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A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge

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  • Sharma, Swarnali
  • Samanta, G.P.

Abstract

In this paper, a predator–prey Leslie–Gower model with disease in prey has been developed. The total population has been divided into three classes, namely susceptible prey, infected prey and predator population. We have also incorporated an infected prey refuge in the model. We have studied the positivity and boundedness of the solutions of the system and analyzed the existence of various equilibrium points and stability of the system at those equilibrium points. We have also discussed the influence of the infected prey refuge on each population density. It is observed that a Hopf bifurcation may occur about the interior equilibrium taking refuge parameter as bifurcation parameter. Our analytical findings are illustrated through computer simulation using MATLAB, which show the reliability of our model from the eco-epidemiological point of view.

Suggested Citation

  • Sharma, Swarnali & Samanta, G.P., 2015. "A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 69-84.
    • Handle: RePEc:eee:chsofr:v:70:y:2015:i:c:p:69-84
    DOI: 10.1016/j.chaos.2014.11.010
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    References listed on IDEAS

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    1. Shufan Wang & Zhihui Ma, 2012. "Analysis of an Ecoepidemiological Model with Prey Refuges," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-16, November.
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    Cited by:

    1. Liu, Junli & Liu, Bairu & Lv, Pan & Zhang, Tailei, 2021. "An eco-epidemiological model with fear effect and hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    3. Agus Suryanto & Isnani Darti, 2019. "Dynamics of Leslie-Gower Pest-Predator Model with Disease in Pest Including Pest-Harvesting and Optimal Implementation of Pesticide," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-9, June.
    4. Aihua Kang & Yakui Xue & Jianping Fu, 2015. "Dynamic Behaviors of a Leslie-Gower Ecoepidemiological Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, November.
    5. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.

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