Learning Calibrated and Transferable Node-Level Infection Risk in Stochastic Epidemics on Complex Networks
Year: 2026
Type: preprint
Abstract: Background : Predicting future infection risk on contact networks requires jointly accounting for epidemic state, network structure, and stochastic uncertainty. We investigate whether the probability that a currently susceptible node will become infected can be learned as a calibrated graph function and transferred to unseen network structures. Methods : Stochastic SIR epidemics were simulated on Erd\H{o}s--R\'enyi, Barab\'asi--Albert, Watts--Strogatz, and stochastic block-model networks. For each partially observed epidemic state, repeated Monte-Carlo continuations were used to estimate soft node-level future-infection probabilities. A parameter-conditioned graph neural network (GNN) was trained on these probabilities and evaluated using strict graph-disjoint splits and leave-one-topology-out structural out-of-distribution tests. Performance was compared with ridge regression, gradient boosting, centrality-, exposure-, and diffusion-based baselines. Integrated Gradients and edge occlusion were used for mechanistic auditing, and predicted risk was evaluated for targeted intervention. Results : On 13,097 susceptible nodes from unseen graph realizations, the GNN achieved a Brier score of $7.29\times10^{-4}$, MAE of 0.0173, Spearman correlation of 0.978, and expected calibration error of 0.003. It provided more accurate absolute risk estimates than ridge and gradient-boosted models, although boosting remained competitive for within-episode ranking. Structural transfer remained strong to unseen ER, WS, and SBM networks but degraded on unseen BA graphs, which exhibited substantially greater degree heterogeneity. Integrated Gradients assigned 76.8\% of state-related attribution to the infectious compartment, while removing edges to infectious neighbors changed predicted risk approximately 6.7 times more than removing edges to susceptible neighbors. Targeting 5\% of susceptible nodes according to GNN risk produced approximately three times the attack-rate reduction of random targeting and closely matched a Monte-Carlo oracle. Conclusions : Stochastic future-infection risk can be learned as a calibrated node-level graph function and translated into effective intervention decisions. However, topology-level experiments show that structural heterogeneity can define an important boundary of transferability, emphasizing the need for explicit out-of-distribution evaluation in epidemic graph learning.
Source: Research Square
Institutions: Magna Graecia University, University of Calabria
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204686885