Multiwave COVID-19 Prediction from Social Awareness
using Web Search and Mobility Data

Existing COVID-19 time series models cover multiple types such as auto-regressive integrated moving average (ARIMA) (Kufel et al., 2020), and long short-term memory (LSTM) (Chimmula and Zhang, 2020; Jo et al., 2020). Moreover, biologists and engineering scientists focus on the relationship between fatality rate and biochemical indicators (Zhou et al., 2020a), human mobility (Jo et al., 2020). When it comes to urban district-level disease infection prediction, while the inter-district connections provide crucial pathways for both human movement and disease dissemination, these models are insufficient to capture such spatial dependency between different urban districts. In fact, the spatial dependency information enables us to deal with the data scarcity issue which may occur during the pandemic season. For instance, assume that we have sufficient mobility and social media data for district $\mathcal{A}$ and deficient data for district $\mathcal{B}$, and recognize strong mobility connections between districts $\mathcal{A}$ and $\mathcal{B}$. Considering the connections between the two districts helps to fully utilize the infection information and predict the infection cases for both districts $\mathcal{A}$ and $\mathcal{B}$.

Graph neural network (GNN) is an innovative neural network that captures the relationship between multi-hop neighborhood nodes via the message passing mechanism (Zhou et al., 2020b). In the past years, various GNN models such as graph convolutional network (GCN) (Kipf and Welling, 2016), GraphSage (Hamilton et al., 2017), graph attention network (GAT) (Veličković et al., 2017) were developed and applied to many fields such as neural machine translation (Bastings et al., 2017), visual question answering (Narasimhan et al., 2018), traffic prediction (Yao et al., 2019; Zhang et al., 2021; Chen et al., 2019; Peng et al., 2020), and network metric generation (Xue et al., 2022).

Researchers have harnessed the superiority of the GNN in modeling spatial dependency to perform the disease infection case prediction. Most published GNN approaches (Kapoor et al., 2020; Panagopoulos et al., 2021; Gao et al., 2021) focused on the infection prediction before July 2020 when the first global outbreak occurred using the historical infection and mobility data. The mobility data was sufficient to reflect the disease spreading patterns during the first wave thanks to its simple relationship with the infection. First, areas attracting more passengers had higher risks of experiencing rapidly increasing cases than some lonely areas at the beginning of the first wave. Second, the travel restriction policies during the first wave suppressed the mobility strength and thus decelerated the disease outbreak (Xiong et al., 2020).

Nevertheless, the interaction between infection and mobility evolved into a much more complicated status during the later waves because the infection cases were affected by a large variety of causes such as mask policy, the vaccination, which hindered the ability of raw mobility data to reflect the infection tendency. Besides, many studies have recognized that the available mobility data for COVID-19 infection cases prediction was limited by the period length (Panagopoulos et al., 2021; Rodriguez et al., 2021), which resulted in unstable learned models. In summary, the long-term multiwave infection prediction requests alternative data sources that provide sufficient interconnections with the infection case under the dynamic environment. In this study, we turn to the novel web search data, which directly reveals human’s awareness to the disease and potential symptoms (Yom-Tov et al., 2022), to perform the multiwave disease prediction.

Recall that the web search frequency vector $\mathbf{h}_{t}^{v_{i}}$ reflects the number of potential infected individuals in the urban district $v_{i}$ and $\mathbf{E}_{t}$ records the daily inter-district trips. We therefore perform the convolution operation on $\mathbf{h}_{t}^{v_{i}}$ using the $\mathbf{E}_{t}$ information under the graph neural network framework to capture the disease risk propagation properties. As shown in Figure 2, using the symptom-related web search frequency in each urban district, we employ the one-hot encoding to initialize the representation for each urban district (i.e., each node in $G_{t}$) as the input matrix: $\mathbf{X}_{t}^{(0)}=\mathbf{H}_{t}$. Following the GCN model (Kipf and Welling, 2016), we define the node representation propagation rule between the layers $k$ and $(k+1)$ as:

where

and $\mathbf{W}^{(k)}$ is a learnable weight matrix, $\mathbf{I}_{n\times n}$ is the $n$ by $n$ identity matrix, $\sigma(\cdot)$ is the activation function ReLU.

