# Leveraging Wastewater Monitoring for COVID-19 Forecasting in the US: a Deep
Learning study

1st Mehrdad Fazli  School of Data Science
University of Virginia
Charlottesville, VA
<EMAIL_ADDRESS>2nd Heman Shakeri  School of Data Science
University of Virginia
Charlottesville, VA
<EMAIL_ADDRESS>
###### Abstract

The outburst of COVID-19 in late 2019 was the start of a health crisis that
shook the world and took millions of lives in the ensuing years. Many
governments and health officials failed to arrest the rapid circulation of
infection in their communities. The long incubation period and the large
proportion of asymptomatic cases made COVID-19 particularly elusive to track.
However, wastewater monitoring soon became a promising data source in addition
to conventional indicators such as confirmed daily cases, hospitalizations,
and deaths. Despite the consensus on the effectiveness of wastewater viral
load data, there is a lack of methodological approaches that leverage viral
load to improve COVID-19 forecasting. This paper proposes using deep learning
to automatically discover the relationship between daily confirmed cases and
viral load data. We trained one Deep Temporal Convolutional Networks (DeepTCN)
and one Temporal Fusion Transformer (TFT) model to build a global forecasting
model. We supplement the daily confirmed cases with viral loads and other
socio-economic factors as covariates to the models. Our results suggest that
TFT outperforms DeepTCN and learns a better association between viral load and
daily cases. We demonstrated that equipping the models with the viral load
improves their forecasting performance significantly. Moreover, viral load is
shown to be the second most predictive input, following the containment and
health index. Our results reveal the feasibility of training a location-
agnostic deep-learning model to capture the dynamics of infection diffusion
when wastewater viral load data is provided.

###### Index Terms:

COVID-19 Forecasting, Waste Water Viral Load, Deep Learning, Time Series
Forecasting

##  1 Introduction

SARS-COV-2 (COVID-19) is a highly contagious infection that has taken the
world by storm and impacted millions of lives worldwide since its emergence in
late 2019. In September 2021, the mortality rates of COVID-19 surpassed that
of the 1918 influenza pandemic (Spanish flu), one of the deadliest pandemics
in modern history. One major challenge that COVID-19 has posed to governments
and officials across the globe is predicting its progression in the
communities and developing appropriate safety measures to avoid loss of lives
and diminish its financial damage. In addition, striking a balance between
saving lives by placing restrictions, lockdowns, and curfews; and protecting
the economy from massive recession requires accurate prediction of the
infection incidences by localities and allocating resources accordingly.

One of the hallmarks of the COVID-19 pandemic is its considerable proportion
of asymptomatic or undocumented cases [1, 2, 3]. Another characteristic of
COVID-19 that makes it particularly difficult to curb is its long incubation
period, estimated to be nearly six days [4, 5, 6]. Presymptomatic individuals
can be infectious and unknowingly spread the virus while their infection
remains dormant [7]. In light of the aforementioned findings, researchers have
resorted to SARS-COV-2 viral RNA concentration (viral load) in wastewater as
an early indicator of incoming peaks of cases [8, 9, 10, 11]. All COVID-19
cases, including presymptomatic and asymptomatic cases, excrete SARS-COV-2 RNA
regardless of severity of illness [7]. Thus, viral load captures a critical
information source missed in conventional indicators such as clinically
confirmed cases, hospitalizations, and deaths. With the growing evidence on
the efficiency of wastewater surveillance, the Centers for Disease Control and
Prevention (CDC) launched its National Wastewater Surveillance System (NWSS)
in September 2020 in an attempt to coordinate wastewater surveillance across
the US and help local officials to implement the surveillance system in more
localities across the US [12].

