  Google Scholar 

  75. Wood, R., Middelkoop, K., Myer, L., Grant, A.D., Whitelaw, A., Lawn, S.D., Kaplan, G., Huebner, R., McIntyre, J., Bekker, L.-G.: Undiagnosed tuberculosis in a community with high HIV-prevalence: implications for TB control. Am. J. Respir. Crit. Care 175, 87–93 (2007)

    Article  Google Scholar 

  76. World Health Organization: Global tuberculosis control: surveillance, planning, financing. WHO, Geneva (2007)

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Authors and Affiliations

  1. Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, 93143, Bondy, France

    Nicolas Bacaër

  2. SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, South Africa

    Rachid Ouifki & Carel Pretorius

  3. Desmond Tutu HIV Centre, Institute of Infectious Disease and Molecular Medicine, University of Cape Town, Cape Town, South Africa

    Robin Wood

  4. Stop TB Department, World Health Organization, Geneva, Switzerland

    Brian Williams

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  1. Nicolas Bacaër
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  2. Rachid Ouifki
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  4. Robin Wood
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  5. Brian Williams
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Correspondence to Nicolas Bacaër.

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Bacaër, N., Ouifki, R., Pretorius, C. et al. Modeling the joint epidemics of TB and HIV in a South African township. J. Math. Biol. 57, 557–593 (2008). https://doi.org/10.1007/s00285-008-0177-z

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