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

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## Abstract

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## 1. Introduction

- The implementation of urgent responses, as listed below, to mitigate the progress of coronavirus in São Paulo state, which is the most populous and economically active state in Brazil, responsible for $34\%$ of the Brazilian GDP [35].
- A novel forecasting model that combines the simplicity of SIR-based formulation with the effectiveness of data-driven learning strategies for predicting Covid-19 cases, deaths, recoveries and the virus reproduction number. The designed method is also capable of addressing “the curse of delay”, as usually observed in the Brazilian reports of cases and deaths, determining whether or not a coronavirus-related time-series period is “well-posed”.
- Our predictive approach learns the epidemiological parameters as time-dependent functions, which are calibrated by a recursive training approach based on an Artificial Neural Network, therefore allowing the forecaster to fit and customize Covid-19 curves for each region of the state.
- The availability of a comprehensive Covid-19 data repository and a freely available online platform, which has been accessed by citizens, authorities and media agencies to track and inspect the Covid-19 progress in São Paulo state. New Covid-19 notifications are immediately available throughout the platform, by getting fresh data published daily by 92 city halls spread over the state (the so-called first-hand local sources), in an attempt to reduce the delay in reporting the new cases and deaths as often observed in the Brazilian government updates [36,37].

## 2. Materials and Methods

#### 2.1. Mathematical Modeling: A Time-Dependent SIR-Based Model

#### 2.2. Learning Epidemiological Parameters: An Integrated Data-Driven Approach

#### Improving Data Fitting Robustness and Accuracy

- 1.
- Compute training outputs for several time windows by repeatedly solving the ODE-SIRD system (2) for $M={M}_{i}\in \{{M}_{1},{M}_{2},...,{M}_{n}\}$, where ${M}_{1}=10,{M}_{2}=11,...,{M}_{n}=30$ days, calibrating the net weights, bias, and parameters ${\gamma}_{r}$ and ${\gamma}_{d}$ for different simulation intervals.
- 2.
- Once the set of epidemiological curves $\Lambda =\{{C}_{i}\phantom{\rule{0.166667em}{0ex}}:{C}_{i}=\{{I}_{i}(t),{D}_{i}(t),{R}_{i}(t)\}\}$ is obtained, we compute the Mean Absolute Percentage Error (MAPE) (9), taken here as an error assessment metric, to decide whether or not a subset of ${C}_{i}^{\prime}s$ from $\Lambda $ is classified as “outlier”, i.e., a badly conditioned time-series period whose epidemiological variables ${I}_{i}(t)$, ${D}_{i}(t)$, ${R}_{i}(t)$ and ${R}_{0}(t)$ highly diverge from other periods. In our tests, we discard the ill-behaved ${C}_{i}$’s whose MAPE errors are greater than $20\%$ for any of the variables ${I}_{i}(t)$, ${D}_{i}(t)$ or ${R}_{i}(t)$.
- 3.
- Finally, the remaining trained curves are used to compute the definitive forecasts using the numerical solution of the SIRD system for $t\in [0,M+p]$, where p is the desirable forecast period. This is performed so as to balance the well-behaved contributions in the set of ODE solutions $\Lambda $, taking the mean of these outputs to determine ${I}_{i}(t)$, ${D}_{i}(t)$, ${R}_{i}(t)$ and ${R}_{0}(t)$.

## 3. Results and Discussion

#### 3.1. Data Organization

#### 3.2. Metrics

#### 3.3. The Proposed Forecasting Approach: Main Features and General Capabilities

#### 3.3.1. Badly Conditioned Samples × Data Fitting Robustness and Accuracy

#### 3.3.2. The Transient Behavior of Transmission Rate

#### 3.3.3. Invariance to Training Periods

#### 3.4. Quantitative and Qualitative Analyses

#### 3.4.1. São Paulo State Regions

#### 3.4.2. Brazilian Regions

#### 3.4.3. The Second Wave of Covid-19: Investigations in Brazil and Other Countries

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. SP Covid-19 Info Tracker

**Figure A1.**SP Covid-19 Info Tracker Platform (http://www.spcovid.net.br): First page view.

## Appendix B. Qualitative Results for São Paulo State and Brazilian Regions

## Appendix C. Algorithm

Algorithm 1: Parameter Calibration and Forecast Process |

## References

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**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 $

**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 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 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.

