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Managing infectious diseases over connected populations: a non-convex optimal control

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  • Ceddia, M Graziano

Abstract

The paper develops an optimal control model to analyse various management options for infectious diseases that occur in metapopulations, under both Nash and cooperative behaviour. As pathogens are renewable resources with negative value, the problem may be non-convex. Since the disease can be transmitted across various connected populations, externalities are involved. Both aspects deserve attention as two issues arise: a) is eradication of the disease in finite time preferable to indefinite treatment? b) are cooperative solutions well-behaved? The problem is solved numerically and the results indicate that while eradication is likely to be an optimal strategy when initial levels of infections are relatively low, the internalisation of between-population externalities (as indicated by the first order necessary conditions of the cooperative optimal control problem) might not always be possible. Also, ignoring these two aspects can lead to inadequate policy design.

Suggested Citation

  • Ceddia, M Graziano, 2010. "Managing infectious diseases over connected populations: a non-convex optimal control," MPRA Paper 22344, University Library of Munich, Germany, revised 2010.
  • Handle: RePEc:pra:mprapa:22344
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    File URL: https://mpra.ub.uni-muenchen.de/22344/1/MPRA_paper_22344.pdf
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    References listed on IDEAS

    as
    1. Todd Sandler & Daniel G Arce M, 2002. "A conceptual framework for understanding global and transnational public goods for health," Fiscal Studies, Institute for Fiscal Studies, vol. 23(2), pages 195-222, June.
    2. Tahvonen, Olli & Salo, Seppo, 1996. "Nonconvexities in Optimal Pollution Accumulation," Journal of Environmental Economics and Management, Elsevier, vol. 31(2), pages 160-177, September.
    3. Scott Barrett, 2003. "Global Disease Eradication," Journal of the European Economic Association, MIT Press, vol. 1(2-3), pages 591-600, 04/05.
    4. W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
    5. repec:eee:ecomod:v:220:y:2009:i:1:p:51-59 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    infectious diseases; metapopulation; non-convexities; optimal control;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • Q28 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Government Policy
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • H00 - Public Economics - - General - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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