Three-level global resource allocation model for HIV control: A hierarchical decision system approach

  • Received: 24 August 2016 Published: 01 February 2018
  • MSC : Primary: 92B05, 92D30, 90B50, 91A80; Secondary: 34B60, 91A10, 90C31, 00A71

  • Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources. In this paper, a hierarchical mathematical optimization model is proposed to solve such a problem. Combining existing epidemiological models with the kind of interventions being on practice, a 3-level hierarchical decision making model in optimally allocating such resources has been developed and analyzed. When the impact of antiretroviral therapy (ART) is included in the model, it has been shown that the objective function of the lower level decision making structure is a non-convex minimization problem in the allocation variables even if all the production functions for the intervention programs are assumed to be linear.

    Citation: Semu Mitiku Kassa. Three-level global resource allocation model for HIV control: A hierarchical decision system approach[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 255-273. doi: 10.3934/mbe.2018011

    Related Papers:

  • Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources. In this paper, a hierarchical mathematical optimization model is proposed to solve such a problem. Combining existing epidemiological models with the kind of interventions being on practice, a 3-level hierarchical decision making model in optimally allocating such resources has been developed and analyzed. When the impact of antiretroviral therapy (ART) is included in the model, it has been shown that the objective function of the lower level decision making structure is a non-convex minimization problem in the allocation variables even if all the production functions for the intervention programs are assumed to be linear.
    加载中
    [1] [ Avert, Funding for HIV and AIDS, 2016. Available from URL http://www.avert.org/node/353/pdf
    [2] [ M. L. Brandeau,G. S. Zaric,A. Richter, Resource allocation for control of infectious diseases in multiple independent populations: Beyond cost-effectiveness analysis, Journal of Health Economics, 22 (2003): 575-598.
    [3] [ M. L. Brandeau,G. S. Zaric,V. De Angelis, Improved allocation of HIV prevention resources: Using information about prevention program production functions, Health Care Management Science, 8 (2005): 19-28.
    [4] [ Centers for Disease Control and Prevention (CDC), Achievements in public health, reduction in perinatal transmission of HIV infection -United States, 1985 -2005, MMWR Morb Mortal Wkly Rep, 55 (2006), 592-597.
    [5] [ D. Donnell,J. M. Baeten,J. Kiarie,K. K. Thomas,W. Stevens,C. R. Cohen,J. Mclntyre,J. R. Lingappa,C. Celum, Heterosexual HIV-1 transmission after initiation of antiretroviral therapy: A prospective cohort analysis, Lancet, 375 (2010): 2092-2098.
    [6] [ M. Drummond, B. O'Brien, G. L. Stoddart and G. J. Torrance (Eds. ), Methods for the Economic Evaluation of Health Care Programs, Oxford University Press, New York, 2000.
    [7] [ S. R. Earnshaw,K. Hicks,A. Richter,A. Honeycutt, A linear programming model for allocating HIV prevention funds with state agencies: A pilot study, Health Care Manage Sci, 10 (2007): 239-252.
    [8] [ S. Flessa, Where efficiency saves lives: A linear programme for the optimal allocation of health care resources in developing countries, Health Care Management Science, 3 (2000): 249-267.
    [9] [ A. M. Kassa,S. M. Kassa, A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 3 (2013): 133-144.
    [10] [ A. M. Kassa,S. M. Kassa, A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints, Journal of Global Optimization, 64 (2016): 745-764.
    [11] [ A. M. Kassa,S. M. Kassa, Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers, J Glob Optim, null (2017): 1-19.
    [12] [ S. M. Kassa,A. Ouhinou, The impact of self-protective measures in the optimal interventions for controlling infectious diseases of human population, Journal of Mathematical Biology, 70 (2015): 213-236.
    [13] [ S. M. Kassa,A. Ouhinou, Epidemiological models with prevalence dependent endogenous self-protection measure, Mathematical Biosciences, 229 (2011): 41-49.
