A Modelling Framework for Estimating the Risk of Importation of a Novel Disease

Abstract

Sequential Monte Carlo (SMC) methods are vital in fitting models, without a tractable likelihood, to data. When combined with Markov Chain Monte Carlo, SMC allows for full posterior distributions of states and parameters to be estimated. However, for many problems, these methods can be prohibitively computationally expensive. One such class of models with intractable likelihoods are continuous-time Branching Processes (CTBPs). In this thesis, we leverage the unique properties of CTBPs to derive a method that approximates the results of standard SMC methods, with a significant reduction in computation time. We find that under certain conditions the method we have developed can produce highly accurate results in orders of magnitude less time than standard SMC methods. Continuous-time Branching Processes are often used for epidemic modelling, particularly in the early phases of an outbreak. In light of the COVID-19 pandemic, CTBPs have been used in metapopulation models, where agents are partitioned into subpopulations (usually states or countries) that interact through immigration. In this thesis, we build upon existing work in this area, with a focus on estimating disease importation risk. We show how applying our method to this problem can allow for joint estimation of the parameters mediating disease spread and unobserved cases. Specifically, the speed improvement given by our method allows for full posterior distributions for states, parameters and importation risk to be derived. Furthermore, we find that the increase in speed also allows more parameters to be estimated. Consequently, each subpopulation can have its own parameters. As a result, hierarchical modelling can be employed, meaning that parameter estimates from one subpopulation can inform the estimates of others. We find hierarchical modelling to be vital in estimating importation risk, particularly for counties with low observation probability.