Modeling Emergency Medical Service Volunteer Response

Abstract

Problem definition: Out of hospital cardiac arrest requires immediate treatment and patient survival can be improved by combining traditional ambulance response with the dispatch of volunteers alerted via an app. How many volunteers are needed, and from where should they be recruited? Methodology/Results: We model the presence of volunteers throughout a region as a Poisson point process and derive analytical expressions for the response time distribution of the closest volunteer. Using known survival functions from literature, we then translate these response times to patient survival. Moreover, we introduce the use of optimization to replace the estimation of the volunteer location distribution, and show that the resulting optimization problems are highly tractable. We include a case study for Auckland, New Zealand, where we show how the optimal allocation of volunteers over the region varies, depending on the number of available volunteers as well as the objective function. We also show how ambulance locations affect the optimal distribution of volunteers. Managerial Implications: The optimal allocation of volunteers over the region provides guidance for recruitment of volunteers, both in terms of the number of volunteers needed to make substantial impact on survival rates and in city locations where additional recruitment would be most beneficial.