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Diversify or focus: spending to combat infectious diseases when budgets are tight

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  • Anderson, Soren
  • Laxminarayan, Ramanan
  • 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 >= 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 University Library of Munich, Germany in its series MPRA Paper with number 21860.

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Date of creation: 02 Feb 2010
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Handle: RePEc:pra:mprapa:21860

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Keywords: public health spending; nonconvexity; dynamic programming;

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  1. Gersovitz, Mark & Hammer, Jeffrey S., 2001. "The economic control of infectious diseases," Policy Research Working Paper Series 2607, The World Bank.
  2. Gardner Brown & Ramanan Laxminarayan, 1998. "Economics of Antibiotic Resistance," Discussion Papers in Economics at the University of Washington, Department of Economics at the University of Washington 0060, Department of Economics at the University of Washington.
  3. 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, October.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. GAUDET, Gérard & HERRMANN, Markus, 2007. "The Economic Dynamics of Antibiotic Efficacy under Open Access," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 04-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. 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.
  10. Laxminarayan, Ramanan, 2003. "ACT Now or Later: The Economics of Malaria Resistance," Discussion Papers, Resources For the Future dp-03-51, Resources For the Future.
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