Intermittent Adaptation: A Mathematical Model of Drug Tolerance, Dependence and Addiction

A model of drug tolerance, dependence and addiction is presented. The model is essentially much more complex than the commonly used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a process of intermittently developing adaptation. The oral detection and analysis of endogenous substances is proposed to be the primary stimulus triggering the adaptation process. Anticipation and environmental cues are considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural— oral—route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking to be autonomously functioning adaptation processes. Simulations with the mathematical model demonstrate the model’s behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence.