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A Review of Graph Neural Networks in Epidemic Modeling

Zewen Liu, Guancheng Wan, B. Aditya Prakash, Max S. Y. Lau, Wei Jin

arXiv:2403.19852v4cs.LGcs.SIphysics.soc-phq-bio.PE

TL;DR

Mechanistic models may depend on fixed assumptions, and conventional deep-learning models often miss relational information in epidemiological data. This survey categorizes epidemic tasks and GNN methodologies, reviews methods and limitations, and outlines future directions. It provides a structured overview of GNN applications in epidemic modeling and identifies data challenges that remain under-addressed.

  • Problem

    Mechanistic models can rely on oversimplified or fixed assumptions, while CNNs and RNNs often fail to incorporate relational epidemiological information such as mobility, geography, and contact tracing.

    Source: §1 · p. 1

  • Method

    The survey reviews GNNs in epidemic modeling, categorizing tasks and methods and examining existing approaches, limitations, and future directions.

    Source: §1 · p. 2, §6 · p. 11

  • Results

    The survey organizes epidemic tasks into Detection, Surveillance, Prediction, and Projection, and GNN methods into Neural Models and Hybrid Models.

    Source: §6 · p. 11

  • Takeaways & Limitations

    The survey outlines challenges and promising directions for researchers in GNN-based epidemic modeling.

    Source: §6 · p. 11

    Epidemic data challenges such as noise, incompleteness, and privacy have received limited attention in GNN-related epidemiological work.

    Source: §5.6 · p. 11

Abstract

from arXiv · show

Since the onset of the COVID-19 pandemic, there has been a growing interest in studying epidemiological models. Traditional mechanistic models mathematically describe the transmission mechanisms of infectious diseases. However, they often suffer from limitations of oversimplified or fixed assumptions, which could cause sub-optimal predictive power and inefficiency in capturing complex relation information. Consequently, Graph Neural Networks(GNNs) have emerged as a progressively popular tool in epidemic research. In this paper, we endeavor to furnish a comprehensive review of GNNs in epidemic tasks and highlight potential future directions. To accomplish this objective, we introduce hierarchical taxonomies for both epidemic tasks and methodologies, offering a trajectory of development within this domain. For epidemic tasks, we establish a taxonomy akin to those typically employed within the epidemic domain. For methodology, we categorize existing work into Neural Models and Hybrid Models. Following this, we perform an exhaustive and systematic examination of the methodologies, encompassing both the tasks and their technical details. Furthermore, we discuss the limitations of existing methods from diverse perspectives and systematically propose future research directions. This survey aims to bridge literature gaps and promote the progression of this promising field, with a list of relevant papers at https://github.com/Emory-Melody/awesome-epidemic-modeling-papers. We hope that it will facilitate synergies between the communities of GNNs and epidemiology, and contribute to their collective progress.

1 INTRODUCTION

Mechanistic models can rely on fixed or oversimplified assumptions, while conventional deep-learning models often miss relational information in epidemiological data. The survey reviews GNN approaches to epidemic modeling, organizes their tasks and methods, and identifies gaps in prior surveys and future research directions.

1 INTRODUCTION

  • Mechanistic models’ fixed or oversimplified assumptions can compromise prediction accuracy and generalization across contexts.These models simulate disease spread using biological and behavioral factors, but their assumptions can bias modeling.Source: §1 · p. 1
  • CNNs and RNNs support epidemiological prediction, but often fail to incorporate relational information from mobility, geography, and contact tracing.That deficiency restricts their utility in broader epidemiological applications.Source: §1 · pp. 1–2
  • GNN message passing aggregates graph information, enabling representation of spatial and other complex interactions in epidemic tasks.The introduction also notes that GNNs can be integrated with mechanistic and probabilistic models.Source: §1 · p. 2
  • The survey categorizes epidemic tasks and GNN methodologies, reviews existing methods, and identifies limitations and future directions.Its stated contributions include categorizing tasks, data resources, and graph construction techniques, then classifying methodologies.Source: §1 · p. 2
  • Unlike many earlier surveys focused on COVID-19 or narrow tasks, this review centers GNN approaches across a broader range of epidemic modeling tasks.The introduction notes that some prior GNN surveys focus on virus transmission, a single virus, or forecasting.Source: §1 · pp. 2–3

2 PRELIMINARIES AND DEFINITIONS

This section introduces graph-learning notation and node-level prediction, explains GNN message passing, and reviews mechanistic epidemic models including SIR and its variants.

