Adaptive SIR model for propagation of SARS-CoV-2 in Brazil

Abstract

We study the spreading of SARS-CoV-2 in Brazil based on official data available since March 22, 2020. Calculations are done via an adaptive susceptible-infected-removed (SIR) model featuring dynamical recuperation and propagation rates. We are able reproduce the number of confirmed cases over time with less than 5% error and also provide with short- and long-term predictions. The model can also be used to account for the epidemic dynamics in other countries with great accuracy.

Keywords: Epidemic dynamics; SARS-CoV-2; SIR.

Fig. 1

(a) Number of confirmed cases (accumulated) of SARS-CoV-2 in Brazil. Symbols stand for official data and the solid line represents the results obtained via the SIR model. They both agree quite well, with an error of less than 5%. Dashed line is the prediction for the following ten days, terminating on January 10, 2021. (b) Basic reproduction number $R_0\left(t\right)=S\left(t\right)\beta \left(t\right)∕\gamma \left(t\right)$ versus time. Each point is the outcome of a 5-day average. Estimated $R_0$ currently approaches 1.10 based on data retrieved for the last days of December.

Fig. 2

(Left) Accumulated number of confirmed cases and (right) basic reproduction number $R_0$ for Germany, Italy, France, and UK. Official data is represented by circles and results from the adaptive SIR model are denoted by the solid lines.

Fig. 3

(a–c) 10-day predictions realized on end dates April 10, 20, and 30, respectively, for Brazil. (d) Comparison between official data and predicted outcomes at specific days.

Fig. 4

Number of accumulated cases evaluated via the SIR model considering the evolution trend of $R_0$ as shown in Fig. 1(b). Dotted line is the prediction for times $t>286$.