Common choices for modeling infectious diseases are compartmental models
(e.g., SEIR), autoregressive models (e.g., ARIMA), and machine learning models
[13]. Compartmental models are the most common models for infectious diseases
and have been applied to COVID-19 since the beginning of the outbreak [14,
15]. They offer a mathematical formulation for disease evolution in patients
and the transmission mechanism. Although these models are highly transparent
and interpretable, their simplifying assumptions on population homogeneity and
parameter estimations challenges are restricting their use. On the other hand,
machine learning models do not require significant domain knowledge. They are
generalizable, domain-agnostic, easily transferable to different geographies,
and, nowadays, easy to train. However, they are less interpretable than
compartmental models and require a large amount of data for their training
stage.

Some attempts have been made to incorporate viral load data into the
compartmental modeling of COVID-19 [16, 17]. However, incorporating viral load
into a compartmental model proves to be challenging. Some of the challenges
are determining the appropriate time lag between viral load and incidence data
[18], determining the proper way of incorporating viral load into the
mathematical model, taking into account the dilution of SARS-COV-2 RNA and its
degradation from the source to the sampling site [10, 8], the complexity of
shedding profile of users and its dependence on the infection severity [10,
19], etc. In this paper, we resort to Deep Learning (DL) to eliminate the need
for hand-crafting a mathematical formulation for infection transmission and
including the necessary covariates at the cost of losing some transparency. To
the best of our knowledge, this is the first study that uses viral load data
as another input to a DL-based forecasting model. Our focus in this study is
to make accurate predictions for the number of COVID-19 infections in the near
future. Thanks to health organizations worldwide and the rapid circulation of
data, we now have access to detailed COVID-19 data worldwide. That means we
have hundreds of time series of daily confirmed cases in different granularity
levels. Therefore, a sufficiently large deep learning model can be trained to
learn the cross-series patterns. DL-based forecasting models such as Long-
Short-term memory (LSTM) have been widely applied to forecasting COVID-19
[13]. We use two probabilistic, multi-step forecasting DL-based models that
allow for covariate time series; Deep Temporal Convolutional Networks
(DeepTCN) and Temporal Fusion Transformer (TFT).

The contributions of this paper are threefold:

  * •

Exploring the feasibility of supplementing COVID-19 incidence data with viral
load data to enhance forecasting accuracy.

  * •

Exploring the role of socio-economic factors in forecasting the infections.

  * •

Training a global probabilistic multi-horizon forecasting model to predict
COVID-19 cases in the near future.

###  1.1 Related Works

Since the beginning of the COVID-19 pandemic in late 2019, researchers have
turned to deep learning models to forecast the propagation of COVID-19
infection [13, 20]. This can be attributed to the capacity of these models to
learn complex and nonlinear patterns. Some of the models that have been
studied in the literature are multi-layer perceptron [21, 22], LSTM [23, 24,
25, 26, 22, 27], gated recurrent units (GRU) [24, 26], temporal convolutional
networks (TCN) [28], variational autoencoder (VAE) [24] and attention-based
networks (e.g., TFT) [29, 30, 25, 31, 32].

Zeroual et al. [24] conducted a comparative study on five DL models, simple
RNN, LSTM, bidirectional LSTM, GRU, and VAE. They applied the models to
confirmed cases and recovered cases data from Italy, France, Spain, China,
USA, and Australia. They made predictions for 17 days ahead and concluded that
VAE outperforms other models convincingly. Devaraj et al. [23] also performed
a comparative study on autoregressive integrated moving average (ARIMA), LSTM,
stacked LSTM, and PROPHET models. They investigated the practicality of using
deep learning to forecast cumulative cases globally and achieved an error rate
of less than 2% with stacked LSTM. They also compiled a list of previous
publications on COVID-19 forecasting using deep learning. Kamalov et al. [13]
published one of the few review papers on COVID-19 DL-based forecasting
models. They selected 53 papers published between April 2020 and February
2022. They organized the literature by classifying papers based on their
modeling approaches and establishing a model-based taxonomy.

Transformers [33] are attention-based neural network architectures for
sequence-to-sequence modeling, often outperforming recurrent-based neural
networks [34, 35]. With Transformer’s success, researchers started to adapt
the model and tune it to other types of machine learning problems.

