Optimal control of birth–death processes, with applications to epidemic surveillance

Emerging and re-emerging infectious diseases continue to be a major threat to human health, and a threat to economic and financial stability worldwide. Epidemiological models have proven to be important tools for informing decisions on optimal policies, interventions, and control measures. However, the importance of surveillance and early detection is often overlooked, and the focus on control measures is mostly in terms of existing infections. In this work we present a framework for deciding on the optimal surveillance scheme that will minimize the overall cost of a disease, balancing the costs pertaining to surveys for early detection with other disease-related costs prior to detection. We show that the expected cost can be fully described for a general case of a stationary policy, thus supporting informed decision making between a few (fixed) strategies. In addition, we show that for time-dependent monitoring policies, the optimal policy is a bang-bang policy, whereby resources should be utilized for monitoring only after a critical time-point, to the maximum extent possible.