Health Care Management Science

, Volume 17, Issue 2, pp 162–181 | Cite as

HIV epidemic control—a model for optimal allocation of prevention and treatment resources

  • Sabina S. AlistarEmail author
  • Elisa F. Long
  • Margaret L. Brandeau
  • Eduard J. Beck


With 33 million people living with human immunodeficiency virus (HIV) worldwide and 2.7 million new infections occurring annually, additional HIV prevention and treatment efforts are urgently needed. However, available resources for HIV control are limited and must be used efficiently to minimize the future spread of the epidemic. We develop a model to determine the appropriate resource allocation between expanded HIV prevention and treatment services. We create an epidemic model that incorporates multiple key populations with different transmission modes, as well as production functions that relate investment in prevention and treatment programs to changes in transmission and treatment rates. The goal is to allocate resources to minimize R 0, the reproductive rate of infection. We first develop a single-population model and determine the optimal resource allocation between HIV prevention and treatment. We extend the analysis to multiple independent populations, with resource allocation among interventions and populations. We then include the effects of HIV transmission between key populations. We apply our model to examine HIV epidemic control in two different settings, Uganda and Russia. As part of these applications, we develop a novel approach for estimating empirical HIV program production functions. Our study provides insights into the important question of resource allocation for a country’s optimal response to its HIV epidemic and provides a practical approach for decision makers. Better decisions about allocating limited HIV resources can improve response to the epidemic and increase access to HIV prevention and treatment services for millions of people worldwide.


HIV Resource allocation Basic reproduction number Epidemic control 



This work was supported by Grant Number R01-DA15612 from the National Institute on Drug Abuse. Sabina Alistar was supported by a Stanford Graduate Fellowship.


