# A Mobility-Aware Deep Learning Model for
Long-Term COVID-19 Pandemic Prediction and Policy Impact Analysis

1st Danfeng Guo, Zijie Huang, Junheng Hao, Yizhou Sun, Wei Wang, Demetri
Terzopoulos  Department of Computer Science
University of California, Los Angeles
Los Angeles, USA

###### Abstract

Pandemic(epidemic) modeling, aiming at disease spreading analysis, has always
been a popular research topic especially following the outbreak of COVID-19 in
2019. Some representative models including SIR-based deep learning prediction
models have shown satisfactory performance. However, one major drawback for
them is that they fall short in their long-term predictive ability. Although
graph convolutional networks (GCN) also perform well, their edge
representations do not contain complete information and it can lead to biases.
Another drawback is that they usually use input features which they are unable
to predict. Hence, those models are unable to predict further future. We
propose a model that can propagate predictions further into the future and it
has better edge representations. In particular, we model the pandemic as a
spatial-temporal graph whose edges represent the transition of infections and
are learned by our model. We use a two-stream framework that contains GCN and
recursive structures (GRU) with an attention mechanism. Our model enables
mobility analysis that provides an effective toolbox for public health
researchers and policy makers to predict how different lock-down strategies
that actively control mobility can influence the spread of pandemics.
Experiments show that our model outperforms others in its long-term predictive
power. Moreover, we simulate the effects of certain policies and predict their
impacts on infection control.

###### Index Terms:

graph mining, pandemic modeling, spatial-temporal graph, COVID-19

##  I Introduction

COVID-19 is an infectious disease caused by SARS-CoV-2. This disease has
rapidly spread all over the world since its discovery in December 2019.
Recently, the wide spread of its Omicron variant has further exacerbated the
pandemic and brought it back into the headlines. To date, millions of people
have contracted COVID-19 and it has caused high death tolls, dramatically
evolving from a healthcare system crisis into a worldwide socioeconomic
disruption. This sharply increases the demand for pandemic models that predict
the spread of infections.

Pandemic modeling refers to predicting disease-related statistics in a region
(e.g., state-level daily new cases and deaths) based on historical data. It
helps identify potentially high-risk groups, so that our public health
officials can deploy medical resources in preparation for large-scale
outbreaks of infection. Models that can simulate the effects of multiple
alternative policies in order to assist the decision-making processes of
policy makers would also be helpful.

The challenge of pandemic modeling lies not only in the availability of data,
but also in the complexity of the available data. In addition to the pandemic
statistics, one should also consider mobility data, which reflects the
activity level of residents within a region or across regions. Mobility data
provides information on the spread of disease, because higher mobility usually
leads to more contact, which increases the chance of infection (Fig. 1). Other
demographic and geographic statistics should also be included in pandemic
modeling, such as the population. Since pandemic models may be used to assist
decision making for public health policy, another challenge is that they are
expected to predict further into the future—e.g., 3 weeks, one month, or even
longer, rather than merely predicting the result tomorrow or next week.

Figure 1: The explosion of new COVID-19 cases across the USA after
Thanksgiving is relatable to high mobility nationwide during the holiday
season.

The majority of pandemic models extend the traditional SIR model [1]. It
models the relation among susceptible group, infected group, and recovered
group, and uses the transition rate to compute the number of newly infected
people. Although they may be simple and sometimes less accurate, SIR-based
models are reasonably predictive. In recent years, deep-learning models
powered by data science and neural networks have been widely explored to
predict pandemic growth. With regions represented as nodes in graphs, pandemic
modeling is formulated as a graph mining problem. Graphical Convolutional
Networks (GCN) [2] is an intuitive method to forecast pandemic growth based on
regional and connectivity information. Recursive structures, such as the Gated
Recurrent Unit (GRU) [3] and Long-Short Term Memory (LSTM) [4], have also been
applied to encode pandemic progression through time. Recent GCN approaches
have achieved success in spatio-temporal pandemic forecasting [5].