2.1 Learning on Graph Data

  • Graph data is represented as G = (V, E), with node features X and adjacency A supporting prediction of properties for unlabeled nodes from labeled nodes.Training minimizes a loss between predictions and known node states; RMSE is one example.Source: §2.1 · p. 3

2.2 Graph Neural Networks

  • GNNs learn node representations by repeatedly aggregating information from each node’s neighbors and its own attributes, then projecting the representation to an output prediction.The neighbor set and aggregation function vary by model, and the initial node representation is its feature vector.Source: §2.2 · p. 3

2.3 Mechanistic Models

  • Mechanistic models describe disease transmission using biological and social processes, while empirical models use historical data to discern patterns and forecast spread.Compartmental models such as SIR simplify transmission dynamics into components that can aid understanding for researchers and policymakers.Source: §2.3 · p. 3
  • The SIR model divides a population into susceptible, infectious, and recovered groups, with transmission and recovery rates governing transitions between them.The model computes R0 = β/γ; in a network SIR model, R0 = βλ1/γ, where λ1 is the leading eigenvalue of the adjacency matrix.Source: §2.3 · pp. 3–4
  • SEIR adds an exposed compartment and SIRD adds a dead compartment to the basic SIR framework.The survey also identifies EpiLearn as a toolkit for epidemic modeling and analysis with machine-learning models.Source: §2.3 · p. 4

3 TAXONOMIES

The survey organizes GNN methods in epidemic modeling through taxonomies spanning tasks, data, graph construction, and methodology.

3 TAXONOMIES

  • The taxonomy covers epidemiological tasks, datasets, graph construction, and methodological distinctions, with a comprehensive categorization in Appendix 1 and part of it in Table 3.The authors frame these categories as a way to organize methods in GNN-based epidemic modeling.Source: §3 · p. 4

3.1 Epidemiological Tasks

The section classifies epidemic work by researchers’ goals and also describes tasks through their timing, targets, model inputs, and outputs.

3.1.1 Detection.

  • Detection tasks identify health states, disease spread, or related incidents at a specified time, including source detection and transmission detection.One example is identifying patient zero from the temporal graph.Source: §3.1.1 · p. 4

3.1.2 Surveillance.

  • Surveillance identifies a target statistic at the present moment or in the short term, making real-time processing its key modeling requirement.Examples include prompt identification of infected individuals and real-time location risk estimates.Source: §3.1.2 · p. 4

3.1.3 Prediction.

  • Prediction tasks forecast epidemic events over longer horizons, targeting either quantitative incidence measures or higher-level spreading trends.Incidence examples include future infections, deaths, influenza activity, ILI rates, and vaccine hesitancy; trend targets include the next infected region or dynamics in emerging high-risk groups.Source: §3.1.3 · p. 4

3.1.4 Projection.

  • Projection tasks incorporate evolving conditions such as interventions or changing initial states to understand outcomes and identify effective interventions.The survey generalizes influence maximization to strategies on nodes and edges over time, including quarantine levels and mobility restrictions.Source: §3.1.4 · pp. 4–5

3.1.5 Perspectives from Data Scientists.

  • Across epidemic tasks, the survey categorizes model inputs by node features and graph structure, including spatial-only, temporal-only, and spatial-temporal data.Graph structure may also be distinguished as static or dynamic, based on its temporality and learnability.Source: §3.1.5 · p. 5
  • Model outputs are classified as scalar, graph, or action sequence, with action sequences associated with projection methods that use reinforcement learning.Scalars commonly indicate epidemic measures such as infected cases, while graph outputs can represent constructed epidemic graphs.Source: §3.1.5 · p. 5

3.2 Data Sources

The surveyed work draws on data from multiple parts of the world, though most studies focus on COVID-19 and only a few address ILI or bacteria.

