## 5 Dynamical Results of the Stimulus Response Model (SRM)  
In order to fit the SRM dynamics presented in Section 4 to the scores obtained by the experimental design presented in Section 3, two questions must be answered: (1) how to achieve the SRM outcomes with uncertainty; and (2) how to achieve the best outcomes (also with uncertainty) of the model parameters of Table 4 to reproduce the dynamical patterns followed by the experimental design scores. The answer for question (1) is that the outcomes of the stimulus response model are provided by Equation (17) for the drug in blood variable, \(s(t)\), and by using the 4 th order Runge-Kutta method for the numerical outcomes of the happiness variable, \(y(t)\) through Equations (12) and (16). However, these SRM outcomes do not present uncertainty. Therefore, to consider its uncertainty, the following steps are followed:  
1. Once the SRM outcomes are obtained, the corresponding residuals are computed as the differences between the experimental scores and the SRM outcomes. 2. The \(p\)-value of the Anderson-Darling test is applied to the residuals to determine whether they are distributed as normal distributions of zero mean and \(sd\) standard deviation, N(0, \(sd\)), or not. Note that the \(H_{0}\) hypothesis is that the residuals follow such normal distribution. Subsequently, if the \(H_{0}\) hypothesis holds, the confidence interval for every SRM outcome is computed by the usual way, i.e., by the Student's t distribution with a 0.05 signification level. 3. All corresponding figures present the experimental scores jointly with the SRM mean value line and the two limit lines corresponding to the confidence intervals. The answer for question (2) is that a genetic algorithm, whose algorithmic bases can be found in [31], provides the model happiness responses with random residuals (i.e., the noise, considered as the influence of other sources different to the stimuli), as well as a sample of 40 relatively optimal sets of parameter values (those described in Table 4) that better fit the model outcomes to the experimental scores. To be more precise, the genetic algorithm of [31] just presents the set of values of each parameter that better fits the model outcomes. The genetic algorithm version used in this work is an advance on the [31] version that provides a sample of the best sets of parameter values to achieve the corresponding confidence intervals. For better understanding of how the genetic algorithm works, a brief explanation is provided here (details can be found in [31]). The genetic algorithm tries to imitate natural selection. So, an individual is defined like a set of values for the parameters (genes) of the model and a population is defined as a set of individuals. Reproduction is defined as the creation of a new individual by choosing randomly a gene from every couple of genes one from each parent (may be with random mutation). Consanguinity is restricted to avoid too small differences between individuals. The SRM provides a fitting value for each individual of the considered population. The fitting method consists of calculating the quadratic sum (QS) of the differences between experimental scores and those provided by the SRM. The best fitting individuals (those with lesser values for QS) are chosen as reproducers to produce the next generation. Some immigrants may be considered. Summary: (1) The first population is determined by assigning randomly a value to each parameter (gene) inside a given scale. (2) Calculation of QS for each individual, ordering and selection of reproducers. (3) Random immigration. (4) Random reproduction (with consanguinity control and random mutation) up to completing population. (5) New ordering and selection. (6) Checking the end condition: if yes then exit routine else go to (3). The end condition is \"no lesser QS values are observed\".