Compared with simpler SIR-based models, deep-learning-based models take a
wider range of input features into consideration, are more sophisticated, and
sometimes have better performance. However, they have certain explainability
and interpretability issues. The representation of graph edges usually does
not contain complete information. Another issues is that currently most deep-
learning-based models are short-term models that cannot propagate their
predictions into the long-term future. For example, they use all historical
data only to predict the results on the 7th day from the present. If they must
predict another day into the future, the models must be re-trained. Such
models may have good short-term performance but are unsatisfactory in the long
run. Most of them suffer from large error increases. In addition, they usually
use some input features which they do not predict. The lack of those features
prevents them from predicting further future. However, longer-term prediction
results are much more helpful because they give our public health officials
more time to respond.

The deficiencies of existing epidemic models motivate us to develop a model
that is able to propagate its predictions further into the future and has
better edge design. In this paper, we propose a new two-stream, multitask GCN-
GRU framework. It is a spatio-temporal model that encodes information on the
graphical level during a time span. Our model exploits both pandemic
statistics and mobility information. It has the following four main merits:

  * •

All input features we use is either static or can be predicted by our model.
Hence, our model is able to propagate the predictions further into the future.
It is also more robust in predicting long-term results. This is shown by
comparing our model with others in terms of longer-term predictions.

  * •

The edge weights in our model are learned from multiple factors which are
related to pandemic spread.

  * •

Our model applies an attention mechanism which makes it focus on days most
relevant to prediction.

  * •

We are able to simulate our model under different mobility control policies
and evaluate their impacts, which provides an insight to policy makers.

We test our model on the COVID-19 pandemic prediction task at the state level
within the U.S., showing that it generally outperforms others on predicting
cases 2 weeks ahead and 3 weeks ahead. We also simulate different mobility
control policies and use our model to evaluate their effect in reducing
confirmed cases. Lastly, our model is not limited to COVID-19, but can be
applied to other epidemics which is related to mobility.

##  II Related Work

Models |  Year |  Structure |  Edge Representation | Long-term prediction
---|---|---|---|---
ColaGCN[5] |  2020 |  RNN-GCN |  Geographic adjacency | No
Kapoor[6] |  2020 |  GCN |  Mobility & time | No
ITCGN[7] |  2021 |  GCN |  Geographic distance & time | Yes
STAN[8] |  2021 |  GCN-RNN |  Demographic & geographic similarities | No
Fritz[9] |  2021 |  GCN |  Social connection | No
UNITED[10] |  2021 |  GCN-LSTM |  Mobility | No
La Gatta[11] |  2021 |  GCN-LSTM |  Mobility | No
Ours |  |  two-stream GCN-GRU |  Learned by model | Yes
TABLE I: GCN pandemic models.

#### Traditional SIR/SEIR-based models

The first epidemiology model to be considered is the SIR model [1]. It
consists of three variables: $S$ for the number of susceptible individuals,
$I$ for the number of infected individuals, and $R$ for the number of
recovered or immune individuals. The incremental cases are determined by $S$,
$I$, the regional population, and the computed transition rate. Subsequently,
the SEIR [12] model introduced a new variable $E$, which is the number of
individuals exposed to the disease yet remain asymptomatic. The SuEIR model
[13] makes a further improvement by including individuals that are infected
but untested. DELPHI [14] is another improved SEIR-type model that includes
the underdetection group and outside intervention. [15] developed a recent
SIR-based model that includes the infections not caused by mobility. [16]
introduces an additional mobility network into SEIR that improves performance.