Note that we normalize the matrix $\mathbf{E}_{t}$ such that the sum of each column is equal to 1 (i.e., the sum of incoming edges on one node is 1), which is used in the existing study (Panagopoulos et al., 2021). In practice, it is possible to replace the spectral convolution with other GNN variants such as GAT (Veličković et al., 2017), GraphSage (Hamilton et al., 2017). We also implement them and find quite approximate prediction performance as the GCN. The outcome of the spatial module is a matrix

with $n$ rows that encode the web search frequency and mobility where $K$ is the number of layers.

The symptom-related web search frequency is positively related to the number of actual symptom occurrences among the population (Yabe et al., 2021). As mentioned earlier, the social awareness decay effect informs that probability of symptom-related word searching gradually decreases with time after the first COVID-19 wave. To estimate the actual symptom occurrences, we propose to multiply the observed web search representation by a monotonically increasing function with respect to the time.

Specifically, we first linearly normalize each entry of the web search record vector $\mathbf{h}_{t}^{v_{i}}$ to 0 and 1 by the maximal and minimal web search frequency of each word across all days in the urban district $v_{i}$, and feed them into the spatial module, and obtain $\mathbf{H}_{t}^{S}$. Next, we define an increasing function $r(t|i,t_{0})=e^{\lambda_{i}^{2}(t-t_{0})}$ regarding $t$ to recover the social awareness:

where $\lambda_{i}^{2}$ is learnable and measures the social awareness recovery rate in $v_{i}$. $t$, $t_{0}$ represent the current day and the first day of the study period, respectively. Given that the land use, economy type, demographic characteristic discrepancy may lead to spatially varying social awareness rates, we specify district-dependent $\lambda_{i}^{2}$ to encode its unique awareness decay behavior. A large value of $\lambda_{i}^{2}$ implies that social awareness of COVID-19 for residents living in $v_{i}$ declines rapidly and we therefore adopt this large value to recover the social awareness. Note that we introduce the square in $\lambda_{i}^{2}$ to ensure that it is non-negative. Collectively speaking, the social awareness recovery module transforms $\mathbf{H}_{t}^{S}$ to $\tilde{\mathbf{H}}_{t}^{S}$ by

where $\mathbf{M}_{t,t_{0}}$ is the awareness recovery matrix (ARM):

and $\circ$ is the Hadamard product. This transform implies that the entries in $\mathbf{H}_{t}^{S}$ are amplified to capture the actual disease risk which is underestimated due to the social awareness decay effect when $t$ is large. In the end, we perform 0-1 normalization on the infection matrix $\mathbf{I}_{t}$ to obtain $\tilde{\mathbf{I}}_{t}$, and arrive at the output of the social awareness recovery module by concatenating the web search and infection representations, which is

To capture the temporal dependency of district-level features and infection cases, we adopt the existing LSTM model (Hochreiter and Schmidhuber, 1997). For $i\in\{1,2,...,n\}$, we extract the $i$-th row of matrices $\mathbf{H}_{t}^{A},t\in[T-D_{1}+1,T]$ and feed them into an LSTM sequence (Figure 2). Since we have already modelled the spatial dependency in the spatial module, in the temporal module we pass the node representations from $\mathbf{H}_{t}^{A}$ separately for different nodes, and these LSTM sequences share the identical structures and parameters.

Recall that our objective is to perform the infection case prediction for the next $D_{2}$ days, we define the loss function as the mean squared error, which is:

where $I_{t,i}$ and $\hat{I}_{t,i}$ denote the actual and predicted infection cases for the district $i$ on the day $t$. We present the training process as Algorithm in Supplement.

We utilize four datasets: infection cases, mobile phone location data, web search data, and symptom data in Tokyo from Jan. 6, 2020, to May 15, 2021. The mobility and web search data were owned by Yahoo Japan Corporation with strict privacy protection regulations. The descriptions of these data are as follows:

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  Infection data. We access the daily new infection cases for 23 wards of Tokyo from the Tokyo COVID-19 Task Force website (Tokyo COVID-19 Task Force Website, 2021) which is maintained by Tokyo metropolitan government and open to public.

