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

Ranjit Upadhyay, Parimita Roy, C. Venkataraman, Anotida Madzvamuse

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)98-119
Number of pages22
JournalMathematical Biosciences
Volume281
Early online date14 Sept 2016
DOIs
Publication statusPublished - Nov 2016

Keywords

  • Eco-epidemiological model
  • Bifurcation analysis
  • Diffusion-driven instability
  • Turing patterns

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