#### Graph-based neural network models

Graph analysis powered by machine learning has been developing quickly. GCN
combined with recurrent structure has become a widely used baseline model for
spatial-temporal data analysis. [17] uses an adaptive learning module to learn
the feature of each node as well as the adjacency matrices. The learned
variables are fed into a GCN to encode the spatial features. Then GRU is used
to encode the temporal features. [18, 19] also use GCN, while 1D-convloution
is applied to encode the temporal features. Later, [20] moves one step further
and it embeds GCN into GRU by replacing the matrix multiplications with
graphical convolutions. [21] applies Discrete Fourier Transform to convert
data from time domain to frequency domain and then performs graphical
convolutions. Inspired by those works, researchers have started to formulate
epidemic prediction as a dynamic graph problem, where the nodes represent
target areas with some associated features. [5] proposes ColaGNN, which uses a
Recurrent Neural Network (RNN) to encode the temporal features of each node
and a GCN to encode the spatial features of the whole graph. The edge weights
are the addition of the geographical adjacency matrix and a locally-aware
attention map is computed using the RNN output features. By contrast, [6]
applies a large GCN to encode both spatial and temporal information. At the
spatial level the graph edges encode mobility, and at the temporal level the
edges represent binary connections to earlier days. IT-GCN [7] also includes
spatial and temporal nodes as a large graph whose edges represent the
geographical distance and time connection to earlier days. [9] uses a GCN to
encode the mobility data. The encoder output is concatenated with the epidemic
features and passed to a neural network for prediction. Another GCN-RNN model,
STAN [8], designs nodes as regions with both static and dynamic features, and
the edges represent demographic and geographic similarities. An attention
mechanism is incorporated into the GNN for interaction between neighbors. [10]
uses GCN-LSTM model and designs the edges as the mobility between locations.
The model performs well in predicting the COVID-19 pandemic in England, Spain,
Italy, and France. [11] creates a two-stage model that uses GCN-LSTM to
compute the key factors in SIR, such as the contact rate.

Table I summarizes the aforecited deep-learning-based pandemic models. A
problem common to all of them is that their edge representations may not
provide a good approximation of pandemic spread. They formulate their edge
weights only using one of the infection data, mobility data, and other static
regional features, which only contains partial information. For example, most
models use mobility as edge weights and they ignore the fact that the number
of disease-carriers can be small even though the mobility is large. A more
causal and reasonable approach would include at least both the mobility data,
infection statistics, and other demographic/geographic features. A second
problem is that all these models set an $N$-day window length for data and
predict the results after 1 day, 1 week, or 2 weeks. For example, the model of
[10] is trained to predict the number of cases on the 7th future day. Most of
these models are unable to propagate to more distant days because some input
data is unavailable. For instance, medical claim data used in [8], Facebook
human mobility and connections used in [9, 10], and the radius of people
gyration used in [11]. In addition, although their short-term results seem
satisfactory, an obvious error increase is observed as the prediction time
span increases and they may fail to predict 21 days or one month ahead.
Although IT-GCN is able to predict long future, it only inputs daily case
numbers and its use of geographical distance as edge weights is also
problematic. Another problem lies in the recurrent structures. In traditional
RNN/LSTM, the closest token usually has the largest influence on the results
and farther-away tokens may be discounted or forgotten. However, this may not
be the case for epidemic modeling, since data from earlier days may also play
an important role.

#### Other models

Aside from the above two categories, there exist other pandemic models: e.g.,
Gaussian-based models [22], Hawkes Process models [23, 24], and Graph ODE
models [25].

##  III Methodology

###  III-A Problem Formulation

At time $t$, a graph is represented as
$G^{(t)}=(\textit{V},\varepsilon^{(t)})$, where V is the set of nodes (with
nodal features) and $\varepsilon^{(t)}$ is the set of directed, weighted
edges. In our application, the nodes represent the regions at a certain level
of granularity (e.g., cities, counties, or states). For each pair of nodes,
there is one forward edge and one backward edge indicating the spread of
disease from one state to the other. They are represented by an adjacency
matrix $A\in\Re^{N\times N}$, in which element $A_{ij}$ indicates infections
from state $i$ to state $j$. Within a time span $K$, there is a set of graphs
$\\{G^{(1)},G^{(2)},G^{(3)},\dots,G^{(K)}\\}$. Hence, the input feature set is
formed as $X\in\Re^{K\times N\times D}$, where $N$ is the number of nodes and
$D$ is the node feature dimension. The mobility input is $W\in\Re^{K\times
N\times N}$

Given the inputs $X\in\Re^{K\times N\times D}$ and $W\in\Re^{K\times N\times
N}$, our task is to design a model that predicts the graph of Day $K+1$;
specifically, node features $X^{(K+1)}\in\Re^{N\times D}$ and the mobility
$W^{(K+1)}\in\Re^{N\times N}$. This muti-task learning strategy also yields
two main advantages. Firstly, learning $X^{(K+1)}$ and $W^{(K+1)}$ shares
similar features, so learning them simultaneously can make the model focus on
learning these shared features, thus reducing overfitting. Secondly, we can
use the predicted outputs as new inputs to predict the results of subsequent
days.

