Anderson, Soren and Laxminarayan, Ramanan and Salant, Stephen W. (2010): Diversify or focus: spending to combat infectious diseases when budgets are tight.

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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 continuoustime 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 discretetime 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.
Item Type:  MPRA Paper 

Original Title:  Diversify or focus: spending to combat infectious diseases when budgets are tight 
Language:  English 
Keywords:  public health spending; nonconvexity; dynamic programming 
Subjects:  H  Public Economics > H5  National Government Expenditures and Related Policies > H51  Government Expenditures and Health I  Health, Education, and Welfare > I1  Health > I18  Government Policy ; Regulation ; Public Health D  Microeconomics > D9  Intertemporal Choice > D90  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis 
Item ID:  21860 
Depositing User:  Stephen W. Salant 
Date Deposited:  07 Apr 2010 06:36 
Last Modified:  07 Feb 2016 02:29 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/21860 