Leng, Trystan Stewart (2021) Correlation, concurrency, and clustering in network models of epidemics in human populations. PhD thesis, University of Warwick.

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Abstract

The spread of an epidemic can be conceptualised as a process on a network, where vertices refer to individuals and where edges refer to epidemiologically relevant connections between individuals. Understanding the impact of network structure on epidemiological outcomes is a central task in mathematical epidemiology. Accordingly, a range of mathematical models incorporating network structure have been designed. In this thesis, we develop a range of network models in the context of epidemics in human populations.

Firstly, we consider a novel moment-closure approximation for a disease with susceptible-infected- susceptible dynamics. For diseases without immunity, the possibility of reinfection can introduce correlations in infection status between indirectly connected individuals, limiting the accuracy of moment-closure approaches. By incorporating these correlations into a model, we introduce an improvement to the standard pairwise approximation for two different network structures: the isolated open triple and the k-regular network.

Secondly, we assess the importance of including concurrent sexual partnerships, partnerships that overlap in time, when modelling the control of sexually transmitted infections. We do this in two distinct settings, firstly developing nested pair-formation models before developing an individual-based dynamic network model of a heterosexual population. In both instances we find that while concurrency can have a large impact on epidemiological dynamics, the inclusion of concurrency in models matched to prevalence data has only a modest impact on control measures.

Thirdly, we consider the extent to which the clustering imposed by social bubbles, where two households form an exclusive social group, is an effective way of increasing social contact while minimising the resulting increase in transmission in the context of COVID-19. Using a stochastic, generation-based network model of household and bubble contacts, we find that social bubble strategies are effective at minimising transmission when compared to unclustered increases in contacts.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics R Medicine > RA Public aspects of medicine
Library of Congress Subject Headings (LCSH):	Epidemics -- Mathematical models, Communicable diseases -- Mathematical models, Communicable diseases -- Transmission -- Mathematical models
Official Date:	April 2021
Dates:	Date Event April 2021 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	University of Warwick. Mathematics for Real-World Systems Centre for Doctoral Training
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Keeling, Matt
Extent:	xiv, 252 leaves : illustrations, charts
Language:	eng

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