Long-Term Time Prediction of Cumulative Number of Deaths in Brazil, China, Germany, Italy, Spain, the United States: an application to COVID-19 S-shaped models

Abstract

This research aims to adjust the Gompertz and Bertalanffy nonlinear regression model for the accumulated deaths by COVID-19 in six countries Brazil, United States, Germany, Italy, China, and Spain. It employed three different performance measures in the training process, adjusted determination coefficient , Akaike Information Criterion (AIC), and Residual Mean Square (RMS). The Mean Absolute Percentage Error (MAPE) and the Relative Error (RE) criterion were used to select the best model in the test dataset. On the training dataset, the Bertalanffy model was the one that best described the growth of deaths for China, while the Gompertz model was the best for Brazil, Germany, Italy, Spain, and the United States. In contrast, the Bertalanffy model was the best for Spain in the test dataset, according to MAPE and RE. According to the Gompertz model, 214,100 CI (175,929;267,008) people will die in Brazil, that will reach a maximum of 1,577 with a prediction interval [1,367; 1,819] of daily new deaths at its disease peak. The nonlinear models studied described the number of deaths growth curve satisfactorily, providing parameters with practical interpretations. Evidence was found that Brazil may surpass the United States regarding the total number of deaths. Short and long-term time prediction, as well as the turning point of each country, are presented and compared to other predictive models of the literature.