## 4 The Stimulus Response Model (SRM)  
Following [PERSON]'s methodology [23] for Systems Dynamics, the model to be built (the SRM) can be represented qualitatively by the hydrodynamic diagram (HD) that is showed in Figure 1. It summarizes the factors and patterns of the problem dynamics studied in the specialized literature or obtained from the scholars' knowledge about the problem. In the case here studied, the problem dynamics is given by the individual happiness response to a stimulus (drug), whose knowledge can be taken from [17; 21; 22]. However, before presenting the HD and deducing the equations from it, the variables considered, their symbols and their dimensions and units are presented in Table 4 for the input variables or parameters, and in Table 5 for the output variables. Note that the input variables or parameters are those not influenced causally for any other model variables, and, in general, can depend on time. In the model presented, they are constant, and their values are calibrated from real data with a genetic algorithm, i.e., an informatics program that finds the set of parameter values that provides the SRM dynamical prediction closest to the experimental scores, with their respective confidence intervals and corresponding confidence levels. The last two rows of Table 4 represent (for ES and for SFS) the initial happiness value and the initial drug in blood value, respectively. These values are not computed by the genetic algorithm, because the first one is the score of the participant before consumption (see below: \(y_{0}\) in Equation (12) or Equation (18)), and the second one is the amount of drug in blood before consumption, being always \(s_{0}=0\) because neither alcohol nor caffeine have been consumed since a long time ago for both participants. Figure 1: Hydrodynamic diagram of stimulus response model (SRM). See Tables 4 and 5 for meaning of variables inside icons. Symbols of HD in Figure 1 are shown in Appendix A. The parameter that measures the global effect of the drug on an individual by the SRM is defined as a combination of the three power parameters and the inhibitor effect delay of Table 4, and it is here called as the _overall power parameter_. \(opp=a+p+q\cdot\tau\). Note that the three terms of \(opp\) have the same dimensions (T\({}^{-1}\)) and units (min\({}^{-1}\)). In addition, the output variables of Table 5 depend causally on other model variables through the corresponding equations: every model output variable corresponds to a particular model equation deduced from the HD and the hypotheses stated about its variables. Following [PERSON]'s methodology [23] for Systems Dynamics, the model to be built (the SRM) can be represented qualitatively by the hydrodynamic diagram (HD), as shown in Figure 1. It summarizes the factors and patterns of the problem dynamics studied in the specialized literature or obtained from the scholars' knowledge about the problem. In the case here studied, the problem dynamics is given by the individual happiness response to a stimulus (drug), whose knowledge can be taken from [17; 21; 22]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Variables or Parameters** & **Symbol** & **Dimensions** & **Units** \\ \hline Dose & \(M\) & Amount = M & mL (Phase B); mg (Phase C) \\ Inhibitor effect delay & \(\tau\) & Time = T & min \\ Assimilation rate & \(\alpha\) & T\({}^{-1}\) & min\({}^{-1}\) \\ Consumption rate & \(\beta\) & T\({}^{-1}\) & min\({}^{-1}\) \\ Homeostatic control power & \(a\) & T\({}^{-1}\) & min\({}^{-1}\) \\ Tonic or basal happiness & \(b\) & ES or SFS = H & scale units (su) of adjectives \\ Excitation effect power & \(p\) & T\({}^{-1}\) & min\({}^{-1}\) \\ Inhibitor effect power & \(q\) & T\({}^{-2}\) & min\({}^{-2}\) \\ Initial happiness (initial state) & \(y_{0}\) & H & su \\ Initial drug in blood & \(s_{0}\) & M & mL (Phase B); mg (Phase C) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input variables of the SRM: symbols and dimensions.