Wave of chaos in a spatial eco-epidemiological system: generating realistic patterns of patchiness in rabbit-lynx dynamics

Upadhyay, Ranjit Kumar, Roy, Parimita, Venkataraman, C and Madzvamuse, A (2016) Wave of chaos in a spatial eco-epidemiological system: generating realistic patterns of patchiness in rabbit-lynx dynamics. Mathematical Biosciences, 281. pp. 98-119. ISSN 0025-5564

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In the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.

Item Type: Article
Keywords: Eco-epidemiological model, Bifurcations analysis, Diffusion-driven instability, Turing patterns
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematics Applied to Biology Research Group
Subjects: Q Science
Q Science > QA Mathematics
Q Science > QA Mathematics > QA0297 Numerical analysis
Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Anotida Madzvamuse
Date Deposited: 27 Sep 2016 08:48
Last Modified: 12 Sep 2017 14:35
URI: http://srodev.sussex.ac.uk/id/eprint/63203

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