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Maximum Principle For Age And Duration Structured Systems: A Tool For Optimal Prevention And Treatment Of Hiv

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  • Gustav Feichtinger
  • Vladimir Veliov
  • Tsvetomir Tsachev

Abstract

Age and duration since infection are considered in a model of optimal control of the spread of Human Immunodeficiency Virus (HIV) in countries with high prevalence. Prevention and medical treatment are selected so as to maximize an economic objective function.The model extends the classical McKendrick equation. Necessary optimality conditions in the form of Pontryagin's global maximum principle and numerical solution based on them are presented. “Critical” initial prevalence is established numerically for which there are two optimal medical treatments: one intense and another less demanding. It is shown that treatment alone can be counterproductive: increase in treatment must be accompanied by increase in prevention.

Suggested Citation

  • Gustav Feichtinger & Vladimir Veliov & Tsvetomir Tsachev, 2004. "Maximum Principle For Age And Duration Structured Systems: A Tool For Optimal Prevention And Treatment Of Hiv," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(1), pages 3-28.
    • Handle: RePEc:taf:mpopst:v:11:y:2004:i:1:p:3-28
    DOI: 10.1080/08898480490422301
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    References listed on IDEAS

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    1. W.-J. Beyn, T. Pampel, W.Semmler, 2001. "Dynamic optimization and Skiba sets in economic examples," Computing in Economics and Finance 2001 29, Society for Computational Economics.
    2. V. Barbu & M. Iannelli, 1999. "Optimal Control of Population Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 1-14, July.
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    Cited by:

    1. Yves Fotso Fotso & Suzanne Touzeau & Frédéric Grognard & Berge Tsanou & Samuel Bowong, 2023. "Optimal Control of Coffee Berry Borers: Synergy Between Bio-insecticide and Traps," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 882-899, March.
    2. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle, 2021. "Optimal prevention and elimination of infectious diseases," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    4. Herbert Dawid & Engelbert Dockner & Richard Hartl & Josef Haunschmied & Ulrike Leopold-Wildburger & Mikulas Luptacik & Alexander Mehlmann & Alexia Prskawetz & Marion Rauner & Gerhard Sorger & Gernot T, 2010. "Gustav Feichtinger celebrates his 70th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 437-451, December.
    5. Christian Almeder & Gustav Feichtinger & Warren Sanderson & Vladimir Veliov, 2007. "Prevention and medication of HIV/AIDS: the case of Botswana," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(1), pages 47-61, March.
    6. Raouf, BOUCEKKINE & Bity, DIENE & Theophile, AZOMAHOU, 2006. "The Growth economics of epidemics," Discussion Papers (ECON - Département des Sciences Economiques) 2006021, Université catholique de Louvain, Département des Sciences Economiques.
    7. Radboud J. Duintjer Tebbens & Kimberly M. Thompson, 2009. "Priority Shifting and the Dynamics of Managing Eradicable Infectious Diseases," Management Science, INFORMS, vol. 55(4), pages 650-663, April.
    8. Azomahou, Theophile, 2008. "The Economic Impact of AIDS in Sub-Saharan Africa," MERIT Working Papers 2008-038, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    9. Raouf Boucekkine & Bity Diene & Theophile Azomahou, 2008. "Growth Economics of Epidemics: A Review of the Theory," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(1), pages 1-26.
    10. Gustav Feichtinger & Alexia Prskawetz & Vladimir M. Veliov, 2002. "Age-structured optimal control in population economics," MPIDR Working Papers WP-2002-045, Max Planck Institute for Demographic Research, Rostock, Germany.

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