  1. 1.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) and World Health Organization (WHO) (2010) UNAIDS report on the global AIDS epidemic 2010.
  2. 2.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2009) What countries need: Investments needed for 2010 targets.
  3. 3.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2011) UNAIDS World AIDS Day report. How to get to zero: Faster. Smarter. Better.
  4. 4.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2010) Outlook report 2010.
  5. 5.
    Mathers BM, Degenhardt L, Ali H, Wiessing L, Hickman M, Mattick RP, Myers B, Ambekar A, Strathdee SA (2009) Reference Group to the UN on HIV and Injecting Drug Use (2010) HIV prevention, treatment, and care services for people who inject drugs: a systematic review of global, regional, and national coverage. Lancet 375(9719):1014–1028CrossRefGoogle Scholar
  6. 6.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2005) Resource needs for an expanded response to AIDS in low- and middle-income countries.
  7. 7.
    Bertozzi SM, Laga M, Bautista-Arredondo S, Coutinho A (2008) Making HIV prevention programmes work. Lancet 372(9641):831–844CrossRefGoogle Scholar
  8. 8.
    Hogan DR, Baltussen R, Hayashi C, Lauer JA, Salomon JA (2005) Cost effectiveness analysis of strategies to combat HIV/AIDS in developing countries. BMJ 331(7530):1431–1437CrossRefGoogle Scholar
  9. 9.
    Horton R, Das P (2008) Putting prevention at the forefront of HIV/AIDS. Lancet 372(9637):421–422CrossRefGoogle Scholar
  10. 10.
    Piot P, Bartos M, Larson H, Zewdie D, Mane P (2008) Coming to terms with complexity: a call to action for HIV prevention. Lancet 372(9641):845–859CrossRefGoogle Scholar
  11. 11.
    Dandona L, Sisodia P, Kumar SP, Ramesh Y, Kumar AA, Rao MC, Marseille E, Someshwar M, Marshall N, Kahn J (2005) HIV prevention programmes for female sex workers in Andhra Pradesh, India: outputs, cost and efficiency. BMC Publ Health 5(1):98CrossRefGoogle Scholar
  12. 12.
    Dandona L, Kumar SP, Ramesh Y, Rao MC, Kumar AA, Marseille E, Kahn JG, Dandona R (2008) Changing cost of HIV interventions in the context of scaling-up in India. AIDS 22(Suppl 1):S43–S49CrossRefGoogle Scholar
  13. 13.
    Guinness L, Kumaranayake L, Hanson K (2007) A cost function for HIV prevention services: is there a ‘u’—shape? Cost Eff Resour Alloc 5(1):13CrossRefGoogle Scholar
  14. 14.
    Kaplan EH (1995) Economic analysis of needle exchange. AIDS 9(10):1113–1120CrossRefGoogle Scholar
  15. 15.
    Kaplan EH (1998) Economic evaluation and HIV prevention community planning: a policy analyst’s perspective. In: Holtgrave DR (ed) Handbook of economic evaluation of HIV prevention programs. Plenum PressGoogle Scholar
  16. 16.
    Brandeau ML, Zaric GS, Richter A (2003) Resource allocation for control of infectious diseases in multiple independent populations: beyond cost-effectiveness analysis. J Health Econ 22(4):575–598CrossRefGoogle Scholar
  17. 17.
    Zaric GS, Brandeau ML (2001) Resource allocation for epidemic control over short time horizons. Math Biosci 171(1):33–58CrossRefGoogle Scholar
  18. 18.
    Zaric GS, Brandeau ML (2001) Optimal investment in a portfolio of HIV prevention programs. Med Decis Making 21(5):391–408CrossRefGoogle Scholar
  19. 19.
    Zaric GS, Brandeau ML (2002) Dynamic resource allocation for epidemic control in multiple populations. IMA J Math Appl Med Biol 19(4):235–255CrossRefGoogle Scholar
  20. 20.
    Alistar SS, Owens DK, Brandeau ML (2011) Effectiveness and cost effectiveness of expanding harm reduction and antiretroviral therapy in a mixed HIV epidemic: a modeling analysis for Ukraine. PLoS Med 8(3):e1000423CrossRefGoogle Scholar
  21. 21.
    Lasry A, Sansom SL, Hicks KA, Uzunangelov V (2012) Allocating HIV prevention funds in the United States: recommendations from an optimization model. PLoS One 7(6):e37545CrossRefGoogle Scholar
  22. 22.
    Long EF, Brandeau ML, Owens DK (2010) The cost-effectiveness and population outcomes of expanded HIV screening and antiretroviral treatment in the United States. Ann Intern Med 153(12):778–789CrossRefGoogle Scholar
  23. 23.
    Long EF, Stavert RR (2013) Portfolios of biomedical HIV interventions in South Africa: a cost-effectiveness analysis. J Gen Intern Med In pressGoogle Scholar
  24. 24.
    Robinson NJ, Mulder DW, Auvert B, Hayes RJ (1995) Modelling the impact of alternative HIV intervention strategies in rural Uganda. AIDS 9(11):1263–1270CrossRefGoogle Scholar