###  III-B Edge Representation

As mentioned earlier, existing deep-learning-based pandemic models do not have
a good edge representation. An edge should represent the spread of infection
and it results from the interaction of multiple complex factors including
pandemic statistics, mobility patterns, demographic features, etc. Hence, we
design our edges as variables learned from those factors. The idea of using
learned edges has already been shown helpful in [17] and [20]. [17] points out
that, for traffic forecasting problem, simply using one feature such as node
distance or node similarity as edges does not provide complete information,
which may result in considerable biases. Hence, they prefer the graphs to be
learned instead of pre-defined. [20] proposes that the graphs can be learned
when they are unknown. In our case, the pandemic graph can also be regarded as
unknown because we do not have the number of infected travellers and it can
only be estimated from multiple factors.

###  III-C Model

Figure 2: Our pandemic prediction model. Both predicted cases and mobility can
be used as further inputs, enabling our model to predict the longer term.

Given that we use mobility data as input, our model must be able to predict it
so that it can propagate to the future. Hence, we use two-stream structure as
shown in Fig. 2. The top stream takes pandemic statistics as inputs and
returns the predicted pandemic statistics. It uses GCN to encode spatial
features and GRU with attention to encode temporal features. The output of the
GRU is fed to a Multi-Layer Perceptron (MLP) decoder to generate the
predictions. The bottom stream uses previous mobility, pandemic statistics and
demographic features to predict the future mobility and generate the edge
weights for the GCN layers in the other stream. The inputs first come to a GRU
encoder. The GRU output goes in two directions: one to an attention mechanism
followed by an MLP decoder that generates the predicted mobility data, and the
other goes to an MLP adjacency generator that generates the edges.

#### Learned Edges

As mentioned previously, the bottom stream extracts information from previous
mobility, pandemic statistics and demographic features. The extracted
information comes to an adjacency generator, which acts as a multitask head to
generate the edges at all time steps. The adjacency generator is a stack of
linear blocks with LeakyReLU gates. Sigmoid activation is attached to the end.

#### GCN

We use the GCN developed by [2]. For each node $v$, given its current
representation $x_{v}$, neighbor $\mu\in\varepsilon$, and neighbor
representation $x_{\mu}$, the GCN updates $x_{v}$ using its neighboring
information. Generally,

$X_{\text{new}}=\sigma(\hat{D}^{-\frac{1}{2}}\hat{A}\hat{D}^{-\frac{1}{2}}XW),$
(1)

where $\hat{A}$ is the adjacency matrix with self-loops, $\hat{D}$ is a
diagonal matrix where $D_{ii}=\sum_{j}A_{ij}$, the learnable parameter is $W$,
and $\sigma()$ is the activation function.

Figure 3: The GRU attention mechanism. The output is represented as a weighted
sum of sequential features.

#### GRU

Our task involves the processing of sequential data, i.e., the dynamic changes
of graph nodes and edges through time. Recurrent structures such as the GRU
and LSTM are used to encode this type of information. Although the LSTM was a
popular choice in prior work, we choose the GRU for our model. Both the GRU
and LSTM aim to address the vanishing gradient problem. Compared with the GRU,
the LSTM performs better in processing long sequences, but the sequence for
our model will not be very long. Furthermore, the LSTM has more parameters and
may easily overfit our limited amount of data.

#### Attention Mechanism

The attention mechanism of the GRU/LSTM was first developed by [26]. The key
idea is to use the hidden outputs of all tokens instead of only that of the
last token. The final output is a Softmax weighted sum of the hidden outputs
of all the tokens. The weight of each hidden output indicates the level to
which the predicting target is related to the corresponding token features. In
this way, the model can automatically search for tokens relevant to the
predictions. The attention mechanism is formulated as

$\displaystyle\begin{split}&\text{Output}=\sum_{t=1}^{K}\alpha^{(t)}h^{(t)},\\\
&\\{\alpha^{(1)},...,\alpha^{(K)}\\}=\text{Softmax}(g(h^{(1)}),\dots,g(h^{(K)}),\end{split}$
(2)

where $h^{(t)}$ is the hidden output at position $t$ and $\alpha^{(t)}$ is the
corresponding weight computed by passing $h^{(t)}$ to a neural network
function $g()$. Fig. 3 shows the structure of our attention mechanism. To
process the features at each time step, we use two linear layers with Tanh
activation in between. Then the features at each time are averaged and passed
to a Softmax function to become the feature weights. The final features are a
weighted sum of all the features across the sequence. The use of the attention
mechanism is important. Given that it usually takes days for an infected
person to develop symptoms, we assume that the data of earlier days should
have more importance than that of neighboring days. Additionally, when the
model propagates the predictions to later days, previously predicted results
are used as inputs to generate later results. In this situation, the attention
mechanism can mitigate the influence of the previous prediction errors by
assigning less weight.

