Exact and approximate epidemic models on networks: theory and applications

Taylor, Michael (2013) Exact and approximate epidemic models on networks: theory and applications. Doctoral thesis (PhD), University of Sussex.

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Abstract

This thesis is concerned with modelling the spread of diseases amongst host populations and the epidemics that result from this process. We are primarily interested in how networks can be used to model the various heterogeneities observable in real-world populations.

Firstly, we start with the full system of Kolmogorov/master equations for a simple Susceptible-Infected-Susceptible (SIS) type epidemic on an arbitrary contact network. From this general framework, we rigorously derive sets of ODEs that describe the exact dynamics of the expected number of individuals and pairs of individuals.

We proceed to use moment closure techniques to close these hierarchical systems of ODEs, by approximating higher order moments in terms of lower order moments. We prove that the simple first order mean-field approximation becomes exact in the limit of a large, fully-connected network. We then investigate how well two different pairwise approximations capture the topological features of theoretical networks generated using different algorithms.

We then introduce the effective degree modelling framework and propose a model for SIS epidemics on dynamic contact networks by accounting for random link activation and deletion. We show that results from the resulting set of ODEs agrees well with results from stochastic simulations, both in describing the evolution of the network and the disease. Furthermore, we derive an analytic calculation of the stability of the disease-free steady state and explore the validity of such a measure in the context of a dynamically evolving contact network.

Finally, we move on to derive a system of ODEs that describes the interacting dynamics of a disease and information relating to the disease. We allow individuals to become responsive in light of received information and, thus, reduce the rate at which they become infected. We consider the effectiveness of different routes of information transmission (such as peer-to-peer communication or mass media campaigns) in slowing or preventing the spread of a disease.

Finally, we use a range of modelling techniques to investigate the spread of disease within sheep flocks. We use field data to construct weighted contact networks for flocks of sheep to account for seasonal changes of the flock structure as lambs are born and eventually become weaned. We construct a range of network and ODE models that are designed to investigate the effect of link-weight heterogeneity on the spread of disease.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Library Cataloguing
Date Deposited: 27 Jun 2013 06:01
Last Modified: 15 Sep 2015 11:54
URI: http://sro.sussex.ac.uk/id/eprint/45258

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