A mathematical model of reward-mediated learning in drug addiction*

We propose a mathematical model combining the so-called opponent
process theory (OPT) and the reward prediction error (RPE) in the
context of drug addiction. Using this model, we investigate the
different dynamics towards addiction, describe characteristic features
of drug addiction, and provide a possible description of the process
of detoxification. OPT is modeled by introducing a positive and
negative response to the reward (drug). The time-integration of this
response, over a time window defines a total net perception of the
reward associated with each drug dose. Differences in this perception
form the reward prediction error (RPE) that plays a key role
behavioral modification. With time and repeated exposures to drugs,
parameters governing the response will change based
on neuroadaptive processes. These evolving responses then
change the subsequent RPE, which in turn modifies the timing or dose of
subsequent drug intakes. We show that the dynamics
associated with naive drug users is represented by a trajectory for
which the value of the RPE is always positive but, with time and
repeated exposure to drugs, the trajectory is characterized by
negative values of the RPE.