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

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posted on 2023-06-09, 02:48 authored by Ranjit Kumar Upadhyay, Parimita Roy, Chandrasekhar VenkataramanChandrasekhar Venkataraman, Anotida MadzvamuseAnotida Madzvamuse
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.

Funding

Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1

InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION; 642866 - InCeM

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Mathematical Biosciences

ISSN

0025-5564

Publisher

Elsevier

Volume

281

Page range

98-119

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Mathematics Applied to Biology Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-09-27

First Open Access (FOA) Date

2017-09-15

First Compliant Deposit (FCD) Date

2016-09-10

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