###  III-D Training

Our overall loss function is a multitask loss:

$L=w_{1}\cdot\text{MAE}_{\text{case}}+w_{2}\cdot\text{MSE}_{\text{case}}+w_{3}\cdot\text{MSE}_{\text{mobility}},$
(3)

where MAE and MSE stand for the Mean Absolute Error ($L_{1}$) loss and Mean
Square Error ($L_{2}$) loss, respectively, and the hyperparameters $w_{i}$
balance the trade off between the two tasks.

##  IV Experiments and Results

###  IV-A Experiment Setting

We perform COVID-19 prediction at the state level based on data from the USA.
The graph nodes represent the 50 states plus Washington, DC, for a total of 51
nodes. For our model inputs, we use the previous daily cases, cumulative cases
and regional population to predict the upcoming daily cases. (population is
fixed) Regarding the mobility prediction, we use previous mobility, cumulative
cases and the weekday indicator (integers 0 through 6 represent Monday through
Sunday) as inputs. We include weekdays because mobility has a weekly pattern
that may be helpful to prediction. We choose the window length of previous
data equal to 15. (We discuss this in our ablation study below)

Our mobility data comes from the SafeGraph Mobility dataset [27], which
contains rich mobility information at different granularities. Each location
is assigned an ID and the movement from one ID to another is recorded. We
collected mobility information from 2020/02/01 to 2021/03/31 (424 days) and
grouped it by state. The COVID-19 statistics were obtained from the CDC
Pandemic Data Tracker [28], which provides key statistics of COVID-19 for each
state and DC. We extracted the state-level daily new cases from 2020/02/01 to
2021/03/31. The reason we choose this period is that, vaccinations in the U.S.
started to increase rapidly since Apr 2021. The effect of vaccination is not
included in our model. Therefore, data after Apr may lead to significant
biases. Another reason is that, SafeGraph stopped providing daily mobility
data after May 2021. The data from from 2020/02/01 to 2021/01/31 (366 days)
were used for training and validation. The data from 2021/02/01 to 2021/03/31
(59 days) were used for testing.

Our model was trained using the RMSProp Optimizer for 150 epochs. The learning
rate is $10^{-3}$ and decays every 10 epochs by $10\%$. The weights in the
multitask loss (3) were $w_{1}=1.0$, $w_{2}=1.0$, and $w_{3}=0.5$. Experiments
were run on a Tesla P100. The results were evaluated using the Mean Absolute
Error (MAE). Regarding the evaluation metrics, percentage error could be an
option. However, we notice that the state-level cases vary hugely. The daily
new cases of some states can be less than 10 while other states can have more
than 30,000. Percentage error is not a suitable measure because a small error
in states with few cases may lead to a very large percentage error.

###  IV-B Baseline Models

We compare our model with widely-used benchmarks for state-level prediction of
new cases in the US, including both SIR-based models and deep-learning-based
models. They are:

GCN-LSTM: It is one of the most common spatial-temporal models. It is used by
[11, 10], a recent model for COVID-19 prediction and shares the most
similarities with our model. It uses GCN to encode spatial information and
LSTM to encode temporal information. The difference is that, it has one stream
and the edge represents the mobility. We did not compare our model with those
models directly because we lack specific pandemic statistics, such as the
number of hospitalized patients in [11].

GCN-TSFM: As the success of transformers in natural language processing,
people start to explore its potential on processing time-series data [29]. For
traffic prediction tasks, the recurrent structure in GCN-RNN models could be
replace by transformers, which can lead to performance improvement [30].
Hence, we also apply transformers to our model and report the performance.

