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Emergence of Spatial Patterns in a Damaged Diffusive Eco-Epidemiological System

Ranjit Kumar Upadhyay

Department of Applied Mathematics, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, Jharkhand 826004, India

E-mail Address: ranjit.chaos@gmail.com

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Jyotiska Datta

Department of Applied Mathematics, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, Jharkhand 826004, India

E-mail Address: jyotiska.datta@gmail.com

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Yueping Dong

http://orcid.org/0000-0003-4256-6945

School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China

College of Science and Engineering, Aoyama Gakuin University, Sagamihara, Kanagawa 252-5258, Japan

E-mail Address: dongyueping0531@gmail.com

Corresponding author

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, and

Yasuhiro Takeuchi

College of Science and Engineering, Aoyama Gakuin University, Sagamihara, Kanagawa 252-5258, Japan

E-mail Address: takeuchi@gem.aoyama.ac.jp

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https://doi.org/10.1142/S0218127418300288Cited by:7 (Source: Crossref)

Abstract

In this paper, a spatial model has been designed to study a damaged diffusive eco-epidemiological system of Tilapia and Pelican populations in Salton Sea, California, USA. The nature of different equilibrium points and the existence of Hopf bifurcations are obtained. Conditions for Turing instability caused by local random movement of populations are derived. Numerically, the presence/existence of the wave of chaos phenomena is reported. Further, we show that the contact rate between susceptible and infected Tilapia population plays an important role in the distribution of the infected Tilapia population. The results suggest that the removal of infected Tilapia at regular time duration and controlling salinity will help to restore the system which provides a perspective for conservation strategy.

Keywords:

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