Er et al. [30] implemented an attention-based neural network with an encoder-
decoder structure named COURAGE. However, unlike the original transformer
model, COURAGE uses a linear decoder to make predictions. COURAGE predicts the
number of deaths per county in the US for two weeks ahead. COURAGE aggregates
county-level data and uses mixup [36] as a data augmentation method to make
more accurate predictions on a state level. They compared the mean absolute
error (MAE) of their model to that of the baselines and showed that COURAGE
beats most of the baselines. Zhou et al. [32] proposed Interpretable Temporal
Attention Network (ITANet), a transformer-based model, to forecast the number
of COVID-19 cases and infer the importance of government interventions. ITANet
is a multi-task learning model whose primary objective is to minimize the loss
of the target series (confirmed cases). However, it also has a covariate
forecasting network (CNF) that predicts the values of some unknown covariates
for the forecast horizon. Unknown covariates are the ones that have to be
measured, and their future values are unknown. They also used the Oxford
COVID-19 government response tracker [37] and temperature and air quality
indices as other covariates for their model. They examined their model on
state-level data from Illinois, California, and Texas. Their model
outperformed the baseline models, including TFT and transformer model, by a
considerable margin. They also analyzed the covariate importance and ranked
the government intervention indices based on their importance in the three
states.

Jin et al. [29] developed an attention-based model called Attention Crossing
Time Series (ACTS) focusing on learning the cross-series recurring patterns.
Their method is based on creating embeddings for different time series
segments to find similar trends in other time series. They also feed their
model with several covariates such as total population, population density,
and available hospital beds. They showed that ACTS could outperform the
leading models in forecasting COVID-19 incidence (confirmed cases, death,
hospitalization) in most cases. The forecasts are made for a four-week horizon
and on a state-level granularity. Fitra et al. [25] applied a Deep Transformer
[38] model to Indonesia’s COVID-19 data. Deep Transformer adjusts the original
transformer model by placing the layer normalization before the LSTM
positional encoder. They also compared the Deep Transformer model with RNN and
LSTM. Their results suggest that Deep Transformer with AdaMax optimizer
outperforms RNN and LSTM models. Basu and Sen [31] applied the TFT model to
predict country-wise COVID-19 incidences. They used COVID-19 data from 174
countries and their socio-economic factors, such as social capital, population
density, life expectancy, and healthcare access quality, to forecast the
cumulative cases for 270 days ahead.

##  2 Methodology

We intend to leverage the predictive power of neural networks and their
capability to learn complicated, recurring, and long-range patterns. Peccia et
al. showed that viral load contains valuable information that precedes other
indicators (e.g., confirmed daily cases) by several days [39]. Therefore, it
can guide the model to make more accurate predictions. To test this
hypothesis, given that viral load is an unknown covariate, we need to choose
models that allow for unknown covariates. We are also interested in a global
model that can be trained on multiple geographical locations’ COVID-19 data
and is general enough to make reasonably accurate projections for unseen
locations. We argue that such a model has learned the intrinsic dynamics of
infection. We select the models based on the paradigms of probabilistic
forecasting to quantify the uncertainty and multi-horizon forecasting. Given
these criteria, we chose Temporal Fusion Transformers [40] and DeepTCN [41] as
our candidate models. Firstly, we introduce each model, then present their
results and compare their performance.

###  2.1 Forecasting time series

Assume that we have $U$ related time series, each associated with a location.
We aim to learn a general model on all spatially related time series. This
general model learns the dynamics of the target time series and its
associations with the covariates.

