Gaussian process emulation for exploring complex infectious disease models

Epidemiological models that aim for a high degree of biological realism by simulating every individual in a population are unavoidably complex, with many free parameters, which makes systematic explorations of their dynamics computationally challenging. In this study, we demonstrate how Gaussian Process emulation can overcome this challenge. To simulate disease dynamics, we developed an abstract individual-based model that is loosely inspired by dengue, incorporating some key features shaping dengue epidemics such as social structure, human movement, and seasonality. We focused on three epidemiological metrics derived from the individual-based model outcomes - outbreak probability, maximum incidence, and epidemic duration - and trained three Gaussian Process surrogate models to approximate these metrics. The GP surrogate models enabled the rapid prediction of these epidemiological metrics at any point in the eight-dimensional parameter space of the original model. Our analysis revealed that average infectivity and average human mobility are key drivers of these epidemiological metrics, while the seasonal timing of the first infection can influence the course of the epidemic outbreak. We used a dataset comprising more than 1,000 dengue epidemics observed over 12 years in Colombia to calibrate our Gaussian Process model and evaluated its predictive power. The calibrated Gaussian Process model identified a subset of municipalities with consistently higher average infectivity estimates; the notable overlap between these municipalities and previously reported dengue disease clusters suggests that statistical emulation can facilitate empirical data analysis. Overall, this work underscores the potential of Gaussian Process emulation to enable the use of more complex individual-based models in epidemiology, allowing a higher degree of realism and accuracy that should increase our ability to control diseases of public health concern.