Abstract
This study deals with addictive acts that exhibit a stable pattern not intervening with the normal routine of daily life. Nevertheless, in the long term such behaviour may result in health damage. Alcohol consumption is an example of such addictive habit. The aim is to describe the process of addiction as a dynamical system in the way this is done in the natural and technological sciences. The dynamics of the addictive behaviour is described by a mathematical model consisting of two coupled difference equations. They determine the change in time of two state variables, craving and self-control. The model equations contain terms that represent external forces such as societal rules, peer influences and cues. The latter are formulated as events that are Poisson distributed in time. With the model it is shown how a person can get addicted when changing lifestyle. Although craving is the dominant variable in the process of addiction, the moment of getting dependent is clearly marked by a switch in a variable that fits the definition of addiction vulnerability in the literature. Furthermore, the way chance affects a therapeutic addiction intervention is analysed by carrying out a Monte Carlo simulation. Essential in the dynamical model is a nonlinear component which determines the configuration of the two stable states of the system: being dependent or not dependent. Under identical external conditions both may be stable (hysteresis). With the dynamical systems approach possible switches between the two states are explored (repeated relapses).
Highlights
Addiction refers to a very divers set of substances and behaviours, some common elements are generally recognized
When trying to apply the dynamical systems approach to the process of addiction in real life, it becomes clear that chance plays an important role
We explored its applicability in the analysis of lifestyles with potentially addictive behaviour such as a high alcohol consumption
Summary
Addiction refers to a very divers set of substances and behaviours, some common elements are generally recognized. After stopping, a strong desire arises to resume this frequently exerted action. When this is not possible, withdrawal symptoms will occur. This state of the mind, in which one is fully absorbed by the deprivation of some drug or activity, is called craving [1,2,3]. In this study craving is quantified by a variable C that ranges from 0 to 1. It arises as a result of dopamine activity, which in turn is switched on by other processes in the brain. In a similar way, we study addiction, mainly in relation to alcohol
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