Stochastic Modeling and Optimization to Support Emergency Response Systems

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This award will contribute to the Nation's health and welfare by developing new mathematical and computational tools to inform the design of volunteer schemes for out-of-hospital health emergencies such as cardiac arrest. Cardiac arrest occurs when a patient’s heart enters an atypical rhythm. Death follows rapidly unless the patient receives medical attention. Lives can be saved if the patient receives cardiopulmonary resuscitation (CPR) quickly. Recently, volunteer schemes have arisen whereby volunteers install an app on their smartphone that tracks their location. Volunteers near a cardiac arrest are notified by the app and can choose to respond, thereby saving valuable minutes in the response time to initiate CPR. Volunteer schemes are emerging worldwide, but key questions relating to their design remain unanswered. For example, how many volunteers are needed to ensure impact on survival rates, and when one can potentially recruit volunteers of multiple types, which should be prioritized? This project develops research methods to answer these questions and others. Related research directions address the potential impact of broadband connections that enable a remote paramedic or doctor to advise on-scene treatment by a paramedic or ambulance officer, and how to prioritize dispatch decisions in periods when emergency services are severely loaded and/or traffic is congested.This award develops mathematical and computational tools to inform the design of volunteer schemes. Central principles include the integrated use of spatial Poisson point processes to model volunteer locations with convex optimization to solve problems relating to the distribution of volunteer capacity across a city to maximize patient survival. The related question of ambulance dispatch when ambulances are severely loaded is addressed through use of approximate dynamic programming, exploiting deep neural networks to approximate both the value function and the choice of policy. Simulation optimization will underlie some aspects of this work. In that context, the use of biased gradient estimators in search will be explored. Most methods for gradient estimation in simulation optimization result in biased estimators which are viewed in practice as unsatisfactory. This project will explore their potential efficacy; they have been seen to be of great value in some examples and the research will explore their potential more broadly.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.