Analysis of a logistic model for the waves of covid-19 in Brazil under the presence of uncertainties
Résumé
In 2019, the first cases of COVID-19 were reported in China. In January 2020, recognizing that the disease was spread to 20 other countries, the World Health Organization declared that the outbreak constitutes a Public Health Emergency of International Concern. Nowadays, (April 2021) the novel coronavirus already taken 3.1M lives worldwide. Under this catastrophic situation, mathematical models are extremity necessary to help understand the spread of the disease and guide control measures to contain COVID-19. Under the Brazilian scenario, a good model must be capable of covering the asymmetric 2-wave behavior where the second moment of the pandemic is being more aggressive than the first one. For that, this work applies a generalized logistic model of 5 parameters to the data of new deaths in Brazil. To create the multi-wave behavior, the parameters are considered time variable under the form a sigmoid function between a minimum e maximum value to each one, controlled by two shape parameters. A calibration process was executed and the fitted parameters were used as mean to a global sensitivity analysis through the Sobol index method with use of Polynomial Chaos Surrogate. After the identification of the most important parameters, an uncertainty quantification study was conducted considering the important inputs as random variables described by beta distributions. Confidence intervals of 50, 75 and 95% to the number of new deaths and the cumulative number of deaths were obtained to analyze the model robustness under the presence of uncertainties. Combined with other complementary statistics, the model shows itself efficiently to describe the data and to be used to previous goals.