  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.
