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Mathematical modelling of epidemic systems influenced by maternal antibodies and public health intervention

By James D. Chapman


The general subject area of research considered in this thesis is population level\ud epidemic modelling of infectious diseases, with specific application to the problems\ud of model indeterminacy and systems that include processes associated with\ud maternally acquired immunity. The work presents the derivation and analysis of\ud a lumped systems model framework to study the influence of maternal antibodies\ud on the population dynamics of infection among neonate and young infant age\ud classes. The proposed models are defined by sets of ordinary and partial differential\ud equations that describe the variation of distinct states in the natural history\ud of infection with respect to time and/or age.\ud The model framework is extended to explore the potential population level outcomes\ud and consequences of mass maternal immunisation: an emerging targeted\ud vaccine strategy that utilises the active transfer of neutralising antibodies during\ud pregnancy in order to supplement neonatal immunity during the first few months\ud of life. A qualitative analysis of these models has highlighted the importance of\ud interaction with early childhood targeted vaccination campaigns, the potential to\ud invoke transient epidemic behaviour and the prospective advantages of seasonal\ud administration.\ud The work considers the implications of structural identifiability, indistinguishability\ud and formal sensitivity analyses on a number of fundamental model structures\ud within the proposed framework. These methods are used to establish whether a\ud postulated model structure, or the individual parameters within a known structure,\ud are uniquely determinable from a given set of empirical observations. The\ud main epidemiological measures available for the validation of epidemic models are\ud inherently based on records of clinical disease or age serological surveys, which are\ud not explicitly representative of infection and provide a very limited observation\ud of the full system state. The analyses suggest that these issues give rise to problems\ud of indeterminacy even in the most simple models, such that certain system\ud characteristics cannot be uniquely estimated from available data

Topics: QA, RA
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