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Diversity or Focus? Spending to Combat Infectious Diseases When Budgets Are Tight

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  • Anderson, Soren
  • Laxminarayan, Ramanan

    ()
    (Resources for the Future)

  • Salant, Stephen W.

Abstract

We consider a health authority seeking to allocate annual budgets optimally over time to minimize the discounted social cost of infection(s) evolving in a finite set of "R greater than or equal to 2" groups. This optimization problem is challenging, since as is well known, the standard epidemiological model describing the spread of disease (SIS) contains a nonconvexity. Standard continuous-time optimal control is of little help, since a phase diagram is needed to address the nonconvexity and this diagram is 2R dimensional (a costate and state variable for each of the R groups). Standard discrete-time dynamic programming cannot be used either, since the minimized cost function is neither concave nor convex globally. We modify the standard dynamic programming algorithm and show how familiar, elementary arguments can be used to reach conclusions about the optimal policy with any finite number of groups. We show that under certain conditions it is optimal to focus the entire annual budget on one of the R groups at a time rather than divide it among several groups, as is often done in practice; faced with two identical groups whose only difference is their starting level of infection, it is optimal to focus on the group with fewer sick people. We also show that under certain conditions it remains optimal to focus on one group when faced with a wealth constraint instead of an annual budget.

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Paper provided by Resources For the Future in its series Discussion Papers with number dp-10-15.

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Date of creation: 04 Mar 2010
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Handle: RePEc:rff:dpaper:dp-10-15

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  1. Steven M. Goldman and James Lightwood., 1996. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," Economics Working Papers 96-245, University of California at Berkeley.
  2. Gersovitz, Mark & Hammer, Jeffrey S., 2005. "Tax/subsidy policies toward vector-borne infectious diseases," Journal of Public Economics, Elsevier, vol. 89(4), pages 647-674, April.
  3. Laxminarayan, Ramanan, 2003. "ACT Now or Later: The Economics of Malaria Resistance," Discussion Papers dp-03-51, Resources For the Future.
  4. Philipson, Tomas J & Posner, Richard A, 1996. "The Economic Epidemiology of Crime," Journal of Law and Economics, University of Chicago Press, vol. 39(2), pages 405-33, October.
  5. Gardner Brown & Ramanan Laxminarayan, 1998. "Economics of Antibiotic Resistance," Working Papers 0060, University of Washington, Department of Economics.
  6. Alan D. Lopez & Colin D. Mathers & Majid Ezzati & Dean T. Jamison & Christopher J. L. Murray, 2006. "Global Burden of Disease and Risk Factors," World Bank Publications, The World Bank, number 7039, January.
  7. Mark Gersovitz & Jeffrey S. Hammer, 2004. "The Economical Control of Infectious Diseases," Economic Journal, Royal Economic Society, vol. 114(492), pages 1-27, 01.
  8. GAUDET, Gérard & HERRMANN, Markus, 2007. "The Economic Dynamics of Antibiotic Efficacy under Open Access," Cahiers de recherche 04-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Lars Olson & Santanu Roy, 2008. "Controlling a biological invasion: a non-classical dynamic economic model," Economic Theory, Springer, vol. 36(3), pages 453-469, September.
  10. Mark Eiswerth & Wayne Johnson, 2002. "Managing Nonindigenous Invasive Species: Insights from Dynamic Analysis," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 23(3), pages 319-342, November.
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