A Deep Learning Approach for COVID-19 Trend Prediction
AA Deep Learning Approach for COVID-19 Trend Prediction
Tong Yang ∗ Department of PhysicsBoston CollegeChestnut Hill, Massachusetts, USA
Long Sha ∗ Department of Computer ScienceBrandeis UniversityWaltham, Massachusetts, USA
Justin Li
Del Norte High SchoolSan Diego, California, USA
Pengyu Hong
Department of Computer ScienceBrandeis UniversityWaltham, Massachusetts, USA
ABSTRACT
The ongoing COVID-19 pandemic, due to the novel coronavirusSARS-CoV-2, has affected not only the healthcare system but thewhole society worldwide. While a large number of medical worksand researchers are battling the pandemic crisis on the front line,with large amount of accessible epidemic information, data-drivenresearch and learning based approaches could provide rich insightsabout the challenge on the population and society level. In this work,we apply a recurrent-network based model to study the epidemicdata in the United States. By incorporating both the epidemic timeseries and socioeconomic characteristic data, our model providesboth a promising predictive power in forecasting the trend of newconfirmed cases, and an illustrative description about the interplaybetween the local epidemic evolution and demographic features.
ACM Reference Format:
Tong Yang, Long Sha, Justin Li, and Pengyu Hong. 2020. A Deep LearningApproach for COVID-19 Trend Prediction. In epiDAMIK 2020: 3rd epiDAMIKACM SIGKDD International Workshop on Epidemiology meets Data Miningand Knowledge Discovery.
ACM, New York, NY, USA, 7 pages. https://doi.org/xx.xxxx/xxxxxxxxx.xxxxxxx
In late 2019, the COVID-19 outbreak initially detected and reportedin Wuhan (Hubei, China) due to the severe acute respiratory syn-drome coronavirus 2 (SARS-CoV-2), spread rapidly, firstly acrossregions in China and east-Asian countries, and then, since late Feb-ruary, to nearly all continents in the world. As of June 15, 2020,there have been more than 7.91 million cases confirmed across225 countries and regions, associated with 433 thousands deaths[22, 26]. Declared as a pandemic by the World Health Organizationon March 11, the COVID-19 outbreak has brought severe challengesto not only local healthcare systems (especially in underdevelopedareas) but our society as a whole. At the same time, a large number ∗ Equal ContributionPermission to make digital or hard copies of all or part of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for components of this work owned by others than ACMmust be honored. Abstracting with credit is permitted. To copy otherwise, or republish,to post on servers or to redistribute to lists, requires prior specific permission and/or afee. Request permissions from [email protected]. epiDAMIK 2020, Aug 24, 2020, San Diego, CA © 2020 Association for Computing Machinery.ACM ISBN 978-1-xxxx-XXXX-X...$15.00https://doi.org/xx.xxxx/xxxxxxxxx.xxxxxxx of related research have been emerging recently in various subjectsand fields, attempting to contribute to the battle against COVID-19.Beside pharmacologic and genomics studies on the SARS-CoV-2virus, data-driven research both on the spread of COVID-19 amonglocal population and on general social impacts brought by the pan-demic have been providing valuable insights especially for localpolicy makers.On the one hand, various types of sequential models have beenimplemented to study the spreading behavior of COVID-19 ina generic population, including compartmental model based ap-proaches [3, 5, 12, 18], which are motivated by conventional dynami-cal models in epidemiology, and deep learning based nonparametricapproaches [19, 24]. While the second class, i.e., artificial-learningbase approaches, might produce better predictions on disease re-lated statistics, it lacks interpretability for the most part due to theblack-box nature of neural network estimators.On the other hand, the interaction between social environmentsand the local COVID-19 outbreak remains an important topic. Theidentification of highly related exogenous factors that impact thelocal epidemic evolution significantly, e.g., the local populationdensity and the local age structures, is of great importance. Inaddition to understanding dominant environmental factors thatgovern the outbreak, the relation between the epidemic evolutionand socioeconomic characteristics could potentially also reveal theinverse impact of the COVID-19 on a local community [1].In the current work, we apply a learning-based approach both toproduce an accurate prediction about a near future, and to revealthe interplay between environmental factors and the epidemic evo-lution. To accomplish this, we implement a neural-network basedsequential model, and integrate the time-varying epidemic informa-tion, i.e., related statistics including confirmed cases and deceasedrecords, with environmental factors including both dynamical ones,e.g., local restriction policies, and static ones, such as demographicfeatures. Environmental factors enter the model via an "kick-start"mechanism , which, after being fixed through training, offers asmoking-gun for the relevance of different factors to the epidemicevolution.The rest of the paper is organized as follows. Section 2 intro-duces the ongoing pandemic situation and mentions some relatedworks which motivate our study. In section 3, we enumerate severalcandidate factors that could potentially affect the epidemic evolu-tion process significantly