    [14] [ J. Kates, J. A. Izazola and E. Lief, Financing the response to HIV in low-and middle-income countries: , International assistance from donor governments in 2015,2015. Available from: http://files.kff.org/attachment/Financing-the-Response-to-HIV-in-Low-and-Middle-Income-Countries-International-Assistance-from-Donor-Governments-in-2015
    [15] [ J. Kates, A. Wexler and E. Lief, Financing the response to HIV in low-and middle-income countries: International assistance from donor governments in 2013, UNAIDS Report, July 2014. Available from: https://kaiserfamilyfoundation.files.wordpress.com/2014/07/7347-10-financing-the-response-to-hiv-in-low-and-middle-income-countries.pdf
    [16] [ J. M. Kilby,H. Y. Lee,J. D. Hazelwood,A. Bansal,R. P. Bucy,M. S. Saag,G. M. Shaw,E. P. Acosta,V. A. Johnson,A. S. Perelson,P. A. Goepfert, Treatment response in acute/early infection versus advanced AIDS: Equivalent first and second phase of HIV RNA decline, AIDS, 22 (2008): 957-962.
    [17] [ A. P. Kourtis,C. H. Schmid,D. J. Jamieson,J. Lau, Use of Antiretroviral therapy in HIV-infected pregnant women and the risk of premature delivery: A meta-analysis, AIDS, 21 (2007): 607-615.
    [18] [ A. Lasry,G. S. Zaric,M. W. Carter, Multi-level resource allocation for HIV prevention: A model for developing countries, European Journal of Operational Research, 180 (2007): 786-799.
    [19] [ F. J. Palella,K. M. Delaney,A. C. Moorman,M. O. Loveless,J. Fuhrer,G. A. Satten, Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection, The New England Journal of Medicine, 338 (1998): 853-860.
    [20] [ L. Palombi,M. C. Marazzi,A. Voetberg,N. A. Magid, Treatment acceleration program and the experience of the DREAM program in prevention of mother-to-child transmission of HIV, AIDS, 21 (2007): S65-S71.
    [21] [ A. Prendergast,G. Tudor-Williams,S. Burchett,P. Goulder, International perspectives, progress, and future challenges of paediatric HIV infection, Lancet, 370 (2007): 68-80.
    [22] [ N. Siegfried, L. van der Merwe, P. Brocklehurst and T. T. Sint, Antiretrovirals for reducing the risk of mother-to-child transmission of HIV infection, Cochrane Database of Systematic Reviews 2011, 7 (2011), Art. CD003510.
    [23] [ J. A. C. Sterne,M. A. Henán,B. Ledergerber,K. Tilling,R. Weber,P. Sendi, Long-term effectiveness of potent antiretroviral therapy in preventing AIDS and death: A prospective cohort study, Lancet, 366 (2005): 378-384.
    [24] [ UNAIDS, AIDS by the numbers, 2016. Available from: http://www.unaids.org/sites/default/files/media_asset/AIDS-by-the-numbers-2016_en.pdf.
    [25] [ UNAIDS, Fast-track update on investments needed in the AIDS response, UNAIDS Reference, 2016. Available from: http://www.unaids.org/sites/default/files/media_asset/UNAIDS_Reference_FastTrack_Update_on_investments_en.pdf
    [26] [ R. Vardavas and S. Blower, The emergence of HIV transmitted resistance in Botswana: When will the WHO detection threshold be exceeded? PLoS ONE, 2 (2007), e152.
    [27] [ M. C. Weinstein, From cos-effectiveness ratios to resource allocation: where to draw the line?, in Valuing Healthcare: Costs, Benefits, Effectiveness of phramaceuticals and other medical technologies (eds. F. A. Sloan), Cambridge University Press, New York (1995), 77-97.
    [28] [ World Health Organization, Towards Universal Access: Scaling up Priority HIV/AIDS Interventions in the Health Sector: Progress Report 2009, WHO, 2009.
    [29] [ A. T. Woldemariam,S. M. Kassa, Systematic evolutionary algorithm for general multilevel Stackelberg problems with bounded decision variables (SEAMSP), Annals of Operations Research, 229 (2015): 771-790.
    [30] [ G. S. Zaric,M. L. Brandeau, Resource allocation for epidemic control over short time horizons, Mathematical Biosciences, 171 (2001): 33-58.
    [31] [ G. S. Zaric,M. L. Brandeau, A little planning goes a long way: Multilevel allocation of HIV prevention resources, Medical Decision Making, 27 (2007): 71-81.

    © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
  • Reader Comments
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(619) PDF downloads(527) Cited by(1)

Article outline

Figures and Tables

Figures(6)  /  Tables(5)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog