Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil
Abstract
: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 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 , where days, calibrating the net weights, bias, and parameters and for different simulation intervals.
- 2.
- Once the set of epidemiological curves 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 from is classified as “outlier”, i.e., a badly conditioned time-series period whose epidemiological variables , , and highly diverge from other periods. In our tests, we discard the ill-behaved ’s whose MAPE errors are greater than for any of the variables , or .
- 3.
- Finally, the remaining trained curves are used to compute the definitive forecasts using the numerical solution of the SIRD system for , where p is the desirable forecast period. This is performed so as to balance the well-behaved contributions in the set of ODE solutions , taking the mean of these outputs to determine , , and .
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
Appendix B. Qualitative Results for São Paulo State and Brazilian Regions
Appendix C. Algorithm
Algorithm 1: Parameter Calibration and Forecast Process |
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Notation | Description |
---|---|
number of susceptible at time t | |
number of infected at time t | |
number of recovered at time t | |
number of deaths at time t | |
transmission rate | |
transient transmission rate | |
rate of recovered | |
rate of mortality | |
or | time-dependent reproduction number |
prediction for the transmission rate at time t | |
M | pre-specified training period |
p | desirable forecast period |
and | real and predicted daily values with respect to a given target variable |
Region | Variance Norm | 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 |
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 |
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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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
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 StyleAmaral, 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
APA StyleAmaral, F., Casaca, W., Oishi, C. M., & Cuminato, J. A. (2021). Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil. Sensors, 21(2), 540. https://doi.org/10.3390/s21020540