Unifying Physics- and Data-Driven Modeling via Novel Causal Spatiotemporal Graph Neural Network for Interpretable Epidemic Forecasting

TL;DR

This work tackles epidemic forecasting by unifying physics-based SIR dynamics with data-driven graph learning in a Causal Spatiotemporal Graph Neural Network (CSTGNN). It introduces the Spatio-Contact SIR (SCSIR) as a causal prior and combines an adaptive static mobility graph with a learned dynamic graph, enhanced by temporal decomposition, to model inter-regional transmission and temporal evolution. Empirical results on China and Germany datasets show CSTGNN achieving strong or state-of-the-art accuracy across short- and long-term horizons while providing interpretable parameters such as the contact matrix $c$ and the effective reproduction number $R_0(t)$. The framework offers actionable epidemiological insights and a principled path to deploy interpretable, data-driven forecasts in public health decision-making.

Abstract

Accurate epidemic forecasting is crucial for effective disease control and prevention. Traditional compartmental models often struggle to estimate temporally and spatially varying epidemiological parameters, while deep learning models typically overlook disease transmission dynamics and lack interpretability in the epidemiological context. To address these limitations, we propose a novel Causal Spatiotemporal Graph Neural Network (CSTGNN), a hybrid framework that integrates a Spatio-Contact SIR model with Graph Neural Networks (GNNs) to capture the spatiotemporal propagation of epidemics. Inter-regional human mobility exhibits continuous and smooth spatiotemporal patterns, leading to adjacent graph structures that share underlying mobility dynamics. To model these dynamics, we employ an adaptive static connectivity graph to represent the stable components of human mobility and utilize a temporal dynamics model to capture fluctuations within these patterns. By integrating the adaptive static connectivity graph with the temporal dynamics graph, we construct a dynamic graph that encapsulates the comprehensive properties of human mobility networks. Additionally, to capture temporal trends and variations in infectious disease spread, we introduce a temporal decomposition model to handle temporal dependence. This model is then integrated with a dynamic graph convolutional network for epidemic forecasting. We validate our model using real-world datasets at the provincial level in China and the state level in Germany. Extensive studies demonstrate that our method effectively models the spatiotemporal dynamics of infectious diseases, providing a valuable tool for forecasting and intervention strategies. Furthermore, analysis of the learned parameters offers insights into disease transmission mechanisms, enhancing the interpretability and practical applicability of our model.

Figures (28)

• Figure 1: Schematic illustration of the interactions between compartments in the SIR model.
• Figure 2: Illustration of individual homogeneity and heterogeneity. Each black circle represents a distinct region, as shown in the center-left of the figure. The central part of the figure illustrates individual movements between two regions, $i$ and $j$. The right side of the figure depicts individuals transitioning between the $S$, $I$, and $R$ types within a single region.
• Figure 3: Difference between the general SIR model and the Spatio-Contact SIR model, NI denotes no interaction between regions.
• Figure 4: Illustration of the problem formulation. The observed data $\mathcal{X}$ over $T_{\rm obs}$, combined with the dynamic adjacency matrix $\mathcal{A}_{1:T_{\rm obs}}$, predicts the epidemic states $Y$ over $T_{\rm pre}$, where $T_{\rm obs}$ and $T_{\rm pre}$ denote observed and predicted time horizons, respectively.
• Figure 5: Illustration of the causal spatiotemporal graph neural network framework.