Cyclic Dynamics of Spatially Heterogeneous Populations - From Biodiversity to Disease Prevalence

Cyclic Dynamics of Spatially Heterogeneous Populations - From Biodiversity to Disease Prevalence

David Lamouroux

Doctoral thesis

Date of Examination: 2012-12-14

Date of issue: 2013-01-31

Advisor: Geisel, Theo Prof. Dr.

Referee: Geisel, Theo Prof. Dr.

Referee: Kree, Reiner Prof. Dr.

Persistent Address: http://hdl.handle.net/11858/00-1735-0000-000D-F289-9

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Abstract

English

Cyclic dynamics and spatial heterogeneity are pivotal aspects both of ecological populations in which species compete cyclically for dominance as well as of epidemiological populations in which diseases elicit life-long or temporal immunity. In ecology, the understanding of mechanisms that endanger or conserve biodiversity is a persistent challenge. In this respect, cyclic competition was proposed as a mechanism that maintains biodiversity as it allows more than one species to exploit an ecological niche. Spatially explicit models were found to exhibit a transition from a pattern forming state, which supports the stability of coexistence to a well-stirred state, in which coexistence is unstable. In the first part of this dissertation, a spatially discrete model is extended to include a non-unit carrying capacity that allows more than one individual to be accommodated on a single lattice site. It is demonstrated - in contrast to earlier works - that this allows to sharply distinguish the pattern forming state from the well-stirred state. This discrimination is achieved by studying the dependency of the typical time until coexistence is lost on the newly introduced carrying capacity, revealing that this dependency exhibits an opposite behaviour in the two regimes. In epidemiology, the prediction of the spread of emerging diseases and the design of control measures is a core issue. In this context, the interplay between spatial heterogeneity and cyclic disease dynamics is of central importance. In the second part of this dissertation, a metapopulation model is studied for diseases that elicit temporal or life-long immunity. In contrast to existing studies, this model assumes that the risk of infection depends on the location where the disease is contracted – taking into account that the influence of regional variations of, e.g., climatic conditions or cultural habits on the infection dynamics becomes ever more important in a modern world. In this framework it is found that connections to communities with a higher (lower) infection rate can startlingly decrease (increase) the case numbers of infections. This counter-intuitive effect has potentially profound implications for the design of containment strategies such as travel restrictions.

Keywords: population dynamics; metapopulation; pattern formation; stochastic processes; spatial heterogeneity; epidemiology; spatially varying infection rate; cyclic competition; carrying capacity