ISOLAT-Mixture [31]: Developed by MIT, it views the curve of daily cases as
the sum of multiple Gaussian curves each of which represents an outbreak.

Bucky [32]: It is a spatially distributed SEIR model developed by Johns
Hopkins University. It consists of a collection of multiple SEIR models, which
are stratified via the age demographic structure of a geographic region.

SuEIR [13]: It is a variant of SEIR model proposed by UCLA. It includes the
estimation of untested/unreported cases of COVID-19.

DELPHI [14]: Similar to SuEIR, it includes underdetection and also considers
the effect of government intervention.

(a) 2-weeks-ahead MAE for Feb 2021. Feb 6 is excluded because our model uses
data up to Jan 31 for training. UCLA-SuEIR misses the prediction on Feb 27.

(b) 2-weeks-ahead MAE for Mar 2021.

(c) 3-weeks-ahead MAE for Mar 2021. UCLA-SuEIR misses Mar 6.

Figure 4: MAE comparison. The forecasts of ISOLAT-Mixture, Bucky, SuEIR and
DELPHI were retrieved from the COVID-19 Forecast Hub repository [33].

###  IV-C Results

The results are reported in the form of weekly cumulative new cases. The week
used is the epidemiological week defined by the US CDC, which runs Sunday
through Saturday. We made the comparison using results in February 2021 and
March 2021. All predictions were made 2 weeks in the future, which means that
only data up to 2 weeks prior to the target date (before Jan 17) were made
available. We also generated predicted results using data up to 3 weeks prior,
for which data before Jan 10 were available. The reason to choose 2 weeks and
3 weeks is to follow the rule of [33], which is a public COVID-19 forecast
repository where researchers report and compare their results. Predictions are
all published as 2-weeks-ahead and 3-weeks-ahead.

The result comparisons are shown in Fig. 4. Note that our model has less error
than GCN-LSTM, which illustrates that our learned edge representation works
better than pure mobility. We also notice that transformer does not show
expected performance on our task. One possible explanation could be the
limitation of data. Transformers usually take a large amount of data to train,
while we only have data for one year. Comparing across the two figures, one
notices that several models suffer a large error increase when the prediction
is changed to 3-weeks-ahead, as is summarized by Table II. Our model has the
smaller error increase. GCN-TSFM has the minimum error increase, which
benefits from its global attention mechanism. We belive that, in the future,
with sufficient amount of data, it could achieve better performance.

Models | Increase in MAE
---|---
JHUAP-Bucky | 636
MIT-ISOLAT Mixture | 640
UCLA-SuEIR | 1279
MIT-DELPHI | 630
MPNN-LSTM | 650
GCN-TSFM | 271
Ours | 608
TABLE II: Average MAE increase for March 2021 after changing the prediction
from 2-weeks-ahead to 3-weeks-ahead.

###  IV-D Ablation Studies

The window length (number of days used for predictions) is an important
parameter during the training phase. The attention mechanism provides guidance
on tuning because the attention weights reflect how important one day’s data
is. Hence, we initially set the window length to $K=30$, and the average
attention weights are shown in Fig. 5. There is a valley from Day $N-17$ to
Day $N-27$, which indicates that the data from 27 days prior to 17 days prior
is less useful for prediction. Hence, the model may have better
generalizability by choosing smaller window lengths. We conducted another
three experiments, setting window lengths to 10, 15 and 45. The results are
compared in Fig. 6(a). We choose $K=15$ as our final setting. Lastly, we
conducted another experiment in which we disabled the attention mechanism to
assess its contribution. The result, in Fig. 6(b), shows that adding attention
generally improves model performance.

Figure 5: Average attention weights from Day $N-30$ to Day $N-1$. Length of
data is 30.

(a) (b)

(c)

Figure 6: (a) Comparison of models with different time window lengths. (b)
Ablation study of the attention mechanism. (c) Average MAE with different
values of $w_{3}$.

We also studied how the multitask weights in Eqn. (3) affect accuracy. We set
$w_{1}=w_{2}=1.0$ and tuned $w_{3}$ over a set of values. The result is shown
in Fig. 6(c), and we chose $w_{3}=0.5$ as the preferred setting.