and discuss the potential epidemiological See Section 4 for details. a r X i v : . [ c s . C Y ] A ug piDAMIK 2020, Aug 24, 2020, San Diego, CA Tong Yang, Long Sha, Justin Li, and Pengyu Hong dependence, along with other important socioeconomic character-istics, which could be used to analyze the inverse social impact ofthe ongoing public health crisis. Section 4 elaborates our applica-tion approach in details, explaining both the information flow inthe model and the way to extract the relevance of environmentalfactors to the local epidemic outbreak. Section 5 explains modeltraining, including data sources, model structures, and trainingresults. In section 6, we firstly demonstrate the prediction power ofthe trained model, and then discuss the relevance of different envi-ronmental factors to the epidemic emergence extracted from thetrained representation. Finally, we summarize our work in Section7 and discuss potential directions for further investigations withmore data and complex models. As of June 15, 2020, the COVID-19 has hit countries worldwide. Wesummarize the latest pandemic situation in Table 1.
Category Statistics
Number of countries reporting COVID-19 cases 225Number of confirmed cases reported worldwide 7,912,426Number of deceased cases reported worldwide 433,391Number of recovered cases reported worldwide 377,131Currently estimated fatality rate 5.5%
Table 1: Summary statistics of the ongoing COVID-19 pan-demic situation worldwide. Data is from the CovidNetproject [26].
Governments and organizations across the world have been tak-ing measures at different levels in response to this pandemic crisis.Extreme measures were adopted by the Chinese government inWuhan, where a complete lock-down of the whole city was im-plemented. This has been proved later to be very effective to slowdown the spread of SARS-CoV-2, the contagious level of which waslater revealed to be much higher than two previous deadly viruses,i.e., MERS and SARS. The response in Wuhan then inspired othercountries and regions, including South Korea, Thailand, Italy andetc., addressing the importance of social distancing. In spite of thefact that extreme measures have been proven to be effective in fight-ing against the coronavirus spread, regional lock-down remainsa difficult decision to be made for any local government takinginto account the economic expense. Therefore, it is of extreme im-portance to provide policy makers necessary tools to both predictthe future trend and understand the social impacts brought by thepublic health emergency [7, 13, 20].On the prediction side, conventional
Susceptible Infectious Re-covered ( SIR ) model based approaches have been widely imple-mented [3, 12, 18], with model parameters estimated from regionalepidemic data. Motivated by the data-driven estimation process,deep-learning models have also been hybridized into predictionmodels [5]. While the
SIR model and its variants indeed could Or Susceptible Infectious Removed in some literature, which also considered deceasedcases. roughly capture the epidemic law of a generic disease spreadingbehavior, there are two major problems in practice: • ODE systems capture continuous dynamics, howbeit real-life epidemic data is usually collected in discrete time. Thereare also delays in case reporting, which, even worse, neveruniform in time . Therefore, there exists a significant mis-match between the true ongoing epidemic process, whichcan be approximately described by ODEs, and the reporteddata, which highly depends on human-involved operations. • SIR and its variants only take into account the lowest-orderdynamics, which includes the linear terms describing popu-lation transitions between compartments and product termsdescribing interaction/contact between compartments, whilekeeping transition parameters constants. In reality, how-ever, human responses would also evolve along with theepidemic evolution, which, reversely, could remarkably af-fect the transmission (due to restriction policies and changein crowd behaviors) and the fatality (due to the improvedmedical response) of the disease.Above problems, especially the first one due to human operations,make the task of prediction with compartmental models impractical.Beside the predictive power, another drawback of ODE basedcompartmental models is the absence of environmental factors. Thetrend prediction alone is not enough for designing policy. Instead,understanding the interplay between environmental factors and theepidemic evolution could benefit local policy makers [7, 13, 20], andthe dependence of the local outbreak on demographic features andtransportation data is essential to calibrate restriction/reopeningstrategies [6]. At the same time, it is also of great importance toexamine the social impact of the public health emergence on thelocal community, especially on different population groups charac-terized by genders, races, and ages. Most recent works only provideeither qualitative arguments [21] or simple statistical analysis, e.g.,the linear regression [1], which has limited modeling capability.Compared with above methods, our current approach attemptsto incorporate environmental factors into the prediction moduledirectly. The explicit factor-dependence and therefore interpretabil-ity of the model are available via a proper analysis on the learntrepresentation. Details of our modeling and training can be foundin Section 4 and 5.
