Computational Methods for Epidemic Simulation, Inference and Uncertainty Quantification: Applications to Measles in Samoa and COVID-19 in Aotearoa New Zealand

Abstract

Infectious disease modelling has recently seen a resurgence due to the COVID-19 pandemic. For mathematical models to be useful in the control of such a pandemic, they must be calibrated with the available and often evolving data. This is a statistically difficult and computationally expensive process that typically requires repeated simulation of the model, and is subject to statistical problems of (non-)identifiability and model misspecification. This thesis considers a range of computational methods for the simulation inference and uncertainty quantification of epidemic models. First, the generalised profiling method is considered in order to sidestep the necessity to repeatedly simulate a model, while allowing for a partially observed model. By developing an explicit likelihood-based formulation of the generalised profiling method, we can also natively perform uncertainty quantification and hyperparameter tuning, as well as include methods for performing identifiability analysis with the profile likelihood and bootstrapping. We apply this formulation to a case study of a measles outbreak in Samoa in 2019-2020 and show that it can provide accurate predictions. In order to further tackle model misspecification, more complex models can be used. However, these models are computationally expensive to simulate accurately. For the COVID-19 outbreaks in New Zealand, considerations for a heterogeneous population were important for analysing the effects of proposed government interventions. To this end, an individual-based network model was developed with testing, quarantine and contacting tracing mechanisms. The model was simulated with a first-family variant of the Gillespie algorithm, modified to handle non-Markovian behaviours using delayed effects and thinning. It was used to analyse the potential effects of interventions and assimilate data for multiple COVID-19 outbreaks in New Zealand. Finally, in order to reduce the computational cost of using such a complex model, the exploration of surrogate modelling using analogous cheap ODE models is done for a toy system. We show that there are systematic bias and temporal registration issues, but resolving those with parameter transformations and time shifts provides useful estimates. This research provides improvements in and synthesis of multiple computational and statistical methods for modelling epidemic outbreaks.