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The Optimal Control of Infectious Diseases via Prevention and Treatment


  • Rowthorn, Robert
  • Toxvaerd, Flavio


This paper fully characterizes the optimal control of a recurrent infectious disease through the use of (non-vaccine) prevention and treatment. The dynamic system may admit multiple steady states and the optimal policy may be path dependent. We find that an optimal path cannot end at a point with maximal prevention; it is necessarily zero or at an intermediate level. In contrast, an optimal path must end at a point at which treatment is either maximal or minimal. We find that the comparative statics of the model may radically differ across steady states, which has important policy implications. Last, we consider the model with decentralized decision making and compare the equilibrium outcomes with the socially optimal outcomes. We find that steady state prevalence levels in decentralized equilibrium must be equal to or higher than the socially optimal levels. While steady state treatment levels under decentralization are typically socially optimal, steady state prevention (if used) is socially suboptimal.

Suggested Citation

  • Rowthorn, Robert & Toxvaerd, Flavio, 2012. "The Optimal Control of Infectious Diseases via Prevention and Treatment," CEPR Discussion Papers 8925, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:8925

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    References listed on IDEAS

    1. Anderson, Soren T. & Laxminarayan, Ramanan & Salant, Stephen W., 2012. "Diversify or focus? Spending to combat infectious diseases when budgets are tight," Journal of Health Economics, Elsevier, vol. 31(4), pages 658-675.
    2. Klein, Eili & Laxminarayan, Ramanan & Smith, David L. & Gilligan, Christopher A., 2007. "Economic incentives and mathematical models of disease," Environment and Development Economics, Cambridge University Press, vol. 12(05), pages 707-732, October.
    3. Goldman Steven Marc & Lightwood James, 2002. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-24, April.
    4. Mark Gersovitz & Jeffrey S. Hammer, 2004. "The Economical Control of Infectious Diseases," Economic Journal, Royal Economic Society, vol. 114(492), pages 1-27, January.
    5. Doris A. Behrens & Jonathan P. Caulkins & Gernot Tragler & Gustav Feichtinger, 2000. "Optimal Control of Drug Epidemics: Prevent and Treat---But Not at the Same Time?," Management Science, INFORMS, vol. 46(3), pages 333-347, March.
    6. Geoffard, Pierre-Yves & Philipson, Tomas, 1996. "Rational Epidemics and Their Public Control," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 603-624, August.
    7. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    8. Michael Kremer, 1996. "Integrating Behavioral Choice into Epidemiological Models of AIDS," The Quarterly Journal of Economics, Oxford University Press, vol. 111(2), pages 549-573.
    9. Mark Gersovitz & Jeffrey S. Hammer, 2003. "Infectious Diseases, Public Policy, and the Marriage of Economics and Epidemiology," World Bank Research Observer, World Bank Group, vol. 18(2), pages 129-157.
    10. Robert Halvorsen & David F. Layton (ed.), 2006. "Explorations in Environmental and Natural Resource Economics," Books, Edward Elgar Publishing, number 3697.
    11. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
    12. Toxvaerd, Flavio, 2010. "Recurrent Infection and Externalities in Prevention," CEPR Discussion Papers 8112, C.E.P.R. Discussion Papers.
    13. 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.
    14. Michael Kremer, 1996. "Integrating Behavioral Choice into Epidemiological Models of the AIDS Epidemic," NBER Working Papers 5428, National Bureau of Economic Research, Inc.
    15. Toxvaerd, Flavio, 2010. "Infection, Acquired Immunity and Externalities in Treatment," CEPR Discussion Papers 8111, C.E.P.R. Discussion Papers.
    16. Brito, Dagobert L. & Sheshinski, Eytan & Intriligator, Michael D., 1991. "Externalities and compulsary vaccinations," Journal of Public Economics, Elsevier, vol. 45(1), pages 69-90, June.
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    Cited by:

    1. Park, Hojeong, 2016. "A real option analysis for stochastic disease control and vaccine stockpile policy: An application to H1N1 in Korea," Economic Modelling, Elsevier, vol. 53(C), pages 187-194.
    2. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    3. Berry, Kevin & Finnoff, David & Horan, Richard D. & Shogren, Jason F., 2015. "Managing the endogenous risk of disease outbreaks with non-constant background risk," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 166-179.
    4. Telalagic, S., 2012. "Optimal Treatment of an SIS Disease with Two Strains," Cambridge Working Papers in Economics 1229, Faculty of Economics, University of Cambridge.

    More about this item


    Economic epidemiology; Hysteresis; Non-convex systems; Optimal and equilibrium policy mix; Treatment and prevention;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health


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