Uncertainty quantification for complex network contagion simulation models

Abstract

Mathematical models for epidemic spread can be used to guide public health responses and policy development. At Te P¯unaha Matatini, we have developed a complex network contagion model for the spread of COVID-19 in New Zealand. The complexity in this model gives rise to many sources of uncertainty. Here we consider simulation-based inference and prediction based on fitting Gaussian Process (GP) surrogate models to limited numbers of realisations from the network contagion model. Using these GP surrogates, we can then efficiently perform simulation-based prediction, inference, and parameter estimation. By conditioning our predictive GP surrogate on data, we show how we can make predictive forecasts for COVID-19 outbreaks in New Zealand without requiring parameter updates or re-running of simulations. We also demonstrate a parameter estimation methodology using a conditional GP surrogate. We note that GP surrogates do not naturally respect the mechanistic behaviour and constraints of an epidemic process, leading to some inaccuracies. However, in a field where quick decisions often have to be made, we have shown that GP surrogates can provide a fast and simple alternative that we can use to assess the uncertainty in a complex model.