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  Mobility data. Table 2 in Supplement presents a sample piece of raw mobility data. The mobility data consists of a fake ID (after privacy protection operations), the user’s geolocation in terms of longitude and latitude at a specific time. The data collection frequency was around 30 mins on average, which depends on the movements of the user: the frequency is higher if the user moves faster. In this study, the mobility data is utilized to identify Tokyo residents’ home locations and mine the Mobility Matrix $\mathbf{E}_{t}$.

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  Web search data. Table 2 in Supplement presents a sample of raw web search record. Each record contains the user ID, web query words, as well as web search time. The web search data is used to get COVID-19 symptom-related web search counts. Note that Yahoo Japan Corporation maintains these data to promote users’ experiences and does not share any individual-level data with other agencies.

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  Symptom data. Based on two existing COVID-19 symptom studies (Sarker et al., 2020; Wang et al., 2021) and the COVID-19 symptom list released by the Centers for Disease Control and Prevention (Centers for Disease Control and Prevention, 2021), we finally specify 44 symptoms, which are used to measure the counts of symptom-related web search records. These symptoms are shown in Table 3 in Supplement. We translate these symptoms from English to Japanese, and then count the number of corresponding web searches in Japanese. Note that a few symptoms have a large number of web search counts, and we therefore utilize the most frequent $1\leq n_{w}\leq 44$ symptoms in our prediction framework.

Note that the raw mobility and web search data are at the individual level. To prepare the features $\mathbf{E}_{t}$, $\mathbf{H}_{t}$ used in the machine-learning framework, we conduct the data preprocessing to aggregate the raw mobility and web search data to the urban district level. Please find the complete description of data prepossessing in the Appendix.

The statistics of aggregate daily new infection cases, web search number, and inter-district trip number are shown in Figure 3. The vertical dash lines in Figures 3ac mark March 1, 2020, May 1, 2020, and January 1, 2021, whose web search distribution and mobility flow are visualized in Figures 3bd, respectively. We find from Figure 3a that the dynamic of symptom-related web search exhibits consistent peaks with daily infection cases, especially near April 2020, January 2021, and May 2021, which provides the direct evidence to inspire us to utilize the web search data in the multiwave pandemic prediction.

We conduct experiments to predict two outbreak waves, i.e., the third wave (from Dec. 10, 2020 to Feb. 7, 2021) and the fourth wave (from March 17 to May 15, 2021). The period for each experiment covers 10 months of observations where the train/validation/test ratio is 70%/10%/20%. We use the first 8 months (months 1 to 8) as training and validation data, and the last 2 months (months 9 and 10) as testing data. Note that the validation data has the size of 1 month and is evenly distributed from months 7 to 8. Since most existing disease prediction studies (Panagopoulos et al., 2021; Rodriguez et al., 2021; Wang et al., 2020) predict the infection at the week-level, we design three scenarios: $(D_{1},D_{2})=(21,7),(21,14),(21,21)$ (recall that we use the past $D_{1}$ days’ features to predict the future $D_{2}$ days’ infection cases).

We train the model using PyTorch and Adam optimizer (Kingma and Ba, 2014). We use the validation set to determine the learning rate as 1e-4, the epoch number, the batch size, and the dropout rate as 100, 8, and 0.50, respectively. The experiments run on an Intel Xeon w-2155 3.3 GHz CPU and 32 GB of RAM. Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are utilized to evaluate the prediction performance: RMSE = $\sqrt{\frac{1}{D_{2}n}\sum_{t=T+1}^{T+D_{2}}\sum_{i=1}^{n}(I_{t,i}-\hat{I}_{t,i})^{2}}$, MAE = $\frac{1}{D_{2}n}\sum_{t=T+1}^{T+D_{2}}\sum_{i=1}^{n}|I_{t,i}-\hat{I}_{t,i}|$.

To benchmark our model, we also implement 9 existing prediction models: (1) Historical average (HA) infection cases until the day $T$; (2) Historical average of the last $D_{1}$ days; (3,4) LSTM; (5,6) Seq2seq: encode the input infection case and decode the sequence using two separate LSTMs (Cho et al., 2014); (7) ST-GNN: an Spatio-Temporal GNN model whose inputs are past infection cases and mobility patterns (Kapoor et al., 2020); (8) MPNN+LSTM: a message passing neural network with the LSTM (Panagopoulos et al., 2021); (9) GraphLSTM: a prediction frameworks integrating GraphSage and LSTM (Sesti et al., 2021).