  25. 25.
    Alistar SS, Brandeau ML (2012) Decision making for HIV prevention and treatment scale up. Med Decis Making 32(1):105–117CrossRefGoogle Scholar
  26. 26.
    Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University PressGoogle Scholar
  27. 27.
    Diekmann O, Heesterbeek JA, Metz JA (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):365–382CrossRefGoogle Scholar
  28. 28.
    van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1–2):29–48CrossRefGoogle Scholar
  29. 29.
    Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42(4):599–653CrossRefGoogle Scholar
  30. 30.
    Longini IM, Nizam A, Xu S, Ungchusak K, Hanshaoworakul W, Cummings DA, Halloran ME (2005) Containing pandemic influenza at the source. Science 309(5737):1083–1087CrossRefGoogle Scholar
  31. 31.
    Ferguson NM, Cummings DA, Cauchemez S, Fraser C, Riley S, Meeyai A, Iamsirithaworn S, Burke DS (2005) Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 437(7056):209–214CrossRefGoogle Scholar
  32. 32.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2010) Getting to zero: 2011–2015 strategy.
  33. 33.
    President’s Emergency Fund for AIDS Relief (PEPFAR) (2012) PEPFAR blueprint: creating an AIDS-free generation.
  34. 34.
    Brandeau ML, Zaric GS, De Angelis V (2005) Improved allocation of HIV prevention resources: using information about prevention program production functions. Health Care Manag Sci 8(1):19–28CrossRefGoogle Scholar
  35. 35.
    Marseille E, Dandona L, Marshall N, Gaist P, Bautista-Arredondo S, Rollins B, Bertozzi S, Coovadia J, Saba J, Lioznov D, Du Plessis J-A, Krupitsky E, Stanley N, Over M, Peryshkina A, Kumar SP, Muyingo S, Pitter C, Lundberg M, Kahn J (2007) HIV prevention costs and program scale: data from the PANCEA project in five low and middle-income countries. BMC Health Serv Res 7(1):108CrossRefGoogle Scholar
  36. 36.
    Richter A, Brandeau ML, Owens DK (1999) An analysis of optimal resource allocation for prevention of infection with human immunodeficiency virus (HIV) in injection drug users and non-users. Med Decis Making 19(2):167–179CrossRefGoogle Scholar
  37. 37.
    Brandeau ML, Zaric GS (2009) Optimal investment in HIV prevention programs: more is not always better. Health Care Manag Sci 12(1):27–37CrossRefGoogle Scholar
  38. 38.
    Granich RM, Gilks CF, Dye C, De Cock KM, Williams BG (2009) Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 373(9657):48–57CrossRefGoogle Scholar
  39. 39.
    Lima VD, Johnston K, Hogg RS, Levy AR, Harrigan PR, Anema A, Montaner JS (2008) Expanded access to highly active antiretroviral therapy: a potentially powerful strategy to curb the growth of the HIV epidemic. J Infect Dis 198(1):59–67CrossRefGoogle Scholar
  40. 40.
    Long EF, Brandeau ML, Galvin CM, Vinichenko T, Tole SP, Schwartz A, Sanders GD, Owens DK (2006) Effectiveness and cost-effectiveness of strategies to expand antiretroviral therapy in St. Petersburg, Russia. AIDS 20(17):2207–2215CrossRefGoogle Scholar
  41. 41.
    Vijayaraghavan A, Efrusy MB, Mazonson PD, Ebrahim O, Sanne IM, Santas CC (2007) Cost-effectiveness of alternative strategies for initiating and monitoring highly active antiretroviral therapy in the developing world. J Acquir Immune Defic Syndr 46(1):91–100Google Scholar
  42. 42.
    Zaric GS, Barnett PG, Brandeau ML (2000) HIV transmission and the cost-effectiveness of methadone maintenance. Am J Public Health 90(7):1100–1111CrossRefGoogle Scholar
  43. 43.
    Zaric GS, Brandeau ML, Barnett PG (2000) Methadone maintenance and HIV prevention: a cost-effectiveness analysis. Manag Sci 46(8):1013–1031CrossRefGoogle Scholar
  44. 44.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2008) Epidemiological fact sheet on HIV and AIDS: Uganda 2008 update.
  45. 45.
    United States Agency for International Development (USAID) (2002) What happened in Uganda? Declining HIV prevalence, behavior change, and the national response.
  46. 46.
    Government of Uganda (2010) United Nations General Assembly Special Session (UNGASS) Country Progress Report, Uganda: January 2008–December 2009.
  47. 47.
    Altman LK (2005) U.S. blamed for condom shortage in fighting AIDS in Uganda. NY Times, Aug 30Google Scholar
  48. 48.
    Anonymous (2010) Uganda: Public irritated by yet another condom shortage. PlusNews, UN Office for the Coordination of Humanitarian Affairs.
