The aim of this paper is to present a mathematical dynamic modelling of the effect a stimulant drug has on different people which, at the same time, can be a useful tool for future brain studies. To this end, a dynamic model of the evolution of extraversion (considering its tonic and phasic aspects) has been constructed taking into account the unique personality trait theory and the general modelling methodology. This model consists of a delayed differential equation which, on one hand, considers that the active stimulus, a consequence of a single intake, is not constant; on the other hand, it contemplates that the state variable representing the phasic extraversion also represents the brain activation. The derivative of this state variable is calculated as the sum of the homeostatic control flow, the excitatory effect flow and the inhibitor effect flow. The solutions of this equation relate the tonic activation of an individual (that characterizes his or her personality) with his or her phasic activation level, whose evolution over time describes the organism's response to a single drug intake. These solutions quantitatively reproduce the predictions of current personality theories and anticipate vulnerability to drug misuse and addiction development.