Host–pathogen systems in a spatially patchy environment

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Abstract
A discrete model for a host–pathogen system is developed and is used to represent the dynamics in each patch within a landscape of n x n patches. These patches are linked by between-generation dispersal to neighbouring patches. Important results (compared to similar ‘coupled map lattice’ studies) include an increase in the likelihood of metapopulation extinction if the natural loss of pathogen particles is low, and the observation of a radial wave pattern (not previously reported) where the wavefront propagates uniformly from a central focus. This result has additional significance in that it permits the system to exhibit ‘intermittency’ between two quasi-stable spatial patterns: spirals and radial waves. With intermittent behaviour, the dynamics may look consistent when viewed at one time scale, but over a longer time scale they can alter dramatically and repeatedly between the two patterns. There is also evidence of clear links between spatial structure and temporal metapopulation behaviour in both the intermittent and ‘pure’ regions, verified by results from an algorithmic complexity measure and a spectral analysis of the temporal dynamics.

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