Before introducing specific model structures and training designs,it is necessary to discuss and distinguish candidate environmentfactors, which either directly govern the epidemic evolution process,a.k.a. exogenous factors , or reveal the social impact of COVID-19from essential perspectives.
In reality, many exogenous factors would affect the transmissionbeside disease characteristics. Most intuitively, there is a higher For example, the obvious periodic (week-wise) pattern in the U.S. death data is due tothe reporting schedule of the official departments.
Deep Learning Approach for COVID-19 Trend Prediction epiDAMIK 2020, Aug 24, 2020, San Diego, CA probability in regions with denser population distributions that afast outbreak would emerge. New York City, being the most denselypopulated county-equivalence in the United States, would serveas a typical example. The outbreak in NYC evolved rather rapidlyfrom the beginning and, as of May 30, 2020, NYC has accounted forthan 55 percents of cumulatively confirmed cases across the wholestate.Another dominating factor for transmission would be the restric-tive order issued by the local government. Restrictions have beenimplemented onto various industry/business activities as well aslocal residents’ daily life. While industry/business restrictions differregion by region, and are usually difficult to study quantitatively, inthe present work we instead use the restriction on local residents’daily life, i.e. the stay-at-home order or its equivalencies , as an ag-gregated representation of the local restriction level to capture theoverall impact of local policies . Importantly, the change of the re-strictive level, from the no-restriction stage, to the restrictive-orderstage, and finally to the reopen stage, results into a time-varyingtransmission behavior of COVID-19, which is in contrast to ODE-based compartmental models that assume a constant transmissionfactor β .More generally, the interaction within a local population con-tributes significantly to the transmission. We therefore adopt theaverage annual enplanements per capital [16] to capture the activelevel of human interactions. It has been confirmed by data from multiple countries and regions[9, 14, 17] that the patient’s age is highly related to the developmentof severe pneumonia symptoms. Aged people are in general morevulnerable to the virus. We therefore incorporate the age structureas an important demographic category.More generally, the physical condition of individuals would re-sult into differences in the probability of infection. For instance,people with poor respiratory condition experience higher risk ofbeing infected. We therefore include the population with high risk [10] as an input feature of modeling.
While above mentioned environmental factors focus more on thebiological aspects of the epidemic evolution, there are also othersocioeconomic characteristics, which, although not biologically rel-evant, could be potentially correlated with the evolution behavior.For example, a study [1] focusing on the New York data hasshown that a higher probability of positive testing rate is in poorerneighborhoods, in neighborhoods where large numbers of peoplereside together, and in neighborhoods with a large black or immi-grant population. At the same time, however, people residing inpoorer or immigrant neighborhoods were less likely to be tested.As a result, an understanding of which types of neighborhoods are Practically, this is also the only consistent data category accessible to the generalpublic disproportionately affected by the pandemic requires an examina-tion of how socioeconomic characteristics correlate with differentepidemic statistics.Motivated by the above discussion, we selected several socioeco-nomic characteristics, which are not only related to the epidemicstatistics from the pure data perspective, but also important inrevealing potential disproportions of the COVID-19 impacts, in-cluding local gross domestic product (GDP) per capita and localrace compositions.
