Mathematical and computational approaches to contagion dynamics on networks

In this thesis, we firstly introduce the basic terminology and concepts needed for the the following chapters. In particular we introduce the basics of graph/network theory, epidemiological models (both well mixed and on networks), and mobility models (the gravity and radiation models). After the introduction of these topics, we propose a general framework for epidemiological network models from which the known individual-based and pair-based models can be derived. We then introduce a more exact pair-based model by showing previous iterations are a linearised version of it, and then we extend it further to the temporal setting. Next, we present a meta-population model for the spread of COVID-19 in Ireland which makes use of temporal commuting patters generated from the radiation model. Finally, we analyse a year worth of Irish cattle trade data. We then fit a number of mobility models and show that an altered version of the radiation model, which we call the generalised radiation model, is able to accurately reproduce the distance distribution of cattle trades in the country.

Grantor dc:publisher

University College Cork

Year dc:date.issued

2022

Author dc:creator

• Humphries, Rory

Advisors dc:contributor.advisor

• Hoevel, Philipp
• Mulchrone, Kieran F.

• Epidemiology
• Network science
• Applied mathematics

Statement dc:rights

• © 2022, Rory Humphries.

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10468/14049

OAI identifier oai:identifier

oai:cora.ucc.ie:10468/14049