arXiv:2512.05227v2 Announce Type: replace-cross Abstract: We develop a Bayesian nonparametric framework for modeling collections of related epidemic trajectories using exchangeable Gaussian processes. The proposed formulation induces structured dependence across time-varying transmission processes through shared latent Gaussian process components, leading to interpretable pooling behaviour, variance decompositions and intra-class correlation parameters that quantify information sharing across populations. The framework accommodates both direct and indirect observation regimes, including noisy measurements of effective reproduction numbers, latent transmission models for Chikungunya outbreaks and age-structured epidemic systems driven by partially observed infection dynamics. We discuss connections with broader multi-output Gaussian process formulations, including coregionalisation and latent factor models, while emphasising the interpretation of the proposed approach as a functional random-effects framework for related temporal trajectories. A simulation study investigates the behaviour of the proposed models under varying cross-population dependence structures including dependent, weakly dependent and independent settings. Across several epidemic applications, the proposed models demonstrate strong predictive performance while providing interpretable insights into shared and population-specific transmission dynamics.