3.2 Data Sources

  • Surveyed works cover datasets from different parts of the world, but most research focuses only on COVID-19; only a few study Influenza-Like Illnesses (ILI) or bacteria.Source: §3.2 · pp. 5–6
  • Demographic and health records provide population, infection, or individual and group health information for node features or graph construction.These data may come from public databases released by universities, governments, or other organizations.Source: §3.2 · p. 6
  • Mobility information from transportation websites, maps, or contact records is usually used to construct graph structure.Source: §3.2 · p. 6
  • Online searches and social-media records can provide epidemic signals, such as regional searches for disease-related questions used as node features.Source: §3.2 · p. 6
  • Sensor data, including images, can support tasks such as exposure-risk prediction but may require specialized preprocessing before integration as node features.The survey gives ResNet image encoding as an example.Source: §3.2 · p. 6
  • Some studies use simulated data for training and testing, generated with models such as TimeGEO, ICM, or SIR to produce temporal graphs.Source: §3.2 · p. 6

3.3 Graph Construction

Graph construction is organized by whether node features and graph structure are static or dynamic.

3.3 Graph Construction

  • The graph-construction taxonomy distinguishes static from dynamic node features and graph structures.It frames four dimensions for describing epidemic graphs.Source: §3.3 · p. 6

3.3.1 Static Node Features.

  • Static node features are time-invariant characteristics, such as individuals’ age, gender, infection order, or symptoms.They can also supplement time-series tasks.Source: §3.3.1 · p. 6

3.3.2 Dynamic Node Features.

  • Dynamic node features change over time; daily confirmed cases are one example, and inputs may cover one time slice or the full sequence.Their representation includes node, time-point, and feature dimensions.Source: §3.3.2 · p. 6

3.3.3 Static Graph Structure.

  • Static graph structure remains fixed and may encode regional geography, mobility links, or individual contact relationships.Edges can carry weights such as distances or other features.Source: §3.3.3 · p. 6

3.3.4 Dynamic Graph Structure.

  • Dynamic graph structure changes over time through updated edges or learned adaptive relationships between nodes.Attention weights can represent one node’s influence on another.Source: §3.3.4 · p. 6

3.4 Methodological Distinctions

The review divides GNN methodologies for epidemic modeling into data-driven Neural Models and theory-informed Hybrid Models.

3.4 Methodological Distinctions

  • The survey classifies GNN methodologies for epidemic modeling as Neural Models or Hybrid Models.Both categories use neural networks but differ in how they incorporate epidemiological mechanisms.Source: §3.4 · p. 6
  • Neural Models use GNNs to learn disease-dynamics patterns without explicitly encoding epidemiological processes.They represent the data-driven category.Source: §3.4 · p. 6
  • Hybrid Models combine mechanistic epidemiological models with neural networks to seek interpretable, accurate predictions grounded in theory.Mechanistic structure complements the neural networks’ data-driven flexibility.Source: §3.4 · p. 6

4 METHODOLOGY

The methodology review organizes GNN epidemic models into Neural and Hybrid Models, tracing how they represent spatial and temporal dynamics, interventions, and mechanistic knowledge.

4 METHODOLOGY

  • Figure 3 depicts neighborhood aggregation followed by temporal processing, mechanistic-parameter estimation, or direct prediction.The review divides methods into Neural Models and Hybrid Models, which differ in whether they incorporate mechanistic models.Source: §4 · pp. 6–7, Figure 3 · p. 7

4.1 Neural Models

  • Neural Models use GNNs alone to learn patterns across spatial spread, temporal evolution, and intervention strategies.The review examines these models through those three perspectives.Source: §4.1 · p. 7

4.1.1 Spatial Dynamics Modeling.

  • Adaptive structure learning addresses unavailable real-world adjacency during training; Wang et al. calculate node similarities, HierST builds a unified graph across administrative levels, and MSGNN integrates immediate and broader regional influences.Source: §4.1.1 · pp. 7–8

4.1.2 Temporal Dynamics Modeling.

  • Temporal approaches combine recurrent or convolutional modules with graph processing, while RESEAT updates attention weights to track evolving regional relationships.Some methods process temporal node features before graph convolution; others apply graph convolution at each time step and feed its outputs to a temporal module.Source: §4.1.2 · p. 8

4.1.3 Intervention Modeling.

  • Intervention models use reinforcement learning to adjust public-health actions or social interaction graphs, balancing infection control against economic costs.Song et al. [30] optimize interventions for infection reduction while maintaining economic activity; Meirom et al. [99] modulate social graphs to intervene indirectly in epidemic spread.Source: §4.1.3 · p. 8

4.2 Hybrid Models

  • Hybrid Models combine neural prediction with mechanistic principles through parameter estimation or by informing neural architectures and learning with mechanistic knowledge.The review distinguishes these two integration strategies.Source: §4.2 · pp. 8–9

