Effects of population mobility on the COVID-19 spread in Brazil

Abstract

This article proposes a study of the SARS-CoV-2 virus spread and the efficacy of public policies in Brazil. Using both aggregated (from large Internet companies) and fine-grained (from Departments of Motor Vehicles) mobility data sources, our work sheds light on the effect of mobility on the pandemic situation in the Brazilian territory. Our main contribution is to show how mobility data, particularly fine-grained ones, can offer valuable insights into virus propagation. For this, we propose a modification in the SENUR model to add mobility information, evaluating different data availability scenarios (different information granularities), and finally, we carry out simulations to evaluate possible public policies. In particular, we conduct a case study that shows, through simulations of hypothetical scenarios, that the contagion curve in several Brazilian cities could have been milder if the government had imposed mobility restrictions soon after reporting the first case. Our results also show that if the government had not taken any action and the only safety measure taken was the population's voluntary isolation (out of fear), the time until the contagion peak for the first wave would have been postponed, but its value would more than double.

Fig 1. Probability distribution of the delay in the notified cases.

The distributions of delay and number of cases estimated from the data notified by Opendata SUS platform and the Coronavirus Panel before and after adjustments of the lag between symptom onset and official notification in Fortaleza/CE (Brazil). From right to left, we have: empirical delay distribution (with μ = 25.72 and σ = 31.85), estimated delay distribution(with μ = 10.85 and σ = 9.61), cases distribution before fits, cases distribution after fits. In addition, μ is the mean of the distribution and σ is the standard deviation and the vertical lines on the first and second plots represent the mean of the delay value in each analyzed distribution.

Fig 2. SENUR model.

Schematic for the SENUR model used in this work.

Fig 3. Methodology scheme.

Overview of the methodology used for the evaluation of the mobility effects on transmission and control of COVID-19.

Fig 4. Mobility parameters estimated by our model for Fortaleza.

Estimated values of mobility parameters q₁ and q₂ via MCMC and their resulting distributions. (a) q₁ (From 03/15 to 03/20). (b) q₂ (From 03/20 to 05/05).

Fig 5. Simulation results for coarse-grained data.

Number of infected people estimated by our model for the cities of Belo Horizonte, Porto Alegre, São Paulo, Rio de Janeiro, and Fortaleza when analyzed in the context of Waze mobility indexes. The shaded areas represent the 95% confidence region provided by the model; the black line represents the average model prediction and the points the official values released. (a) Belo Horizonte. (b) Porto Alegre. (c) São Paulo. (d) Rio de Janeiro. (e) Fortaleza.

Fig 6. Simulation results for daily infected cases reported.

Number of infected people estimated by our model for the cities of (a) Belo Horizonte and (b) São Paulo. The shaded areas represent the 95% confidence region provided by the model and the points the official daily values released.

Fig 7. Results of hypothetical scenarios for coarse-grained data.

The model response when simulating two hypothetical scenarios: I) the population and neither the government prioritized measures to restrict mobility and II) after the first case notified in the city, the government decreed the closure of trade. Here we analyze the ratio between the number of infected individuals in the analyzed scenarios and the actual number of infected individuals to observe the curve trend over time.

Fig 8. Social analysis of the pandemic spread to the city of Fortaleza.

Results of the social analysis of the spread of the virus under the context of HDI in the neighborhoods of the city of Fortaleza. As we can see, we found that the higher the HDI, the higher the percentage of infected people in the region, as well as the higher recovery, which we believe is directly associated with the greater number of patients with access to quality private hospital treatment. On the other hand, in regions with the lowest HDI rates, we observed the highest percentage of treatments performed independently, which can be explained by the lack of access to public service.

Fig 9. Cross-correlation between mobility data and disease spread.

Representation of the cross-correlation between R(t) is the cars’ flow obtained by DETRAN-CE. We observe that, the correlation is maximum (in module) for lag = −1.

Fig 10. Aggregate flow of vehicles and the reproduction number between the dates 03/20/2020 and 05/04/2020.

Plots in the left show mobility indexes extracted from the Google report, and plots in the right depict the R(t) estimated from DETRAN-CE’s data. We can see similarities between trends in DETRAN-CE’s data and the mobility indexes extracted from the Google report. The highest cross-correlation results are in places labeled as retail and recreation, grocery and pharmacy, and parks.

Fig 11. Model results.

Our model applied to data from the city of Fortaleza. The shaded areas represent the 95% confidence region provided by the model; the black line represents the average model prediction and the points the official values released.

Fig 12. R(t) estimate for all 16 regions of the city of Fortaleza.

We use the number of infected cases estimated by our model for each of the regions. (a) BARROSO. (b) CAVALCANTE. (c) MOURA. (d) PINZON. (e) RE1. (f) RE2. (g) RE3. (h) RE4. (i) RE5. (J) RE6. (k) RE7. (l) RE8. (m) RE9. (n) RE10. (o) RE11. (p)RE12.

Fig 13. Results of hypothetical scenarios for fine-grained data.

Model’s response when simulating hypothetical scenarios in Fortaleza when we apply fine-grain spatial mobility data.

Fig 14. Sensitivity analysis.

Comparison between our mobility quantifier with some real mobility data used in our work.