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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
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 11 (2004)
    Issue (Month): 1 ()
    Pages: 3-28

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    Handle: RePEc:taf:mpopst:v:11:y:2004:i:1:p:3-28

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    Keywords: age-structured systems; population dynamics; McKendrick equation; Pontryagin's maximum principle; infectious diseases; HIV;


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    Cited by:
    1. 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, Springer, vol. 15(1), pages 47-61, March.


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