The Question
When a health authority has a limited budget, should it focus its resources on one population group or divide its resources across groups? Which action would minimize the overall burden of disease?
What We Found
Taking insights from economics and epidemiology, the model demonstrates that when there is a fixed budget it is most optimal to focus resources on one group. Furthermore, it is more effective to treat the group with the fewer number of infected people. These findings run counter to conventional wisdom.
Why It Matters
Health authorities often have limited resources when tackling public health challenges. Research that draws insights from both economic and epidemiological modeling is needed to determine the most effective outcomes.
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 2 R 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 di fference 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.
Keywords
health economics
