Estimating epidemiological parameters and underreporting of Covid-19 cases in Brazil using a multi-wave mathematical model

Abstract In this study, we reproduce the first four waves of Covid-19 in Brazil and present a comprehensive analysis. Using a Susceptible-Infected-Recovered-Dead-Susceptible (SIRDS) model with breakpoints, we estimated the Basic Reproduction Number (R0), Infection Fatality Rate (IFR), and immunity period. Our model inferred an R0 of 1.8, decreasing to 1.02 during the first wave, aligned with early outbreak stages characterized by reduced human mobility. Our model suggests that approximately half of the Brazilian population was exposed in the first two waves, indicating substantial underreporting (1:5) for this period. For the third and fourth waves, the model estimated 17 and 19 times more infections than reported cases, suggesting increasing underreporting in these waves. Furthermore, our model estimates an IFR of 0.57% for the first two waves and 0.03% for the third and fourth waves. In conclusion, Brazil successfully reduced the R0 during the first wave; however, the absence of public health measures, such as the reduction of human mobility and a most effective vaccine campaign, during the second wave resulted in higher mortality rates. The third and fourth waves exhibited lower mortality rates, which we attribute to vaccination coverage, prior exposure to the virus, and lower lethality of the Omicron variant.