The epidemiology of COVID-19 presented major shifts during the pandemic period. Factors such as the most common symptoms and severity of infection, the circulation of different variants, the preparedness of health services, and control efforts based on pharmaceutical and non-pharmaceutical interventions played important roles in the disease incidence. The constant evolution and changes require the continuous mapping and assessing of epidemiological features based on time-series forecasting. Nonetheless, it is necessary to identify the events, patterns, and actions that were potential factors that affected daily COVID-19 cases. In this work, we analyzed several databases, including information on social mobility, epidemiological reports, and mass population testing, to identify patterns of reported cases and events that may indicate changes in COVID-19 behavior in the city of Araraquara, Brazil. In our analysis, we used a mathematical approach with the fast Fourier transform (FFT) to map possible events and machine learning model approaches such as Seasonal Auto-regressive Integrated Moving Average (ARIMA) and neural networks (NNs) for data interpretation and temporal prospecting. Our results showed a root-mean-square error (RMSE) of about 5 (more precisely, a 4.55 error over 71 cases for 20 March 2021 and a 5.57 error over 106 cases for 3 June 2021). These results demonstrated that FFT is a useful tool for supporting the development of the best prevention and control measures for COVID-19.