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.