Now we introduce our learning based approach which, in a nut-shell, implements a recurrent-neural-network model for the trendprediction along with an embedding of environmental factors toextract relevant information. There are two classes of inputs: theepidemic time series, including both confirmed cases and deceasedcases, and environmental socioeconomic factors.The epidemic time series data enters the learning module througha stacked Gated Recurrent Unit (GRU) model, which is well-knownfor both its power in dealing with sequential data by incorporatinghistory information properly, and its efficiently simplified structure.We cast a fixed-length ( L ) sequence with recent history informa-tion to predict each subsequent data point, by implementing asliding window on the full time series. Importantly, we would liketo address that this GRU-based model structure is powerful in thefollowing sense:(1) Firstly, this GRU model structure, at least, is capable of cap-turing the dynamics of compartmental models in the discrete-time regime of compartmental models, where the value ofthe next time-step only relies on the current state. For in-stance, this can be easily shown through the following setof difference equations : s t + − s t = − β · s t · i t , i t + − i t = β · s t · i t − γ · i t , r t + − r t = γ · i t , (1)where { s t , i t , r t } represent susceptible, infectious, and re-moved population fractions respectively, and { β , γ } describetransmission rate and removal rate of the disease. This setof equations can be viewed as a discrete version of a SIR model [2], and they clearly only depend on the current snap-shot of epidemic statistics; The above dynamics, in the idealscenario, can be captured by a GRU model with only L = L >
1, and more layers in the GRU module tocapture complicated nonlinear terms.Another input feature with time-varying values is the status ofthe local restriction policy, i.e., the stay-at-home policy or similar piDAMIK 2020, Aug 24, 2020, San Diego, CA Tong Yang, Long Sha, Justin Li, and Pengyu Hong
Figure 1: The task on testing states: NJ, MI, SC, AZ, the data from which has never been accessible tothe model. The predicted curves follow the true values closely. The 95% confidence interval regions are obtained by bootstrapre-sampling from the training set. measures , which, different from numeric data, is categorical witha binary status: "stay-at-home" or "reopen". It is naturally expectedthat the epidemic evolution would be different under different re-striction statuses. Therefore, we apply a "double-channel" structurein the GRU module: a sequential data point would enter channel-1if there is a restriction policy on the corresponding date, and wouldenter channel-2 otherwise.In addition to time-series data, we have also integrated the fol-lowing list of environmental factors as static input features: • local population density; • local GDP per capita; • local age structure (fractions of 6 non-overlapping age groups); • local race structure (fraction of 7 different race categories); • high risk population; • local annual enplanements per capital; • local restrictive order level;where all factors are summarized and represented on state level. Dif-ferent from the sequential data of epidemic statistics which entersthe model via a black-box, although reasonable, as explained above,model structure, we would like to investigate the interplay betweenthe epidemic evolution and various socioeconomic characteristics.Therefore, when we incorporate the input of environmental factors,we apply a linear embedding, which produces interpretable weightson each input dimension. Technically, the embedded representationof environmental factors is taken as the initialization of the hiddenstate in the GRU model , which we call as a "kick-start" mechanism.Through the above design of the information flow, we implic-itly construct a desired interaction between environmental factorsand the epidemic time series data: these two input-categories areconducted to interact with each other via various gates in the GRUmodule. From an epidemic perspective, within the GRU structure,the hidden state could be regarded as an evolving "environment",whose initial status, i.e., before the first infectious case emerges, This includes the stay-at-home advisory issued in Massachusetts, the curfew issuedin Puerto Rico, and so on only depends on exogenous demographic factors of the local com-munity.
In this section, we elaborate the practice of model implementation,including data sources, hyperparameters of implemented model,and details of the training procedure.
