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International Journal of Mathematical Research

January 2017, Volume 6, 1, pp 22-28

Analysis of an Eco-Epidemiological Model with Disease in the Prey and Predator

Lihong Wang

,

Fanghong Zhang

,

Cuncheng Jin

Lihong Wang 1 ,

Fanghong Zhang 1 Cuncheng Jin 1 
  1. Longqiao College of Lanzhou University of Finance and Economics, Lanzhou, China 1

Pages: 22-28

DOI: 10.18488/journal.24.2017.61.22.28

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Article History:

Received: 23 December, 2016
Revised: 20 January, 2017
Accepted: 08 March, 2017
Published: 20 April, 2017


Abstract:

We analyze and formulate an Eco-Epidemiological model with disease in the prey and predator, study the existence of the non-negative equilibria, obtain the sufficient conditions of locally asymptotical stability of the equilibria, then analyze the global stability of the positive equilibria.

Contribution/ Originality
This study contributes in the existing literature of Eco-Epidemiological model. We get the conditions of local asymptotic and the existence of the boundary balance, and we proved the positive balance point is global asymptotical stability by constructing Liapunov function.

Keywords:

Eco-epidemiological model, Asymptotically stable, Equilibria, Liapunov function, Prey, Predator.

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Reference:

  1. Y. Jianya and Z. Fengqing, "The prey-predator model with epidemic in the predator [J]," Mathematical Bioscien, vol. 22, pp. 419-423, 2007. View at Google Scholar 
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  3. S. Shulin and Y. Cunde, "Analysis of eco-epidemiological SIS model with epidemmic in the predator [J]," Chinese Journal of Engineering, vol. 22, pp. 30-31, 2005. View at Google Scholar 
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  6. X. Yanni and C. Lansun, "Modeling and analysis of a predator-prey model with disease in the prey [J]," Mathematical Biosciences, vol. 171, pp. 59-82, 2001. View at Google Scholar | View at Publisher
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Funding:

This study received no specific financial support.

Competing Interests:

The authors declare that they have no competing interests.

Acknowledgement:

All authors contributed equally to the conception and design of the study.

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