Analyzing client behavior in a syringe exchange program

Multiple syringe exchange programs serve the Chicago metropolitan area, providing support for drug users to help prevent infectious diseases. Using data from one program over a ten-year period, we study the behavior of its clients, focusing on the temporal process governing their visits to service locations and on their demographics. We construct a phase-type distribution with an affine relationship between model parameters and features of an individual client. The phase-type distribution governs inter-arrival times between reoccurring visits of each client and is informed by characteristics of a client including age, gender, ethnicity, and more. The inter-arrival time model is a sub-model in a simulation that we construct for the larger system, which allows us to provide a personalized prediction regarding the client’s time-to-return to a service location so that better intervention decisions can be made with the help of simulation.