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An optimal control theory approach to non-pharmaceutical interventions
Feng Lin1, Kumar Muthuraman, Mark Lawley
1School of Biomedical Engineering, Purdue University, 206 S Martin Jischke Drive, West Lafayette, IN 47907-2032, USA. fenglin@gmail.com
Optimal control theory provides a framework for balancing pandemic influenza control and societal costs. A "bang-bang" policy, triggered by specific conditions, minimizes deaths and intervention impacts.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Public Health Interventions
Background:
- Non-pharmaceutical interventions (NPIs) are crucial for managing pandemic influenza by reducing transmission.
- NPIs must be carefully balanced against their societal costs.
- Optimal control theory offers a method to balance epidemic control and intervention costs.
Purpose of the Study:
- To develop NPI implementation triggers using optimal control theory.
- To minimize both influenza-related deaths and NPI implementation costs.
- To analyze the sensitivity of optimal policies to model parameters.
Main Methods:
- Application of optimal control theory to an epidemiologic compartmental model.
- Multivariate sensitivity analysis using Latin Hypercube Sampling.
- Investigation of model assumption departures (e.g., terminal time, NPI cost structure).
Main Results:
- A linear NPI cost yields a
- bang-bang
- policy (maximum NPI strength when criteria are met).
- NPI cost, death rate, and recovery rate significantly influence policy structure.
- Death rate, basic reproductive number, and recovery rate most impact cumulative deaths.
- The
- bang-bang
- policy's outcomes are robust to assumptions about terminal time.
- Quadratic NPI cost results in a multi-level policy with varying NPI strengths.
- Linear cost, though more expensive to implement, leads to fewer deaths.
Conclusions:
- Optimal control theory is valuable for developing effective pandemic control strategies.
- A sensitive and timely surveillance system is essential for pandemic preparedness.
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