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A predator–prey model with diseases in both prey and predator

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  • Gao, Xubin
  • Pan, Qiuhui
  • He, Mingfeng
  • Kang, Yibin

Abstract

In this paper, we present and analyze a predator–prey model, in which both predator and prey can be infected. Each of the predator and prey is divided into two categories, susceptible and infected. The epidemics cannot be transmitted between prey and predator by predation. The predation ability of susceptible predators is stronger than infected ones. Likewise, it is more difficult to catch a susceptible prey than an infected one. And the diseases cannot be hereditary in both of the predator and prey populations. Based on the assumptions above, we find that there are six equilibrium points in this model. Using the base reproduction number, we discuss the stability of the equilibrium points qualitatively. Then both of the local and global stabilities of the equilibrium points are analyzed quantitatively by mathematical methods. We provide numerical results to discuss some interesting biological cases that our model exhibits. Lastly, we discuss how the infectious rates affect the stability, and how the other parameters work in the five possible cases within this model.

Suggested Citation

  • Gao, Xubin & Pan, Qiuhui & He, Mingfeng & Kang, Yibin, 2013. "A predator–prey model with diseases in both prey and predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5898-5906.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:23:p:5898-5906
    DOI: 10.1016/j.physa.2013.07.077
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    References listed on IDEAS

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    1. Sangamaheswaran, A.P. & Jeyaseelan, M.J.P., 2001. "White spot viral disease in penaeid shrimp-a review," Naga, The WorldFish Center, vol. 24(3-4), pages 16-22.
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    Cited by:

    1. Juneja, Nishant & Agnihotri, Kulbhushan & Kaur, Harpreet, 2018. "Effect of delay on globally stable prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 146-156.

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