Fig 1.
Prediction models based on neural networks.
Neural network architecture illustration. The architecture has as input a matrix of size [119, 52] containing the time series of weekly dengue cases of size 52 for each of the 119 neighborhoods. The temporal and spatial dependence between these values is learned in the LSTM layer with dim neurons and the prediction for the 119 neighborhoods one-step-ahead is made in the Dense layer with 119 neurons. A dropout of d% is applied before each N LSTM and Dense layers to prevent over-fitting. Dim represents the number of neurons, d the dropout value, and N the number of LSTM layers. These values were selected via Grid Search during the training process. The range of values used in Grid Search to define the neural network’s hyperparameters is presented in S1 Table.
Table 1.
Data Division: The data was split into test, evaluation, and training data.
The test data is used for prediction and analysis purposes, the evaluation data for adjusting the model parameters during the training phase, and the training data to learn the historical pattern of dengue case evolution. For consistency, we chose one epidemic year (e.g., 2016) and one non-epidemic year (e.g., 2018) for the evaluation phase, ensuring the model was tested across different outbreak scenarios.
Fig 2.
Time series of the weekly dengue cases observed in the city of Fortaleza during the interval [2011, 2020].
(a) Typically, the annual behavior of dengue epidemic curves is well represented by bell-shaped functions, where the period of highest incidence is usually observed between April and June (Week 9 to Week 20). However, in 2020, urban mobility was dramatically reduced by governmental actions imposing restrictions on mobility to mitigate COVID-19 dissemination. Restrictions such as Social Isolation (03–20-2020 to 05–07-2020) and Lockdown (05–08-2020 to 05–31-2020) have substantially influenced the shape of the curve of cases, causing different moments of highest contamination (Week 9 and Week 16). Orange time zones between Weeks 12 and 24 of 2020 represent the mobility restriction periods. In (b), we show the total number of cases observed in the city of Fortaleza at different moments of contagion. The years 2011, 2012, 2015, 2016, and 2017 are dubbed epidemic since they exhibit a large quantity of confirmed cases. The remaining years are considered non-epidemic. To draw a comparison with the timeframe immediately preceding the implementation of mobility restrictions in 2020, we limit our analysis in (c) to the total case count for the initial 11 weeks of dengue infection each year. Although 2020 initially demonstrates a contamination pattern akin to epidemic years, suggesting that high rates of serotype DENV2 contagion would occur in the subsequent weeks of the year, the ultimate figures do not validate that projection. Consequently, by year-end, 2020 is categorized as a non-epidemic year.
Fig 3.
Time series of validations on buses using smart-cards during the COVID-19 pandemic period in 2020.
The solid curve corresponds to the ratio (V − V0)/V0, where V is the number of weekly validations and V0 is a baseline given by the time average in the period [01–03-2020, 01–13-2020]. During the pandemic period, it is possible to observe a quick decrease in urban mobility in intervals [03–20-2020, 05–07-2020] (week 12—week 18) and [05–08-2020, 05–31-2020] (week 18—week 22), corresponding to Social Isolation and Lockdown, respectively. After the lockdown, a process of partial reopening of commercial establishments took place leading to a slow return to the mobility patterns usually observed. Orange time zones within the interval [week 12 to week 22] represent the intervals of mobility restrictions.
Fig 4.
Time series of the number of dengue cases (actual and predicted) for the city of Fortaleza in the years 2020 (a) and for the epidemic years of 2011 (b), 2012 (c), and 2015 (d).
The solid blue curves in the graphs represent the actual time series data, while the red curves represent the averages of the total cases for five predictions made for each year, along with the 90% confidence interval (C.I. 90%). In 2020, there were a total of 7,753 cases recorded. However, the neural network model predicted 27,792 cases, following a typical pattern observed in epidemic years.
Fig 5.
Interrupted Time Series analysis using Poisson GAM with Bootstrapped confidence intervals.
This figure illustrates the observed and the predicted dengue cases intervention as well as the predicted dengue cases without intervention over time, namely, the counterfactual estimation. The solid blue curve represents the observed weekly dengue cases. The red curve represents the predicted cases assuming no intervention, while the green curve represents the predicted cases with the intervention. The shaded areas indicate the 95% confidence intervals for the predicted values. The actual number of cases in 2020 was 7,753, closely matching the predicted cases with intervention (7,752), whereas the prediction without intervention was significantly higher at 14,077 cases.
Table 2.
Comparison of LSTM and ITS model predictions.
The table provides a detailed comparison between the predictions of the LSTM and ITS, namely the total predicted dengue cases for 2020, the predicted peak dengue cases, and the predicted time to peak. Additionally, the effective reduction in dengue cases is presented, highlighting the strong correlation with the lockdown measures. The time difference between the predicted and real peak times in the dengue case series is also compared.
Fig 6.
Exponential relation between total incidence of dengue cases, and the arrival time,
, of the dengue virus for each neighborhood in the city of Fortaleza.
In (a)-(j) are the relations against
. The dashed lines represent fits through the Eq (2). Thus, it is possible to obtain the characteristic time of spread of the disease τy for each analyzed year. In the particular case of 2020, as shown in (j), due to the changes in urban mobility, a significantly different contamination pattern can be observed. It is possible to estimate a value of τy for before the implementation of mobility restrictions,
days (dashed purple line), and another for after the implementation of such restrictions,
days (dashed green line). Here,
days (March 22nd) is the effective time of enforcement of mobility restrictions.
Fig 7.
Prediction of the effective time of dengue transmission in 2020.
Using a neural network model, it was possible to estimate the total number of dengue cases for each neighborhood i of the city of Fortaleza in 2020 in a hypothetical scenario where mobility restrictions had not been implemented. Such measure is observed at the end of the year and stored at the variable Pred(i). We compute the time series that was predicted for each neighborhood during the year 2020 and calculate the time of arrival of the predicted disease from the network, . The relation
against
follows an exponential behavior, as expressed by Eq (2). Thus, it is possible to estimate the effective time of transmission of the disease where τ ≈ 61 days. Therefore, our predictions indicate that in 2020 dengue would contaminate neighborhoods in Fortaleza more quickly if there were no implementation of measures restricting urban mobility.