Given a look-back window of size $k$, from time $t$, we assume a forecast
horizon of size $\tau$. Hence the past window is $[t-k,t-k+1,...,t]$ and the
future window is $[t+1,t+2,...,t+\tau]$. Also, for the duration of the
forecast horizon, we suppose that $\textbf{z}^{(u)}_{i}$ and
$\textbf{x}^{(u)}_{i}$ are unknown and known covariates, respectively. Then
the forecasting problem can be summarized as [40]:

$\displaystyle\hat{y}^{(u)}(q,t,\tau)=f_{q}(\tau,y^{(u)}_{t-k:t},\textbf{z}^{(u)}_{t-k:t},\textbf{x}^{(u)}_{t-k:t+\tau})$
(1)

where $y^{(u)}_{t}$ is the actual $u^{th}$ series and
$\hat{y}^{(u)}(q,t,\tau)$ is the predicted $q^{th}$ quantile of $\tau$-step-
ahead forecast of $u^{th}$ target series. We note that TCN and TFT produce
$\tau$-step-ahead forecast simultaneously as opposed to iterative methods like
RNN-based models.

We quantify the population behavior driven by the enforced restrictions using
the Oxford Covid-19 government response tracker (OxCGRT) [37]. Furthermore, we
assume the indices are known for the forecast horizon since any change in
governmental policies and restrictions guidelines is usually announced days or
sometimes weeks in advance. On the other hand, the viral load is a real-time
emission from epidemics and has to be measured. Thus viral loads are instead
measurements of the dynamical states and not covariates. From a practical
point of view, however, viral load can guide the model as a covariate, and its
past measurements are available when making predictions. Thus, abusing the
terms and considering it as another covariate seems justifiable.

###  2.2 Deep Temporal Convolutional Networks

Bai et al. [42] compared TCN and different types of RNN (simple RNN, LSTM,
GRU) and found that for most of the sequence modeling tasks, TCN outperforms
the RNN models. Additionally, they conclude that TCN converges considerably
faster than RNN models owing to its non-autoregressive nature. TCN uses a 1-D
fully convolutional network [43] to map the input sequence into the output
sequence. It also takes advantage of causal convolutional layers to avoid
leakage of data from the future into the past. However, stacking convolutional
layers in this manner can only increase the look-back window linearly with the
number of layers. Therefore, to achieve a long receptive field, one has to
stack many convolutional layers, drastically increasing the model’s
computational burden and making it difficult to train. Van den Oord et al [44]
suggested dilated causal convolutions, which only applies convolution on nodes
that are multiplicative of the dilation factor in the previous layer instead
of consecutive nodes. For instance, with the dilation factor being one, we
restore the regular causal convolutions, while with the dilation factor being
two, the model looks at every other node. Fig. 1(a) depicts a dilated causal
convolutional network with three different dilation factors for each layer.

A more recent study by Chen et al. [41] proposed a modified version of TCN
(DeepTCN) for probabilistic forecasting on multiple time series. They
suggested an encoder-decoder structure that takes covariates in addition to
the target series as inputs. The encoder consists of two dilated causal
convolutional networks with batch normalization and ReLU activation function
after each. It also has a residual connection inspired by RESNET [45]. The
decoder resembles the encoder, with convolutional networks replaced with dense
layers and applied to known covariates. The residual connection combines the
output of the encoder with transformed covariates. DeepTCN makes probabilistic
forecasts either by predicting the parameters of a predefined future
distribution or by predicting the quantiles of the target value. These
modifications added much more flexibility and value to TCN, particularly for
the task of time series forecasting. Therefore, we use DeepTCN in our study
for its added value while retaining all the characteristics of TCN, such as
the long receptive field.

(a)

(b)

Figure 1: (a) A dilated causal convolutional network with two hidden layers
and dilation factors 1, 2, and 4. (b) Schematic of an encoder-decoder DeepTCN
with the inputs and outputs shown. Y, V, and C denote daily cases, viral load,
and covariates.