Sources of Different Data Categories . • COVID-19 case data:
Case data is from the CovidNet project[26], including confirmed and deceased counts of 50 U.S.states and the District of Columbia, ranging from January21, 2020, to June 14, 2020. • State restriction policy:
Restriction policy information iscollected from "The Coronavirus Outbreak" forum on theNew York Times [23]. • Population and density:
We have used population datafrom the U.S. Census Bureau [25]. • Population with higher risk:
Population in each statewith higher risk to develop severe symptoms are estimatedin [10], and used as an exogenous factor in our application. • Age structure data:
We have used the age structure datasetbuilt by the Kaiser Family Foundation [11]. • Race structure data:
Race structure data is collected fromthe COVID Tracking Project [4]. • Annual enplanements data:
We collected the data of an-nual enplanements per capital in each states (not includingD.C.) from the U.S. Department of Transportation [16]. • Gross domestic product per capita:
We collect the datafrom the United States Census Bureau [25]
Hyper-parameters of the Implemented Model . Our model isimplemented with an embedding module, recurrent module andoutput module. The embedding module sparsely encodes the 21-dimension state-specific demographic vector into a 100-dimensionvector; the recurrent module is using 3 stacked GRU layers with 100-dimension hidden states, the recurrent module takes the previous
Deep Learning Approach for COVID-19 Trend Prediction epiDAMIK 2020, Aug 24, 2020, San Diego, CA embedding result as its first latent state and the windowed statetotal confirmed cases and new cases as inputs; a dense layer isused for the output layer in order to predict the target. We trainedthe model using Adam optimizer [15] with 1e-4 learning rate anddiscounted the learning rate with a factor of 0.3 if the training lossdidn’t decrease over 20 epochs. The model is trained on an MacBookPro with 6-Core CPU.
Details on the Training Design and Process . The detailed modelarchitecture is demonstrated in Figure. 3. We use a five-day windowtime-series historical data and use recurrent module for predic-tion. The input data for recurrent module are total confirmed cases( cc ) and new confirmed cases ( dc ), we pro-process each of theminto two series: one contains value only when there is restrictionpolicy undergoing ( cc _ res and dc _ res ) and another only containsvalue when there is no restriction policy ( cc _ nores and dc _ nores ) asshown in the model architecture. The processed state demographicdata feeds into the state demographic embedding layer, and we useSigmoid activation function inside the layer. All three layers of GRUreceive the embedding output as its first hidden state h . Root meansquared error(RMSE) is chosen as the loss function. We separateour data firstly withholding 5 states as test data. The others areprocessed as windowed input-output pairs and separated into aproportion of 80% for training and 20% for evaluation. The modelis learned via back-propagation utill convergence. As mentioned earlier, the current work targets both a predictionof the epidemic evolution, and an understanding of the interplaybetween environmental factors and the local epidemic outbreak. Inthis section, we discuss the two aspects with the trained model.
As we have applied the random shuffling during training amongthe training data, which is transformed into sequence-to-point pairs,we would demonstrate the prediction power in two ways:(1) "1-step-ahead prediction" on testing states: during the train-ing stage, we have randomly eliminated several states fromthe complete dataset . We would test the performance of thetrained model on these states, whose history records havenever been acknowledged by the model;(2) Long-term prediction from an auto-regressive process: themodel was trained for 1-step-ahead prediction only duringthe training stage, therefore long term prediction would bea non-trivial demonstration for the model’s capability ofcapturing the true dynamics.Figure 1 shows the performance of the model on the . Clearly, even though data from testing states havenever been accessible to the model, the trained model can stillpredict the future value very well. It is therefore reasonable to statethat, rather than over-fitting the given data during the trainingstage, the model instead capture the general law of the epidemicevolution in a generic population. The existence of such a law is See details explained in Section 5 In our practice, we have randomly selected 4 states for testing purpose: AZ, MI,NJ,SC. not a surprise, and has already been hypothesised in conventionalcompartmental-model methods. However, the general law couldeasily become intractable from real data due to the human operationin reporting schemes . By applying the proposed learning-basedmethod, we extract this general law from the noisy real-life data.Compared with the task, the long-termprediction is much more challenging, in the sense that the tasknature has