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Modeling COVID-19 spread in the USA using metapopulation SIR models coupled with graph convolutional neural networks

Petr Kisselev, Padmanabhan Seshaiyer

TL;DR

The paper addresses forecasting COVID-19 spread across the United States under region-specific mobility and policy heterogeneity by extending a hybrid Graph Convolutional Network–metapopulation SIR framework. It learns region-wise infection and recovery parameters ${\beta_n}$ and ${\gamma_n}$ through a spatio-temporal GCN that leverages a mobility-informed graph, enabling real-time estimation of ${\cal R}_t$ and daily infections. The authors adapt the approach to US data, introducing a flight-aware mobility term and handling data gaps in recoveries, achieving improved national forecasts over a standard SIR and providing time-varying ${\cal R}_0$ estimates, while noting state-level limitations due to granularity. Overall, the work demonstrates the potential of GCN-SIR models for real-time epidemic forecasting and policy-relevant decision support, with clear avenues for refinement via finer geographic resolution and policy-aware mobility modeling.

Abstract

Graph convolutional neural networks (GCNs) have shown tremendous promise in addressing data-intensive challenges in recent years. In particular, some attempts have been made to improve predictions of Susceptible-Infected-Recovered (SIR) models by incorporating human mobility between metapopulations and using graph approaches to estimate corresponding hyperparameters. Recently, researchers have found that a hybrid GCN-SIR approach outperformed existing methodologies when used on the data collected on a precinct level in Japan. In our work, we extend this approach to data collected from the continental US, adjusting for the differing mobility patterns and varying policy responses. We also develop the strategy for real-time continuous estimation of the reproduction number and study the accuracy of model predictions for the overall population as well as individual states. Strengths and limitations of the GCN-SIR approach are discussed as a potential candidate for modeling disease dynamics.

Modeling COVID-19 spread in the USA using metapopulation SIR models coupled with graph convolutional neural networks

TL;DR

The paper addresses forecasting COVID-19 spread across the United States under region-specific mobility and policy heterogeneity by extending a hybrid Graph Convolutional Network–metapopulation SIR framework. It learns region-wise infection and recovery parameters and through a spatio-temporal GCN that leverages a mobility-informed graph, enabling real-time estimation of and daily infections. The authors adapt the approach to US data, introducing a flight-aware mobility term and handling data gaps in recoveries, achieving improved national forecasts over a standard SIR and providing time-varying estimates, while noting state-level limitations due to granularity. Overall, the work demonstrates the potential of GCN-SIR models for real-time epidemic forecasting and policy-relevant decision support, with clear avenues for refinement via finer geographic resolution and policy-aware mobility modeling.

Abstract

Graph convolutional neural networks (GCNs) have shown tremendous promise in addressing data-intensive challenges in recent years. In particular, some attempts have been made to improve predictions of Susceptible-Infected-Recovered (SIR) models by incorporating human mobility between metapopulations and using graph approaches to estimate corresponding hyperparameters. Recently, researchers have found that a hybrid GCN-SIR approach outperformed existing methodologies when used on the data collected on a precinct level in Japan. In our work, we extend this approach to data collected from the continental US, adjusting for the differing mobility patterns and varying policy responses. We also develop the strategy for real-time continuous estimation of the reproduction number and study the accuracy of model predictions for the overall population as well as individual states. Strengths and limitations of the GCN-SIR approach are discussed as a potential candidate for modeling disease dynamics.
Paper Structure (7 sections, 2 theorems, 10 equations, 7 figures)

This paper contains 7 sections, 2 theorems, 10 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Graph Convolutional Neural Networks
  3. Model description
  4. Extending the model to US data
  5. Real-time tracking of the reproduction number
  6. Numerical results
  7. Discussion and future work

Key Result

Lemma 1

Metapopulation model model is consistent with the standard SIR model if and only if $2\alpha P^2 = \epsilon$.

Figures (7)

  • Figure 1: Structure of a traditional neural network
  • Figure 2: Structure of a GCN
  • Figure 3: Model architecture used in cao
  • Figure 4: Metapopulation model prediction for US data based on real COVID-19 data, compared against the standard SIR model. Left panel: SIR-GCN Predictions on US COVID-19 data, 1 day horizon; Right Panel: SIR-GCN Predictions on US COVID-19 data, 7 day horizon
  • Figure 5: Metapopulation model predictions for six US states.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Theorem 1
  • proof