Diversify or Focus? Spending to Combat Infectious Diseases When Budgets are Tight

Resources for the Future DP 10-15

26 Pages Posted: 11 Mar 2010 Last revised: 10 Apr 2010

See all articles by Soren Anderson

Soren Anderson

Michigan State University - Department of Economics; Michigan State University - Department of Agricultural Economics; National Bureau of Economic Research

Ramanan Laxminarayan

The Center for Disease Dynamics, Economics & Policy (CDDEP); Center for Disease Dynamics, Economics & Policy; Princeton University

Stephen W. Salant

University of Michigan; Resources for the Future

Date Written: February 2, 2010

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.

Suggested Citation

Anderson, Soren T. and Laxminarayan, Ramanan and Salant, Stephen W., Diversify or Focus? Spending to Combat Infectious Diseases When Budgets are Tight (February 2, 2010). Resources for the Future DP 10-15. Available at SSRN: https://ssrn.com/abstract=1565008

Soren T. Anderson

Michigan State University - Department of Economics ( email )

East Lansing, MI 48824
United States

Michigan State University - Department of Agricultural Economics ( email )

East Lansing, MI 48824
United States

National Bureau of Economic Research ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Ramanan Laxminarayan (Contact Author)

The Center for Disease Dynamics, Economics & Policy (CDDEP) ( email )

1616 P St NW
Suite 600
Washington DC, DC 20036
United States

Center for Disease Dynamics, Economics & Policy ( email )

1616 P Street, NW
Washington, DC 20036
United States

HOME PAGE: http://www.cddep.org

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Stephen W. Salant

University of Michigan ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
313-764-2370 (Phone)
313-764-2769 (Fax)

Resources for the Future ( email )

1616 P Street, NW
Washington, DC 20036
United States

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