###  2.3 Temporal Fusion Transformer

Another successful deep learning architecture for time series forecasting is
Temporal Fusion Transformer (TFT) [40]. Similar to the Transformer model, TFT
has an encoder-decoder structure. TFT (Fig. 2) is designed to accept all types
of inputs in addition to target series, such as static covariates, known
covariates, and unknown covariates. All inputs are processed through a Gated
Residual Network (GRN), which is a gating unit with a skip connection to allow
the model to skip nonlinear transformation for any input when necessary.
Moreover, all inputs (historical data, static and dynamic covariates) are
further processed through a variable selection unit to find their weighted
average to be fed into the LSTM encoder/decoder. These weights allow us to
quantify the importance of each input in the trained model. LSTM acts as a
positional encoding unit in the Transformer model. All known inputs are
processed through the encoder, while the decoder takes the output of the
encoder and known covariates. Similar to the Transformer model, temporal
patterns are learned through a multi-head attention mechanism with the
difference that the key weights are not head-specific. That enables us to
quantify which inputs the model is attending to (relative importance of the
past information in forecasting the future).

Figure 2: Temporal Fusion Transformer. Y, V, and C denote daily cases, viral
load, and covariates.

###  2.4 Data

We use the Biobot Analytics dataset [46] on national wastewater monitoring. It
contains weekly measures of SARS-COV-2 viral genome copies for more than 70
counties across the US. It also includes the number of cases extracted from
USA Facts111https://usafacts.org/issues/coronavirus/ scaled for 100k people.
Daily cases were computed by subtracting cumulative counts for two consecutive
days, and then a 7-day rolling average was applied. To enrich the models with
socioeconomic and behavior change information, we used the OxCGRT dataset
collected at Oxford University [37]. This dataset contains several indices,
quantifying each state’s government response, public health restrictions, and
economic support. In particular, we selected four indices, overall government
response index, containment and health index, stringency index, and economic
support index. For simplicity, we call these four covariates Oxford
covariates. These indices serve as known covariates whose future values are
known during the forecast horizon.

To prepare the data for modeling, we performed several preprocessing steps. As
the viral load data is sparser, we focused on the time window in which we have
viral load data. Furthermore, to avoid data loss, we changed the granularity
of the viral load data from weekly to daily by interpolating the days between
two consecutive recordings. We also cut off the tail of data for counties with
ragged daily cases due to insufficient recordings. Additionally, we scaled the
viral load, case count, and oxford covariates values to be between 0 and 1.
Finally, we created four date-time covariates, namely year, month, week of the
year, and day of the week, to help the model extract seasonality in the data.

Out of all counties in the Biobot dataset, we chose 13 counties with the most
viral load measurements. In addition, two of the counties were kept as a
holdout set to better assess the generalizability of our model by testing them
on holdout counties. Fig. 3 shows the processed time series of confirmed
cases, viral load, and Oxford covariates that are input to our models. We take
80% of the historical data for each county as training and the rest as test
data. Also, 10% of the training data is taken as the validation data. We used
validation data to identify the optimal hyperparameters of our models. We set
the look-back window to 30 days and the forecast horizon to 10 days. For the
implementation, we used the Darts package in Python [47], which is a
comprehensive time series analysis package. Our codes can be found the
project’s GitHub page222github.com/mehrdadfazli/DeepLearning-
COVID19-wastewater

(a)

(b)

Figure 3: Processed data of two sample counties (a) Jefferson county, KY (b)
Dauphin county, PA.

###  2.5 Results and Discussion

We present the predictions of TFT and DeepTCN models for the 11 training
counties and the two holdout counties (Fig. 4). The predictions are the 10-day
ahead point estimates and their corresponding 90% confidence intervals
associated with the test period for each county. DeepTCN’s predictions are
smoother but less accurate in some counties with considerably larger
confidence intervals. On the other hand, TFT is relatively consistent and
accurate for all counties with reasonably smaller confidence intervals.
Another interesting observation is that the models, especially TFT, have
effectively generalized to the two unseen counties. This can particularly be
witnessed in the case of Lake county, as both models comfortably captured the
spike in the confirmed cases in December 2021 and January 2022.