Notation | Description |
---|---|

$S(t)$ | number of susceptible at time t |

$I(t)$ | number of infected at time t |

$R(t)$ | number of recovered at time t |

$D(t)$ | number of deaths at time t |

$\beta $ | transmission rate |

$\beta (t)$ | transient transmission rate |

${\gamma}_{r}$ | rate of recovered |

${\gamma}_{d}$ | rate of mortality |

${R}_{0}(t)$ or ${R}_{t}$ | time-dependent reproduction number |

${\beta}_{net}(t)$ | prediction for the transmission rate at time t |

M | pre-specified training period |

p | desirable forecast period |

${Y}_{i}$ and $\dot{{Y}_{i}}$ | real and predicted daily values with respect to a given target variable |

**Table 2.**Variance computed during the training process, and average MAPE for active cases (infected) with respect to Figure 6 results.

Region | Variance Norm $(|\left|{\mathit{s}}^{2}\right|{|}_{2})$ | MAPE for Active Cases (%) |
---|---|---|

Greater São Paulo North | 0.098 | 2.658 |

Greater São Paulo Southeast | 1.478 | 4.414 |

Marília | 0.378 | 1.928 |

Ribeirão Preto | 0.063 | 3.894 |

Region | MAPE Error for Cumulative Cases (%) | MAPE Error for Cumulative Recovered Cases (%) | MAPE Error for Cumulative Deceased Cases (%) |
---|---|---|---|

15 August 2020–24 August 2020 | |||

Coastal | 1.513 | 0.951 | 1.046 |

Greater São Paulo | 0.753 | 3.731 | 1.394 |

Interior (East) | 0.454 | 1.491 | 3.465 |

Interior (West) | 1.085 | 1.826 | 2.618 |

15 September 2020–24 September 2020 | |||

Coastal | 1.536 | 0.347 | 2.503 |

Greater São Paulo | 0.598 | 0.344 | 0.926 |

Interior (East) | 0.937 | 0.461 | 1.157 |

Interior (West) | 1.277 | 0.753 | 0.603 |

15 October 2020–24 October 2020 | |||

Coastal | 0.533 | 0.249 | 0.268 |

Greater São Paulo | 0.105 | 0.438 | 0.776 |

Interior (East) | 1.413 | 0.886 | 0.236 |

Interior (West) | 0.832 | 1.097 | 0.881 |

Training Windows | MAPE Error for Cumulative Cases (%) | MAPE Error for Cumulative Deceases (%) | MAPE Error for Cumulative Recovereies (%) |
---|---|---|---|

10-30 days | 0.285 | 0.753 | 0.293 |

10-40 days | 0.762 | 0.928 | 0.321 |

10-50 days | 1.179 | 0.894 | 0.592 |

**Table 5.**Tabulated errors for the predictions depicted in Figure 11 (São Paulo state regions).

Region | Cases | Recoveries | Deaths | |||
---|---|---|---|---|---|---|

MAPE | NRMSE | MAPE | NRMSE | MAPE | NRMSE | |

Costal | 0.325 | 0.004 | 0.907 | 0.010 | 1.200 | 0.012 |

Greater São Paulo | 0.680 | 0.007 | 0.371 | 0.004 | 0.714 | 0.007 |

Interior (East) | 0.818 | 0.010 | 0.592 | 0.007 | 0.312 | 0.004 |

Interior (West) | 0.376 | 0.005 | 0.626 | 0.007 | 0.826 | 0.009 |

State of São Paulo | 0.219 | 0.003 | 0.455 | 0.005 | 0.475 | 0.005 |

**Table 6.**Tabulated errors with respect to predictions depicted in Figure 12 (Brazilian regions).

Region | Cases | Recoveries | Deaths | |||
---|---|---|---|---|---|---|

MAPE | NRMSE | MAPE | NRMSE | MAPE | NRMSE | |

Midwest | 1.169 | 0.014 | 0.989 | 0.013 | 0.856 | 0.009 |

North | 0.889 | 0.010 | 0.282 | 0.003 | 0.173 | 0.003 |

Northeast | 0.244 | 0.003 | 0.342 | 0.005 | 0.487 | 0.005 |

South | 4.413 | 0.047 | 7.111 | 0.072 | 0.397 | 0.004 |

Southeast | 0.815 | 0.009 | 0.675 | 0.009 | 0.427 | 0.005 |

Brazil | 0.323 | 0.004 | 0.638 | 0.008 | 0.273 | 0.003 |

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**MDPI and ACS Style**

Amaral, F.; Casaca, W.; Oishi, C.M.; Cuminato, J.A.
Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil. *Sensors* **2021**, *21*, 540.
https://doi.org/10.3390/s21020540

**AMA Style**

Amaral F, Casaca W, Oishi CM, Cuminato JA.
Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil. *Sensors*. 2021; 21(2):540.
https://doi.org/10.3390/s21020540

**Chicago/Turabian Style**

Amaral, Fabio, Wallace Casaca, Cassio M. Oishi, and José A. Cuminato.
2021. "Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil" *Sensors* 21, no. 2: 540.
https://doi.org/10.3390/s21020540