## 1 Introduction  
The main objective of this paper is to demonstrate that the inferential statistics method and the Systems Dynamics method can provide similar results when studying the short-term evolution of individual happiness because of a single drug dose. To achieve this, an application case, where drugs are alcohol and caffeine, is analyzed through a single-case experimental design with replication with two participants. There is a scientific debate about whether happiness is a trait or a state (see [1] for a review). However, some authors go beyond this controversy by offering an inclusive proposal about the happiness nature: it is both a trait and a state [2]. We adopt this inclusive approach in this study. If happiness has a state nature as well as a trait one, then we must be able to study its short-term and long-term dynamics, even because of a single eliciting stimulus in a single session, as a drug intake is. For instance, it has been demonstrated that, after a single dose intake of alcohol or caffeine, both stimuli can increase happiness and other feelings such as euphoria in the short term [3; 4; 5; 6; 7; 8]. The relationship between alcohol and happiness depends on doses and lifestyle. In fact, moderate drinkers tend to be happier than abstainers and heavy drinkers [9; 10], and also tend to reduce their depression and stress [11]. In addition, happiness and team cohesion are significant predictors of alcohol consumption in university sports people [12]. In a longitudinal study with a Russian sample, a hump-shaped relationship among men but not among women was obtained [13]. In addition, there exists a nonlinear relationship between alcohol and happiness showing that abstainers and occasional drinkers, as well as heavy and problem drinkers, are at risk of reaching high anxiety and depression levels [14]. On the other hand, the existence of individual differences inside the acute effects of both drugs (alcohol and caffeine) has been proved [15; 16; 17], as well as the existence of an interaction between personality, time of the day and caffeine, in such a way that in the morning of the first day of the experiment, low impulsive persons were hindered and high impulsive ones were helped by caffeine. This pattern reverses in the evening of this first day, and it reverses again in the evening of the second day [18]. Furthermore, previous findings of studies using a large single dose, such as increased alertness and anxiety, improved performance on simple and choice reactive tasks, or a cognitive vigilance, may be applicable to normal patterns of the effects of caffeine consumption [19]. Long-term dynamical effects of alcohol consumption have also been studied [20]: the result of a meta-analysis show that the positive effect intensity of alcohol consumption decreases over time. In fact, the study [20] proposes the construction of a mathematical model to study accurately this dynamical response. However, even the corresponding short-term dynamics have not been well described yet. Therefore, a mathematical dynamical model, the stimulus response model (SRM), is here presented to fill this gap. The SRM is capable of predicting and describing how the whole personality (the General Factor of Personality or GFP) changes during a single session in response to a single dose of caffeine or alcohol, and also how its responses vary between individuals [21; 22]. However, it has not been applied to the study of happiness dynamics yet. Then, this study applies the SRM to predict the evolution of a subject's happiness in response to a single dose of alcohol or caffeine. In fact, the advantages of the SRM are as follows: (a) it is capable of reproducing happiness dynamically as a consequence of a single dose of a stimulus such as alcohol or caffeine; (b) it points out how much the obtained happiness response is due to the stimulus; and (c) it provides the changes in the happiness trait at short term.