We use backtesting without retraining to make predictions and evaluate models.
With backtesting, we shift the look-back window by a certain number of time
steps and then make predictions for the forecast horizon. In our case, the
forecast horizon and the stride (shift in the look-back window) are set to 10
days. Also, We have the choice to retrain the model before making predictions.
In a real-world scenario, we retrain our model as new data becomes available
and as frequently as the computational resources allow. However, retraining
requires plenty of computational resources and many retraining iterations. For
the sake of model comparison and evaluating the contribution of covariates,
retraining is not necessary. Nonetheless, it is worth noting that by
retraining the models with the availability of new data, one can achieve
remarkably smaller errors in the predictions.

Figure 4: Predictions of TFT and DeepTCN for 13 counties. Union county and
Lake county are the two holdout counties.

To facilitate the comparison of the models, we selected three metrics; mean
absolute error (MAE), symmetric mean absolute percentage error (SMAPE), and
coefficient of variation (CV) (equations 2-4). MAE is the average raw
difference between the predicted and actual time series. It is a simple yet
interpretable and effective accuracy metric for forecasting tasks. We also
chose SMAPE over MAPE since MAPE produces large errors when the actual series
approaches zero. As our target series is daily confirmed cases, we have zeros
in our target series, which prevents us from using MAPE. Instead, SMAPE is the
symmetric version of the MAPE that can handle zeros in the target series.
Also, similar to MAPE, SMAPE is a scale-free metric suitable for cross-studies
comparisons. CV is another scale-free metric based on root mean square error
(RMSE) expressed in percentage, which shows the variation in the errors with
respect to the average of the actual series.

$\displaystyle\operatorname{MAE}=\frac{1}{T}\Sigma_{t=1}^{T}|y_{t}-\hat{y}_{t}|$
(2)
$\displaystyle\operatorname{SMAPE}=200\times\frac{1}{T}\Sigma_{t=1}^{T}\frac{y_{t}-\hat{y}_{t}}{|y_{t}|+\hat{y}_{t}}$
(3)
$\displaystyle\operatorname{CV}=100\times\operatorname{RMSE}(y_{t},\hat{y}_{t})/\bar{y_{t}}$
(4)

(a) Training counties Model | MAE | SMAPE | CV
---|---|---|---
TFT | 16.00 | 41.20 | 75.88
TFT - no viral load | 17.92 | 44.88 | 90.62
DeepTCN | 25.95 | 59.30 | 100.80
DeepTCN - no viral load | 29.94 | 61.32 | 119.79

(b) Holdout counties Model | MAE | SMAPE | CV
---|---|---|---
TFT | 10.73 | 32.92 | 56.10
TFT - no viral load | 9.92 | 36.50 | 42.88
DeepTCN | 20.98 | 51.17 | 83.35
DeepTCN - no viral load | 21.87 | 46.24 | 110.06

TABLE I: Performance comparison for the four models of TFT, TFT without viral
load data, DeepTCN, and DeepTCN without viral load data.

To better validate the role of viral load data, we conducted an ablation study
by training one TFT model and one DeepTCN model without the viral load data.
Table I shows the performances of the four models for the three selected
metrics. The first takeaway is that TFT outperforms DeepTCN by a considerable
margin. We can also conclude that viral load has significantly helped the TFT
and DeepTCN models produce more accurate predictions for training counties
(Table I(a)). Using viral load can reduce MAE by nearly $2$ units for TFT and
$4$ units for DeepTCN. It also decreases SMAPE by more than 3% for TFT and 2%
for DeepTCN.

Moreover, TFT allows for extracting the importance of the different variables.
Although, this is different for the holdout counties as we only have two
counties in the holdout set selected at random, and their data might have been
easier to predict. On the other hand, the point of the holdout set is merely
to assess the generalizability of our models, not to compare them. Comparing
the results of table I(a) and table I(b), one can verify that the models
performed equally well for the unseen localities.

(a) TFT models’ predictions.

(b) DeepTCN models’ predictions.

Figure 5: Impact of viral load on (a) TFT and (b) DeepTCN models’ predictions
with 90% confidence interval for four counties.