4.2.1 Parameter Estimation for Mechanistic Models.

  • Parameter-estimation methods use GNN outputs to estimate transmission and recovery rates or SIR states, with MepoGNN [75, 131] also learning mobility between sub-populations.EpiGCN [134] maps node features into SIR states; Epi-Cola-GNN incorporates a mobility matrix and Next-Generation Matrix [133].Source: §4.2.1 · p. 9

4.2.2 Mechanistic-Informed Neural Models.

  • Mechanistic-informed models use epidemiological knowledge in GNN architecture or training, including simulated SIR targets and encoded compartment states.CausalGNN encodes SIRD state counts as causal features and infers rates for SIRD updates.Source: §4.2.2 · p. 10

5 FUTURE WORK

The survey identifies unresolved challenges in GNN-based epidemic modeling and outlines directions for addressing them. These include richer scale and modality handling, continuous diffusion and interventions, explainability, and data-related concerns.

5.1 Epidemic at Scales

  • Current multi-scale approaches use only two predefined scales, while finer-grained graphs can become time-consuming and complicate real-time processing.The survey calls for models spanning multiple dynamic scales and adapting to diverse epidemiological tasks.Source: §5.1 · p. 10

5.2 Cross-Modality in Epidemiology

  • GNN studies have made limited use of cross-modality: some use text or images as node features, but do not combine modalities in node features.The survey describes multimodal data as potentially augmenting one another and compensating for single-modality noise.Source: §5.2 · p. 10

5.3 Epidemic Diffusion Process

  • Current methods aggregate information at discrete time points, whereas disease diffusion is continuous; Continuous GNNs are proposed to model that process.Disease spreading and infection may also occur asynchronously, and an attention-based approach still models time discretely.Source: §5.3 · p. 10

5.4 Interventions for Epidemics

  • Most reviewed intervention methods use only one intervention type, at node or edge level, while real-world interventions may span graph levels and scales.The survey calls for multi-level and multi-scale interventions.Source: §5.4 · pp. 10–11

5.5 Generating Explainable Predictions

  • Neural epidemic models have not emphasized interpretability, although general GNN explanation approaches may be useful in epidemiological settings.The survey notes that hybrid models primarily rely on mechanistic models for explanations.Source: §5.5 · p. 11

5.6 Handling Challenges from Epidemic Data

  • Epidemic GNN research has not sufficiently addressed noisy or incomplete data, including node- and edge-level noise and the effects of missing data.The survey notes that neighbor aggregation, simulation, or interpolation may mitigate missing features, but their influence in epidemiological GNN settings has received little study.Source: §5.6 · p. 11
  • Reliance on large-scale epidemic data raises privacy concerns; Federated Graph Learning keeps data distributed rather than centrally aggregating it.The survey connects this approach to minimizing risks associated with centralized storage and processing.Source: §5.6 · p. 11

6 CONCLUSION

The survey organizes GNN research in epidemic modeling through taxonomies of tasks and methods. It also identifies challenges and future directions, aiming to connect GNN and epidemiology communities.

6 CONCLUSION

  • The survey classifies epidemic tasks into Detection, Surveillance, Prediction, and Projection.These are the four parts of its epidemiological task categorization.Source: §6 · p. 11
  • Its methodology taxonomy separates GNN-based methods into Neural Models and Hybrid Models.The survey also introduces definitions for epidemiology, epidemic modeling, and GNNs.Source: §6 · p. 11
  • The survey outlines challenges and potential research directions, with the stated aim of bridging GNN and epidemiology communities.It aims to inspire epidemiologists and data scientists to pursue advances in the field.Source: §6 · p. 11

COMPLETE TAXONOMY

Table 1 is captioned as a summary of epidemiological tasks and methodology. The supplied entries list method combinations and graph descriptors.

COMPLETE TAXONOMY

  • Table 1 is captioned as a summary of epidemiological tasks and methodology.The caption does not specify the table's row or column encoding.Source: Table 1 · p. 16
  • Listed method combinations include GNN with SIR and reinforcement learning, and GCN with modified SIR.The entries include MMCA-GNNA [64], DURLECA [30], IDRLECA, and Mepo GNN [75].Source: COMPLETE TAXONOMY · p. 16
  • Other entries list GNN architectures combined with LSTM, GRU, attention, or Transformer components.Examples include STAN, ATMGNN [70], and HiSTGNN.Source: COMPLETE TAXONOMY · p. 16

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