Stochastic models for the spread of infectious diseases on finite contact networks: exact results and representations

Wilkinson, Robert Stochastic models for the spread of infectious diseases on finite contact networks: exact results and representations. PhD thesis, University of Liverpool.

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Abstract

Mathematical models for the spread of infectious diseases between living organisms are crucial to humanity's endeavour to understand and control its environment. The threat posed by communicable diseases is great. For example, the 1918 flu pandemic resulted in the deaths of over 50 million people and the HIV/AIDS pandemic is still under way with 2.3 million new cases in 2012. Mathematical models allow us to make predictions about the likelihood, impact and time scale of possible epidemics, and to devise effective intervention programmes, e.g. mass vaccination. This thesis considers various stochastic models of disease propagation which utilise the concept of a finite contact (social) network. For such models, we investigate ways in which important information can be extracted without a full mathematical `solution' (often unavailable) or numerous time consuming simulations (often inefficient and uninformative). For example, we consider the probability that a large scale outbreak will occur when a single infected individual is introduced to a susceptible population, and the expected number of infected individuals at time t. Although we focus on the context of epidemiology, the models under investigation are elementary and will be applicable to other domains, such as the spread of computer viruses, the spread of ideas, chemical reactions, and interacting particle systems.

Item Type:	Thesis (PhD)
Additional Information:	Date: 2015-06 (completed)
Subjects:	?? QA ??
Depositing User:	Symplectic Admin
Date Deposited:	27 Aug 2015 09:06
Last Modified:	17 Dec 2022 01:34
DOI:	10.17638/02014701
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2014701