Fig. 5 illustrates the information gained by the viral load data for TFT and
TCN models by placing the predictions of each pair of models on the same plot
for Nantucket county, Arapahoe county, Indiana county, and Miami-Dade county.
Predictions are 10-day ahead forecasts that correspond to the test period of
the time series. Compared with DeepTCN, the TFT model learns a better
relationship between daily cases and viral load and successfully captures the
abrupt rise in the number of cases in early 2022 (Fig. 5(a)). Moreover,
supplementing viral load data to the models reduces the uncertainty in the
model’s predictions.

One of the significant advantages of TFT over other DL-based time series
models is its transparency through its variable selection unit. Once the model
is trained, we can aggregate the variable selection weights to measure how the
model is attending to the input variables. As we have a variable selection
module for the encoder and another for the decoder, we can obtain the variable
importance separately. Fig. 6(a) shows the percentage importance of the input
variables of the encoder unit. The most significant input proves to be
containment and health index. Containment accounts for school closings, public
spaces closings, and other restrictions placed by local governments to slow
down the spread of the virus [37]. On the other hand, the health index
measures healthcare access, quality, budget, and safety measures put in place
by the officials, like contact tracing and public campaigning. The containment
and health index is a weighted average of all the health and containment
indices. The second important input is the viral load with over 20% weight.
This demonstrates the importance of viral load as a complementary data source
for COVID-19 incidence forecasting. The next important inputs are the month
and day of the week, which are associated with the seasonality in the data.
This can be attributed to the seasonal pattern in social gatherings and
superspreading events.

On the other hand, the stringency index dominates the variable importance for
the decoder (6(b)) with 50% importance. The stringency index in OxCGRT is the
containment and health index, excluding testing policy and contact tracing.
Therefore, containment policies followed by the viral load are the most
influential predictors in forecasting COVID-19 cases. It is noteworthy that
the economic support index has the least importance out of all covariates
considering both encoder and decoder variable importance.

(a) Encoder’s variable importance.

(b) Decoder’s variable importance.

Figure 6: Varibale importance for (a) encoder and (b) decoder.

##  3 Conclusion

In this study, we explored the possibility of leveraging deep learning to
automatically learn the complex relationship between viral load and daily
confirmed cases of COVID-19. Evidence has been abundant on the effectiveness
of viral load in the early detection of an outbreak in communities.
Nevertheless, there need to be more methodological approaches that incorporate
viral load data in developing more accurate forecasting models. We proposed a
deep learning framework to extract useful information in the viral load and
enhance prediction accuracy. In addition to viral load, we augmented our data
with socio-economic indicators and automatically generated seasonality
covariates. We tested two multi-step probabilistic forecasting models that
allow for covariates: DeepTCN and TFTFT. Our analysis showed the superiority
of the TFT, a transformer-based model, over the DeepTCN model in extracting
the relationship between viral load and COVID-19 incidence data. Despite
DeepTCN, TFT offers some degree of transparency regarding how the model
attends to the inputs. We demonstrated that containment policies and the viral
load are essential factors in predicting daily cases of COVID-19.

This work can be extended using more data with finer granularity. Deep
learning models unleash their full capacity when provided with a large amount
of data. Also, the wastewater sampling frequency in Biobot’s nationwide
wastewater monitoring dataset is weekly. We interpolated viral load
measurements for the days between two recordings which could introduce some
errors in the analysis. Also, many counties implemented their wastewater
surveillance system long after the CDC launched the national wastewater
surveillance system. We dropped those counties in our analysis due to
insufficient data. In addition to the viral load, daily cases provided with
USA Facts also suffered from occasional misreports and corrections leading to
inaccurate data for some counties. Moreover, with the growing data on
wastewater viral load, adding other covariates, such as air quality index and
temperature, could help the models learn a more holistic picture of the
infection dynamics.

Wastewater signal is a rich source of pathogens that can monitor the
development of infections in the communities. It has been used for over 40
years to track viral infections [48]. COVID-19 underlined the necessity of
establishing a robust wastewater surveillance system for better monitoring of
an outbreak and taking timely preventative measures.

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