Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil

Abstract

São Paulo is the most populous state in Brazil, home to around 22% of the country's population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country's fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model's coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given.

Keywords: Covid-19; SIRD; data-driven models; interactive platform; machine learning.

Figure A1

SP Covid-19 Info Tracker Platform (http://www.spcovid.net.br): First page view.

Figure A2

Forecasting results covering all the main regions of São Paulo.

Figure A2

Forecasting results covering all the main regions of São Paulo.

Figure A3

Forecasting results for Brazil’s regions.

Figure 1

Comparison of cumulative number of cases and deaths per million: São Paulo state, France, Germany and United Kingdom. Country data are from Johns Hopkins University [4].

Figure 2

(a) Susceptible-Infected-Recovered-Deceased (SIRD) model with its corresponding parameters and (b) the ANN design for learning $\beta (t)$

Figure 3

Illustration of the parameter calibration step.

Figure 4

(a) The complete filtering pipeline. (b) Training outputs for different time windows. (c) The selected ill-behaved training periods (discarded trainings). (d) Training results that have passed the error criteria for good training. (e) Averaged results as the definitive prediction.

Figure 4

(a) The complete filtering pipeline. (b) Training outputs for different time windows. (c) The selected ill-behaved training periods (discarded trainings). (d) Training results that have passed the error criteria for good training. (e) Averaged results as the definitive prediction.

Figure 5

Sub-region maps of São Paulo state: (a) State map showing the 22 state sub-regions, and (b) São Paulo metropolitan region.

Figure 6

Reproduction number $R_0(t)$ and infected $I(t)$ predictions for the mean, minimum and maximum forecasted values as the training window moves, i.e., by varying $M=10,11,\dots 40$ in Equation (2) and training the parameters in a coupled and recursive way. Red lines establish the mean predicted values after the full learning procedure is finished, while the vertical dotted lines split the training and forecasting periods.

Figure 6

Reproduction number $R_0(t)$ and infected $I(t)$ predictions for the mean, minimum and maximum forecasted values as the training window moves, i.e., by varying $M=10,11,\dots 40$ in Equation (2) and training the parameters in a coupled and recursive way. Red lines establish the mean predicted values after the full learning procedure is finished, while the vertical dotted lines split the training and forecasting periods.

Figure 7

Infected and effective reproduction number using constant and transient values for $\beta$: São Paulo region (first row) and Presidente Prudente region (second row).

Figure 8

Comparison of MAPE errors for constant and transient values of $\beta$: SIR and SIRD models.

Figure 9

São Paulo state subregions.

Figure 10

Brazilian regions.

Figure 11

Forecasting results for São Paulo state.

Figure 12

Forecasting results for Brazil.

Figure 13

Infected and deaths for São Paulo state and Brazil over recent data. The high increase in both indicators suggests the eminence of a “second wave” of coronavirus hitting the country and starting in the second half of November.

Figure 14

Infected and deaths for Italy, Portugal and Ukraine over recent data.

Figure 14

Infected and deaths for Italy, Portugal and Ukraine over recent data.