# Gaussian process emulation for exploring complex infectious disease models

## TL;DR

Gaussian Process emulation is used to speed up the analysis of complex disease models, revealing key factors like infectivity and mobility that drive epidemics.

## Contribution

The novel application of Gaussian Process emulation enables rapid exploration of complex individual-based disease models.

## Key findings

- Average infectivity and mobility are key drivers of outbreak dynamics.
- Seasonal timing of first infection influences epidemic course.
- Gaussian Process models accurately predict epidemiological metrics across parameter space.

## Abstract

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.

Detailed individual-based models can capture a high degree of realism, but their complexity often makes them too slow or cumbersome to explore fully. In our work, we explore how Gaussian Process emulation — a statistical method for building fast, accurate surrogate models — can help overcome this challenge. First, we developed an individual-based model that simulates disease spread in a population, accounting for features such as social structure, human mobility, and seasonal variation in infection risk. We then trained a Gaussian Process surrogate model on epidemiological metrics derived from the outputs of this individual-based model, which allowed us to predict these metrics almost instantly across a wide range of parameter values. This approach made it possible to systematically explore which factors drive simulated epidemics. We found that two variables — average infectivity and average mobility — had the greatest influence on whether and how outbreaks occurred. Our results demonstrate that Gaussian Process emulation offers a practical and powerful way to study complex disease systems. While we applied this approach to infectious disease transmission, the underlying method can be useful for analyzing many other types of detailed, simulation-based models.