Identifying Asymptomatic Nodes in Network Epidemics using Graph Neural Networks

TL;DR

This work tackles identifying asymptomatic individuals in a network epidemic when only a snapshot of observed infections is available, formalized on a discrete-time SI model with $A(t_h)=I(t_h)\setminus O(t_h)$. It introduces a Graph Neural Network that ingests eight network-derived features, including $C_o(v,t_h)$, Betweenness, and Observed betweenness, to perform node classification from a single snapshot under supervised learning with Binary Cross-Entropy. The method is evaluated on Barabási–Albert and Watts–Strogatz networks across multiple sizes and observation probabilities, showing that the GNN can outperform the observed betweenness baseline, particularly in WS networks, and generalizes well to larger graphs and different $\theta$ values. These results suggest a practical, network-aware approach for targeting testing and surveillance, with notable implications for public health policy in controlling asymptomatic transmission.

Abstract

Infected individuals in some epidemics can remain asymptomatic while still carrying and transmitting the infection. These individuals contribute to the spread of the epidemic and pose a significant challenge to public health policies. Identifying asymptomatic individuals is critical for measuring and controlling an epidemic, but periodic and widespread testing of healthy individuals is often too costly. This work tackles the problem of identifying asymptomatic individuals considering a classic SI (Susceptible-Infected) network epidemic model where a fraction of the infected nodes are not observed as infected (i.e., their observed state is identical to susceptible nodes). In order to classify healthy nodes as asymptomatic or susceptible, a Graph Neural Network (GNN) model with supervised learning is adopted where a set of node features are built from the network with observed infected nodes. The approach is evaluated across different network models, network sizes, and fraction of observed infections. Results indicate that the proposed methodology is robust across different scenarios, accurately identifying asymptomatic nodes while also generalizing to different network sizes and fraction of observed infections.

Figures (4)

• Figure 1: AUC performance (Y-axis) under different probabilities of observing an infected node (X-axis). Evaluation performed on networks with $3\,\text{k}$ nodes. The lines represent the mean AUC over the $1\,\text{k}$ samples in each dataset. Each full line corresponds to a trained GNN model performance (each one trained under a different observation probability), and the dashed line corresponds to the performance of the observed betweenness metric. Figure (a) shows the results for epidemics generated with the BA networks, and Figure (b) with the WS networks (training and testing conducted on the same network model).
• Figure 2: AUC performance (Y-axis) under different network sizes (number of nodes in the network -- X-axis). The evaluation is performed under the same observation probability of the GNN training ($\theta_\text{eval} = \theta$). The lines represent the mean AUC over the $1\,\text{k}$ samples in each dataset. Each full line corresponds to a trained GNN model performance (each one is trained under a different observation probability), and the dashed line corresponds to the performance of the observed betweenness metric. Figure (a) shows the results for epidemics generated with the BA networks, and Figure (b) with the WS networks (training and testing conducted on the same network model).
• Figure 3: AUC performance (Y-axis) under different probabilities of observing an infected node (X-axis). Evaluation performed on $12\,\text{k}$ nodes WS networks. The lines represent the mean AUC over the $1\,\text{k}$ samples in each dataset. Each full line corresponds to a trained GNN model performance (each one is trained under a different observation probability), and the dashed line corresponds to the performance of the observed betweenness metric.
• Figure 4: AUC performance (Y-axis) under different network sizes (number of nodes in the network -- X-axis). The lines represent the mean AUC over the $1\,\text{k}$ samples in each dataset. The GNNs used were trained with observation probability $\theta=0.9$. The full lines correspond to evaluations on BA data, and the dashed lines correspond to evaluations on the WS datasets. The circle markers stand for the GNN trained on BA data, the "X" markers stand for the GNN trained on WS, and the square markers to the observed betweenness metric. Figure (a) shows the results for epidemics with observation probability $\theta_\text{eval} = 0.1$, and Figure (b) with $\theta_\text{eval} = 0.9$.