## 3 Data and Results
### Prediction Sections Obtained  
The algorithm described previously was applied to the \(y^{*}\) matrix obtaining a total of nine third-order function sections covering from 15 June to 18 October, as shown in Table 1.  
The polynomial regressions are estimated for each sub-period using the standard least squares methodology. Hence, standard tests, such as the mean squared error or \(R^{2}\), are employed to measure the quality of fit for the estimations of the model obtained. Equations (2)-(4) summarize the features of each section, indicating the days of duration of them, the range of the relative errors \(e_{r}\) between \(y^{*}\) and \(\hat{y}^{*}\), the determination coefficient \(R^{2}\), the type of curvature, and the averages of the pandemic velocity \(v\) (cases/day) and acceleration \(w\) (cases/day\({}^{2}\)). As an example, in Figure 4, the curves from section T-6 are represented. In this section, there exists a transition from positive to negative acceleration (from concavity to convexity) with an inflection point in x = 188 (28 August). The set of 14 values corresponding to the total number of cumulative number of cases from 10 August (x = 169) and 23 August (x = 182) was adjusted by linear regression to a cubic polynomial (\(R^{2}=0.9995\)), and from the equation, the three predictive curves were obtained: \(\hat{y}^{*}\), \(\hat{y}^{*}_{f}\), and \(\hat{y}^{*}_{u}\) (standard, favorable, and unfavorable). In order to compare the forecasts with the observed values, the \(y^{*}\) values from August 24 were represented with a different symbol (rhombuses). In this section, it can be seen that they are located between the curves \(y^{*}\) and \(\hat{y}^{*}_{u}\) until 6 September (x = 196), when the observed \(y^{*}\) is higher than unfavorable forecast \(\hat{y}^{*}_{u}\). According to the criteria established in the algorithm, on the day that the section is considered finished, three new predictor curves are calculated. Obviously, in the last observed point, the relative error exceeds the criterion value of \(\pm 3\%\) and reaches a value of 3.30%, indicating the need for a new section. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Section** & **Date** & **Days** & \(\epsilon_{r}\)**Min** & \(\epsilon_{r}\)**Max** & \(R^{2}\) & **Curvature** & **vAverage** & **wAverage** \\ \hline T-1 & 14 June & 14 & \(-\)3.21\% & \(-\)0.05\% & 0.9728 & CONCAVE & 968 & 94.4 \\ T-2 & 28 June & 14 & \(-\)0.05\% & 0.39\% & 0.9880 & CONVEX & 346 & \(-\)3.7 \\ T-3 & 12 July & 14 & \(0.00\%\) & 1.38\% & 0.9994 & CONCAVE & 1082 & 72.7 \\ T-4 & 26 July & 14 & \(-\)0.37\% & 0.38\% & 0.9984 & CONCAVE & 2892 & 106.6 \\ T-5 & 9 August & 14 & \(-\)0.83\% & 1.15\% & 0.9966 & CONCAVE & 4846 & 90.7 \\ T-6 & 23 August & 14 & \(0.03\%\) & 3.30\% & 0.9984 & CONCAVE-CONVEX & 6893 & \(-\)35.4 \\ T-7 & 6 September & 13 & \(0.08\%\) & 3.38\% & 0.9965 & CONVEX & 8078 & \(-\)136.8 \\ T-8 & 19 September & 14 & \(-\)3.29\% & 0.06\% & 0.9970 & CONCAVE & 12,785 & 276.7 \\ T-9 & 3 October & 13 & \(-\)0.08\% & 3.31\% & 0.9937 & CONVEX & 7734 & \(-\)219.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the sections of the standard prediction, using arcs of cubic curves, indicating for each one the date on which it was constructed, the duration in days, the relative error (\(e_{r}\)) range, the coefficient of determination (\(R^{2}\)), the curvature, the average velocity of propagation (v), and the average acceleration (w). Figure 5 shows the arcs of the corresponding predictive curves (\(\hat{g}^{*}\)) in the sections T-1 to T-9 together with the values of the total cumulative number of cases observed between 15 June and 17 October 2020. Figure 4: T-6 predictive segment calculated on 23 August between 10 and 23 August (x = 169 to 182). The black circles represent the 14 values used to obtain the curve \(y^{*}\) by linear regression. The rhombuses are the observed \(y^{*}\) values since 24 August.