Authors Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, and Tzu-Hsuan Liu use the Finite Impulse Response (FIR) linear system filtering method to track and predict the number of people infected and recovered from COVID-19, in a pandemic context in which there was still no vaccine and the only way to avoid contagion was isolation. To estimate the coefficients of these FIR filters, Chen et al. used machine learning methods through a classical optimization problem with regularization (ridge regression). These estimated coefficients are called ridge coefficients. The epidemic mathematical model adopted by these researchers to formulate the FIR filters is the time-dependent discrete SIR. In this paper, we propose a small modification to the algorithm of Chen et al. to obtain the ridge coefficients. We then used this modified algorithm to track and predict the number of people infected and recovered from COVID-19 in the state of Minas Gerais/Brazil, within a prediction window, during the initial period of the pandemic. We also compare the predicted data with the respective real data to check how good the approximation is. In the modified algorithm, we set values for the FIR filter orders and for the regularization parameters, both different from the respective values defined by Chen et al. in their algorithm. In this context, the numerical results obtained by the modified algorithm in some simulations present better approximation errors compared to the respective approximation errors presented by the algorithm of Chen et al.

This research presents an innovative use of parallel computing with the ARIMA (AutoRegressive Integrated Moving Average) model to forecast energy consumption in Peru's Puno region. The study conducts a thorough and multifaceted analysis, focusing on the execution speed, prediction accuracy, and scalability of both sequential and parallel implementations. A significant emphasis is placed on efficiently managing large datasets. The findings demonstrate notable improvements in computational efficiency and data processing capabilities through the parallel approach, all while maintaining the accuracy and integrity of predictions. This new method provides a versatile and reliable solution for real-time predictive analysis and enhances energy resource management, which is particularly crucial for developing areas. In addition to highlighting the technical advantages of parallel computing in this field, the study explores its practical impacts on energy planning and sustainable development in regions like Puno.