BioND — Dynamics of Biological Networks

Dispersal-processes on multi-layer networks

Edmund Barter
PhD thesis in Mathematics, University of Bristol, 2017.

Abstract

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The pattern of interactions between the many parts of a complex system can be represented by a network. A central goal of network science is to uncover the properties of the system that emerge due to this pattern of interactions. Models of the dynamics of diseases are one of a small number of paradigmatic processes that have motivated and demonstrated advances in network science. As the mathematical tools for describing dispersal processes on networks have advanced, new, more complex epidemiological models have been devised. Recently several models have been proposed of systems with multiple interacting diseases, represented by a multilayer network. Very similar systems play an important role in population ecology. In a model proposed by Pillai et al. species disperse over a network of spatial patches while interacting with each other via trophic (feeding) and other relationships. In this thesis I present an analytical approach for a version of this meta-foodweb model, where the network of feeding relationships is a linear chain. I also use agent based simulations to investigate a more complex meta-foodweb model and find that meso-scale spatial variations in spatial networks aid the persistence of species that feed at multiple trophic levels. I investigate a model of a disease in a growing population with an approach comprising analytic, numeric and simulation techniques and find a vanishing epidemic limit and steady dynamic oscillations of population and disease prevalence. I suggest that similarly rich dynamics may be uncovered in ecological systems and using a similar combination of methods may yield new results in meta-foodwebs. This work expands the toolbox of network science and encourages the development of new techniques to increase understanding of the wide variety of multilayer networks that arise in ecology, epidemiology and elsewhere.

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