Abstract
In the mathematical modelling of epidemics, networks are frequently used torepresent population structure and the effects of heterogeneity. The ideal net-
work infection model presents dynamically consistent but mathematically tractable
representations of both the population structure, usually by way of a random
graph, and a stochastic spreading process on it. High levels of observed social and biological complexity, however, mean that compromises must be made
dependent on the primary quantity of interest. This has led to a plethora of
models and techniques in the literature.
In this thesis the primary interest is in models that track infection timings;
how quickly will an infection cross the network and how long after person A is
infected might person B become infected also? We shall see how models tracking
infection time prove effective in capturing the dynamics of multiple coevolving
contagions as, in order to study infection interactions, it must be known where
their time frames overlap.
To this end, we shall consider three main models. Firstly, we use a multi-
type branching process to analyse a secondary infection with dependence upon
a primary infection host; this enables us to determine a window of relative
speed in which the infections must develop in order to have secondary survival.
Secondly, we develop a multi-type variant of the time tracking message passing equations; these enable us to answer questions about local susceptibility in
a model with several interacting infection strains. Finally, by analysing the
simplest version of these same message passing equations, we succeed in presenting some new theory for tracking infection timings with a calculation for
the asymptotic speed of an infection wave front and an approximation of the
expected infection time offset for heterogeneous individuals in the population
bulk.
| Date of Award | 19 Feb 2020 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Tim Rogers (Supervisor) |