We present the prediction performance of the SAB-GNN and other baseline models for the third wave and the fourth wave (Table 1). Our proposed SAB-GNN model yields the smallest MAE and RMSE for most scenarios (5 out 6), which demonstrates our model captures the relationships between past infection, web search, mobility, and future infection. Comparing SAB-GNN and SAB-GNN-wsa (without social awareness recovery), the social awareness recovery mechanism decreases the prediction error for most cases (5 out of 6), and the web search frequency has higher predictability after the awareness recovery operation.

Besides, results from all models reveal a general tendency that the web search and mobility features result in prediction performance improvement, even if the past infection case is already a strong feature to connect with the future infection case. Finally, we observe from the LSTM and Seq2seq that simply concatenating the web search frequency embedding with the past infection cases is unable to consistently boost the prediction, which affirms the necessity of designing a suitable model architecture to utilize the web search data. For each model in Table 1, the running time for each scenario is within 20 minutes on the Ubuntu system with 32 GB RAM and 3.3 GHz Xeon w-2155 CPU.

We visualize the prediction errors and compare the predicted cases with the actual cases for each urban district in Figures 4, 5. As shown in Figures 4ab, the relative prediction errors for most districts are homogeneously lower than 0.50 except for the central district (i.e., Chiyoda). This reveals that SAB-GNN mines the relationships between features and future infection cases in a global manner thanks to the message passing mechanism among neighborhood nodes. The reason for the relatively large prediction error in Chiyoda (i.e., District 1) is because Chiyoda is where Imperial Palace locates and has quite a few real infection cases (Figure 5, the top-left panel). Figure 4c displays that the predicted daily case curve is able to capture the increasing tendency of actual cases from day 240 to day 280 and also maintains a small prediction error, which further demonstrates the power of our proposed SAB-GNN.

Figure 5 exhibits that for most urban districts, the model is able to anticipate the general increasing tendency of infection cases during the fourth wave. This information is especially valuable for local public agencies to make timely preparations at the beginning of a wave. Note that the prediction of District 4 (i.e., Shinjuku) is not as accurate as other districts. One potential interpretation is that Shinjuku is a commercial area with many entertainment industries and thus does not have similar infection patterns as other districts.

The influences of model parameters in the SAB-GNN on the prediction performance are shown in Figure 6. Figure 6a displays the changes of RMSE for the fourth peak prediction with respect to $n_{w}$ (i.e., numbers of symptom-related web search features used in the model). Recall that there is a huge frequency discrepancy between different symptoms and we only feed the most frequent $n_{w}$ symptoms into our model. The result suggests that $n_{w}=8$ provides the best prediction performance. The underlying reason is that: when $n_{w}$ is small, more symptoms contribute stronger connections with future infection cases; when $n_{w}$ is large, many weakly-related symptoms bring noises to the training and thus harm the prediction performance.

Next, we tune the numbers of layers $L_{1},L_{2}$ in the GNN and LSTM modules (Figures 6bc) and conclude that $(L_{1},L_{2})=(1,2)$ yields the best prediction. It is reasonable that the simple model with a small number of parameters is preferred in this infection case prediction task whose training data is at the hundreds level (Qiu et al., 2021) (each day is associated with one training sample). Finally, we test the model in Figure 6d with varying $D_{1}$ and $D_{2}$ and observe the overall tendency that using more days’ (i.e., $D_{1}$ is large) information to predict later fewer days’ (i.e., $D_{2}$ is small) results in higher accuracy, which is consistent with the finding from the existing study (Panagopoulos et al., 2021).

To confirm the effect of each module in the SAB-GNN on prediction results, we perform the ablation experiments for both the third wave and fourth wave (Figure 7). We remove one of the three modules in the SAB-GNN, and perform the prediction for the same temporal horizons as the full SAB-GNN model. We show quantitatively that the SAB-GNN model obtains lower prediction RMSE than other incomplete models, especially for the third wave, which reveals that both the spatial module, temporal module, and social awareness module contribute to the final prediction results in a positive manner. While existing studies have paid much attention to the spatial and temporal relationships between features and infection cases, we recommend introducing suitable social knowledge into the prediction, given the positive effect of the social awareness recovery mechanism.