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Modeling of hunting strategies of the predators in susceptible and infected prey

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  • Lu, Yang
  • Li, Dan
  • Liu, Shengqiang

Abstract

A predator–prey model with epidemic prey and staged structure in the predators, where the predators are assumed to keep constant preference probability of predation on susceptible/infected prey, is formulated to study the hunting strategies of predators for maximum surviving rate as well as maximum density. Given that the disease is endemic among prey before the invasion of predators, global dynamics of the model are obtained and threshold dynamics determined by the predator’s net reproductive number RH are established: the predators go extinct if RH < 1; and predators persist if RH > 1. As an application, the hunting strategies of the predators for the maximum RH are studied, and it is shown that the predators should only hunt the susceptible prey when the disease is just slightly endemic, while if the disease is seriously endemic, they should only hunt the infected prey. Numerical simulations are performed to verify/support the theoretical results and to consider the hunting strategies of predators for their maximum density, for which it is shown that the predators should keep some proper preference probability on both susceptible and infected prey.

Suggested Citation

  • Lu, Yang & Li, Dan & Liu, Shengqiang, 2016. "Modeling of hunting strategies of the predators in susceptible and infected prey," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 268-285.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:268-285
    DOI: 10.1016/j.amc.2016.03.005
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    References listed on IDEAS

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    1. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    2. Mukhopadhyay, B. & Bhattacharyya, R., 2009. "Role of predator switching in an eco-epidemiological model with disease in the prey," Ecological Modelling, Elsevier, vol. 220(7), pages 931-939.
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    Cited by:

    1. Tao, Xiangyu & Zhu, Linhe, 2021. "Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.

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