School of Mathematics and Statistics - Theses

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Author: Alahakoon Mudiyanselage, Punya Tharangani Alahakoon ×

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    A Bayesian hierarchical modelling framework for estimating parameters of stochastic epidemic models
    Alahakoon Mudiyanselage, Punya Tharangani Alahakoon ( 2023-02)
    We consider models for multiple outbreaks of an infectious disease occurring in isolation from one another, such that the status of the epidemic in one (sub)population does not influence the evolution of the epidemic in another (sub)population. However, given the shared biological, epidemiological, behavioural and demographic characteristics of the (sub)populations, it is natural to conduct parameter estimation within a hierarchical statistical framework. This framework allows the study of the outbreaks simultaneously at multiple levels. Standard approaches to Bayesian hierarchical analysis when the outbreaks are modelled as stochastic processes can be computationally prohibitive due to inefficiencies when sampling from the joint posterior distribution. To address this issue, we propose a two-step algorithm that takes advantage of parallel computing methods to estimate parameters within a hierarchical framework in a Bayesian context. This algorithm makes use of existing Approximate Bayesian computation (ABC) methods. After introducing the mathematical (Chapter 2), epidemiological (Chapter 3), and statistical (Chapter 4) background that is required, we introduce the theory and the usage of the novel algorithm (Chapter 5). We explain how our algorithm is different from other methods in the literature and highlight the suitability of the algorithm for the study of infectious disease and other biological data. We apply this algorithm to study different biological questions through three simulationbased studies and application to two epidemiological datasets. In particular, we use the simulation-based studies to examine the methodological aspects of the algorithm. In these studies, we evaluate the probability of epidemic fade-out—extinction of the disease after the first major outbreak when it is possible to observe a second wave (Chapter 6), estimate the waning immunity rates of stochastic models with multiple outbreak data (Chapter 7), and use clustering to improve parameter estimation for stochastic epidemic models (Chapter 8). The two studies applied to epidemiological data explore the applicability of the algorithm. The first study considers outbreaks of influenza that took place on board Australian ships during the pandemic of 1918–19 (Chapter 9) while the second study looks at early COVID-19 outbreaks that took place in rural counties in the United States (Chapter 10).