Is the opioid epidemic truly an epidemic? While drug abuse is not an infection per se, at first look it appears to be a compelling way to reason about the phenomenon. Individuals that are "infected" seem to cluster together, and having an "infected" region seems to increase the probability of more drug abuse in a vicious cycle.
Background
SIR Model
There is substantial literature surrounding methods for using differential equations to model epidemiological phenomena. The simplest and most well known model is the SIR model first described in \citet{Kermack_1927} which characterizes the dynamics of an infection moving through a population.