Learning graph topology from metapopulation epidemic encoder-decoder

TL;DR

This study establishes a robust framework for simultaneously inferring epidemic parameters and topology, addressing a persistent gap in modeling disease propagation.

Abstract

Metapopulation epidemic models are a valuable tool for studying large-scale outbreaks. With the limited availability of epidemic tracing data, it is challenging to infer the essential constituents of these models, namely, the epidemic parameters and the relevant mobility network between subpopulations. Either one of these constituents can be estimated while assuming the other; however, the problem of their joint inference has not yet been solved. Here, we propose two encoder-decoder deep learning architectures that infer metapopulation mobility graphs from time-series data, with and without the assumption of epidemic model parameters. Evaluation across diverse random and empirical mobility networks shows that the proposed approach outperforms the state-of-the-art topology inference. Further, we show that topology inference improves dramatically with data on additional pathogens. Our study establishes a robust framework for simultaneously inferring epidemic parameters and topology, addressing a persistent gap in modeling disease propagation.

Figures (14)

• Figure 1: Representative graph topologies used in this study. Top row: synthetic random graphs - er, ba, ws, rgg.
• Figure 2: Left: A metapopulation epidemic process showing the infection both within and among the populations. The blue blocks indicate the state evolution of subpopulation 1. Right: An example of one pathogen metapopulation epidemic time-series data $\Delta \bar{S}$ in typical ba and rgg graphs with 100 nodes, as well as empirical contiguous US nr, where the nodes are geometric states (two nodes establish a link if they share a border), and global air transportation graphs, which represent the commute between two airports. The x-axis represents the number of days since the start of the epidemic. The nodes are ordered along the y-axis according to the distance from the seed node. The color indicates the fraction of daily new cases $\Delta \bar{S}$.
• Figure 3: Architecture of the self-supervised DTEF model. The input is the daily new infection data $\Delta\bar{S}$. The encoder extracts node--pathogen embeddings and infers the infection matrix $\hat{Z}$, and the decoder uses $\hat{Z}$ to reconstruct the predicted daily new infections $\Delta\hat{{S}}$. Green ovals and rectangles denote modules with learnable parameters, blue ovals denote parameter-free operations, the black box in $\sigma$ is the scalar output of $F$ transform operation, $\sigma$ is the sigmoid activation enforcing $\hat{Z}_{ij}\in[0,1]$(red cell), arrows indicate input sequences, and the highlighted red cell shows a specific reconstructed entry of $\Delta\hat{S}$.
• Figure 4: The loss (Eq. \ref{['eq: loss']}) as a function of the number of optimization epochs (left); four evaluation metrics as a function of the number of optimization epochs (right).
• Figure 5: DTEF model performance PR curves for various random graph models, with 1-4 pathogens and a random baseline.