deviated from the training stage. The performance oflong-term predictions is shown in Figure 2. While in some states,the deviation from the true data become visible, the overall trendhas still been well captured by the auto-regressive process, exceptnoisy fluctuations. In practice, the long-term prediction could pro-vide more timely information to policy makers, and hence is morevaluable than . To reveal the interplay between environmental factors and theepidemic evolution, we start from an analysis on the relevance ofeach input feature to the dynamics. As introduced in Section 4,static environmental factors, after being embedded through a lineartransformation, enter the model via the "kick-start" mechanism.Due to the simple structure of this embedding module, we couldeasily identify the relevance of input features by examining theFrobenius norm of each embedding vector.Firstly, there are two classes of population structure data: theage structure and the race structure. Figure 4(a) and 4(b) show therelevance of different age groups and race groups respectively.In the age group relevance chart, it is clear that the two young-age groups, i.e., age from 19 to 25 and
26 to 34 , show the highestrelevance. This is consistent with the demographic report releasedby CDC on age distribution [8], where the age group 18 −
44 con-tributes the largest portion to the confirmed cases.Among all race groups, the two groups,
Asians and
Black orAfrican American alone , appear to be more relevant in epidemicdynamics, while both
White (non-Hispanic) and
Hispanic/Latino show lower relevance. On the other hand, it is interesting to notethat, according to the report released by CDC [8],
White (non-Hispanic) and
Hispanic/Latino contribute largest portion in theconfirmed cases. While the share in confirmed cases may be morerelated to the absolute population size of different race groups,our relevance analysis, instead, focuses on the fraction of eachrace group in a certain state. The above mismatch between theresults obtained via the two descriptive perspectives suggests apotentially existing disproportional impacts of the COVID-19 ondifferent groups. While the above argument does not provide arigorous causal analysis, it illustrates the importance of diversityof perspectives when studying the social impact of COVID-19.Beside the above two types of population structures, we alsonotice a high relevance (1 . See Section 2 for detailed discussions. piDAMIK 2020, Aug 24, 2020, San Diego, CA Tong Yang, Long Sha, Justin Li, and Pengyu Hong (a) Long-term prediction of Hawaii data.(b) Long-term prediction of New York data. (c) Long-term prediction of Iowa data.(d) Long-term prediction of South Dakota.
Figure 2: The long-term prediction task with 4 instantiating states. The solid vertical blue line represents the starting point ofthe auto-regressive running. The 95% confidence interval regions are obtained by bootstrap re-sampling from the training set.Figure 3: Model architecture
We have demonstrated the predictive power of the proposed recurrent-network based model, and discussed the relevance of different en-vironmental factors by studying the embedding vector of eachsocioeconomic characteristic.On the prediction side, the proposed model performs well in both and long-term prediction tasks.One could conclude that the recurrent structure has successfullyextracted and captured a general law of the epidemic evolution ina generic population, from the real-life noisy data.On the other hand, studying the relevance of environmentalfactors to the epidemic dynamics enables us both to identify poten-tial factors that contribute most to the disease spreading, and tounderstand the social impact of COVID-19 on the local community.More specifically, we noticed that young age groups and averageemplacements are highly relevant to the dynamics, verifying thefact that socioeconomic activities contribute significantly to the (a) Age-group relevance . (b) Race-group relevance . Figure 4: Relevance of different age-group fractions 4(a) andrace-group fractions 4(b). The relevance index is defined asthe Frobenius norm of the embedding vector of each inputfeature. disease spread; besides, there might exist a disproportion of thesocial impact on different race groups brought by the COVID-19.In general, one could expect that more insights about the on-going public health crisis could be gained through data-drivenresearch. Besides medical and clinical studies that directly battlethe COVID-19 emergence, it is also important to obtain a more com-plete understanding about general social impacts of the pandemicon the population and society level. This does not only assist localpolicy makers in decision making, but also helps the whole societyto confront the challenge together.
Funding for the shared GPU-computing facility used in this researchwas provided by NSF OAC 1920147.
Deep Learning Approach for COVID-19 Trend Prediction epiDAMIK 2020, Aug 24, 2020, San Diego, CA
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