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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Abstract
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 |
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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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📧 Request an updateProject Name | Sussex Project Number | Funder | Funder Ref |
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Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces | G0872 | EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL | EP/J016780/1 |
Unravelling new mathematics for 3D cell migration | G1438 | LEVERHULME TRUST | RPG-2014-149 |
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility | G1546 | EUROPEAN UNION | 642866 - InCeM |