  49. 49.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2008) AIDS spending by categories and financing sources: Uganda.
  50. 50.
    Hamers FF, Downs AM (2003) HIV in central and eastern Europe. Lancet 361(9362):1035–1044CrossRefGoogle Scholar
  51. 51.
    Kelly JA, Amirkhanian YA (2003) The newest epidemic: a review of HIV/AIDS in Central and Eastern Europe. Int J STD AIDS 14(6):361–371CrossRefGoogle Scholar
  52. 52.
    Twigg J (2007) HIV/AIDS in Russia: commitment, resources, momentum, challenges.
  53. 53.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2007) Practical guidelines for intensifying HIV prevention: Towards universal access.
  54. 54.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2006) Country progress report of the Russian Federation on the implementation of the Declaration of Commitment on HIV/AIDS. Reporting period: January–December 2005.
  55. 55.
    Luo RF, Cofrancesco JJ (2006) Injection drug use and HIV transmission in Russia. AIDS 20(6):935–936CrossRefGoogle Scholar
  56. 56.
    Mathers BM, Degenhardt L, Phillips B, Wiessing L, Hickman M, Strathdee SA, Wodak A, Panda S, Tyndall M, Toufik A, Mattick RP (2008) Global epidemiology of injecting drug use and HIV among people who inject drugs: a systematic review. Lancet 372(9651):1733–1745CrossRefGoogle Scholar
  57. 57.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2008) Country progress report of the Russian Federation on the implementation of the Declaration of Commitment on HIV/AIDS. Reporting period: January 2006-December 2007.
  58. 58.
    Burchell AN, Calzavara LM, Orekhovsky V, Ladnaya NN, for the Canada AIDS Russia Project and the Russian HIV Response Network (2008) Characterization of an emerging heterosexual HIV epidemic in Russia. Sex Transm Dis 35(9):807–813CrossRefGoogle Scholar
  59. 59.
    World Health Organization (WHO) (2009) Towards universal access: scaling up priority HIV/AIDS interventions in the health sector.
  60. 60.
    Joint United Nations Programme on HIV/AIDS (UNAIDS) (2008) Epidemiological fact sheet on HIV and AIDS: Russia 2008 update.
  61. 61.
    Open Health Institute (OHI) (2006) Harm reduction programs in the civilian and prison sectors of the Russian Federation: assessment of best practices.
  62. 62.
    International Harm Reduction Association (IHRA) (2010) The global state of harm reduction 2010: key issues for broadening the response.
  63. 63.
    Niccolai LM, Shcherbakova IS, Toussova OV, Kozlov AP, Heimer R (2009) The potential for bridging of HIV transmission in the Russian Federation: sex risk behaviors and HIV prevalence among drug users (DUs) and their non-DU sex partners. J Urban Health 85(Suppl 1):131–143CrossRefGoogle Scholar
  64. 64.
    Niccolai LM, Toussova OV, Verevochkin SV, Barbour R, Heimer R, Kozlov AP (2010) High HIV prevalence, suboptimal HIV testing, and low knowledge of HIV-positive serostatus among injection drug users in St. Petersburg, Russia. AIDS Behav 14(4):932–941CrossRefGoogle Scholar
  65. 65.
    Tengs TO, Lin TH (2002) A meta-analysis of utility estimates for HIV/AIDS. Med Decis Making 22(6):475–481CrossRefGoogle Scholar
  66. 66.
    Lasry A, Sansom SL, Hicks KA, Uzunangelov V (2011) A model for allocating CDC’s HIV prevention resources in the United States. Health Care Manage Sci 14(1):115–124CrossRefGoogle Scholar
  67. 67.
    Kaplan EH, Merson MH (2002) Allocating HIV-preventionresources: balancing efficiency and equity. Am J Public Health 92(12):1905–1907Google Scholar
  68. 68.
    Institute of Medicine (IOM) (2001) No time to lose: Getting more from HIV prevention.
  69. 69.
    Alistar SS, Brandeau ML, Beck EJ (2013) REACH: A practical HIV resource allocation tool for decision makers. In: Zaric GS (ed) Operations research and health care policy. Springer PublishersGoogle Scholar
  70. 70.
    Arrow KJ, Enthoven AC (1961) Quasi-concave programming. Econometrica 29(4):779–800CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sabina S. Alistar
    • 1
    Email author
  • Elisa F. Long
    • 2
  • Margaret L. Brandeau
    • 1
  • Eduard J. Beck
    • 3
  1. 1.Department of Management Science and EngineeringStanford UniversityStanfordUSA
  2. 2.School of ManagementYale UniversityNew HavenUSA
  3. 3.Programme BranchUNAIDSGenevaSwitzerland

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