###  IV-E Policy impact analysis:

Government intervention can play an important role in controlling the spread
of pandemics. Policy makers should make effective intervention policies and
mobility control is a crucial part of such policies; for example, the stay-at-
home orders enacted in many countries, states, counties, and cities. Since
mobility control policy has a broad impact on society as a whole, it is
important to estimate its effect in advance, such that policy makers can
assess the trade-off between the negative socioeconomic impact and infection
control.

To this end, we used our model to simulate the effect of two mobility
policies: reducing mobility by half and stopping interstate travel. For the
first simulation, we manually reduced the mobility data by a half and for the
second, we added all interstate mobility back to the origin states and zeroed
out the interstate mobility. We assumed that the interstate travelers would
choose to travel in their own states. All mobility manipulations start from
2021/02/01 and the policy impact is evaluated from 2021/03/01 by the
cumulative change of new cases. The results are shown in Fig. 7(a) and 7(b).
Fig. 7(a) reveals that reducing mobility by half does help to reduce the
infections on a certain level. All states have the new cases reduced except
for California. The cases in Georgia, New Jersey, South Carolina, and Florida
reduce by more than 100. A more interesting result is Fig. 7(b). In some
states, cutting off interstate travel does substantially reduce the new cases.
Especially in Missouri, the number of new cases decreases by over 1,000, which
shows that a large portion of new infections come from outside instead of from
the local residents. However, several states show an increase in cases. This
phenomenon is also explainable as there are virus carriers among the
interstate travelers. When they are kept in their origin states, there are
likely to be more infections in those states. We further explored this policy
by isolating one state, California. Per Fig. 7(c), most states show a decrease
and this sheds light on the infection output of California.

(a) Reducing mobility by half

(b) Stopping interstate travel

(c) Isolating California

Figure 7: Change of total new case prediction in March 2021 with the policies
of (a) reducing mobility by half, (b) stopping interstate travel, and (c)
isolating California.

Neither Fig. 7(a) nor 7(b) show a large decrease in cases. One possible
explanation could be that the USA experienced an infection peak in Feb, 2021,
when the daily new cases nationally exceeded 100,000. Hence, those policies
may not have a short-term influence, but could take longer to manifest their
effect.

We understand that validating our model using real policies would be more
accurate. However, the effect of policies is hard to estimate because mobility
control policies vary on smaller granularity level, e.g., counties. It is hard
to estimate the overall effects on states. In addition, one can never know the
ground truth cases where there are no such policies. Hence, the evaluation
cannot be made.

##  V Conclusion and Discussion

We have proposed a pandemic model that jointly predicts the daily new
infection cases and the daily mobility and it is capable of predicting over
the longer-term future. It is also able to simulate some mobility control
policies and potentially assist in the decision-making process. Technically,
the use of an attention mechanism improves model performance and provides
insight on choosing the time window length. We are also the first to employ
learned edges in GCN pandemic models and it outperforms GCN-LSTM that only
uses mobility as edges.

Modeling the effect of vaccination is a good future research direction as it
is an important factor of pandemic models. Largely vaccinated groups may have
fewer infections even with high mobility levels. We did not consider
vaccination due to the unavailability of data. The number of vaccinations grew
rapidly after March, 2021; however, we lack the corresponding data beyond that
time. Moreover, there is no vaccination information in the training data. We
may include the vaccination factor into our model when there are more data.

There are sources of infection that our model is unable to cover because they
lack representation in our mobility data; e.g., household infections and
infections caused by mobility absent from the SafeGraph dataset. This could be
a major source of prediction error, but it can easily be incorporated into SIR
[15] and could be another direction for future work. In addition, mobility is
not directly linked to infection. Direct/indirect contact is. Hence, relying
on mobility data may reduce the confidence of our predictions. Lastly, more
statistics can also be included in future work, such as the number of deaths
and other demographic features. Our model can also be generalized to support
different types of input.

Lastly, there are ethical concerns which should be addressed because the data
involves privacy issues. Collecting mobility data poses specific challenges
for upholding ethics principles. For the data we use, it was collected by
SafeGraph after receiving the consent of the users. Strict procedures must be
followed to protect people’s privacy. On the other hand, given that some
people may not be willing to provide their mobility patterns, the collected
data may not be very representative. In this case, the accuracy is expected to
drop.

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