Characteristics and evolution of COVID-19 cases in Brazil: mathematical modeling and simulation

Abstract

The pandemic caused by the coronavirus of severe acute respiratory syndrome 2 (SARS-CoV-2), the etiological agent of the 2019 coronavirus disease (COVID-19), represents a threat of great magnitude not faced in this century. As a result, each government has proposed emergency public health measures that are critical to delay the transmission and spread of the virus and mitigate its impacts. In Brazil, the outbreak triggered many cases of people infected with COVID-19. Considering there are no drugs or vaccines proven to be effective to treat the disease, analyzing the data of infection cases and their mathematical interpretation are essential for supporting and guiding governmental measures to suppress and mitigate the impact of COVID-19. This means that estimates with mathematical models to assess the development potential of sustained human-human transmission are needed. Since the disease has its own biological characteristics, the models need to be adapted to the variability of the regions characteristics and the decision-making by both the government and the population, in order to be able to deal with real situations. Thus, in the present paper, we analyzed the official data of COVID-19 in Brazil and used the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation to predict the evolution of the disease. The model indicates that a nucleation rate is of fourth order, which indicates that Brazilians are crowding with no respect to measures of social distance and disease prevention. In our opinion, the political authorities were unable to control the spread of the disease in Brazil, given that social mobility was interrupted by the federal and state governments.