We propose a mathematical framework to describe the neurobiology of
drug addiction. Substances of abuse are known to activate and disrupt
neuronal circuits in the brain reward system To quantify these
disruptions, we incorporate the psychiatric concepts of drug-induced
incentive salience (IST), reward prediction error (RPE), and opponent
process theory (OPT) in a simple and easily interpretable dynamical
system model. Drug-induced dopamine releases activate a biphasic
reward response with pleasurable, positive ``a-processes" (euphoria,
rush) followed by unpleasant, negative "b-processes" (cravings,
withdrawal symptoms). Neuroadaptive processes triggered by successive
intakes enhance the negative component of the reward response, against
which the user compensates by increasing drug dose and/or intake
frequency. This positive feedback between physiological changes and
drug self-administration eventually leads to full addiction. Our
model gives rise to qualitatively different pathways to addiction that
allow us to represent a diverse set of user profiles (genetics, age)
or drug potencies. Finally, we include possible mechanisms to
mitigate withdrawal symptoms, such as through methadone or other
auxiliary drugs used in detoxification.
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