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An eco-epidemiological model with fear effect and hunting cooperation

Author

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  • Liu, Junli
  • Liu, Bairu
  • Lv, Pan
  • Zhang, Tailei

Abstract

In this paper, we propose an eco-epidemiological model with disease in the prey population, the model incorporates fear effect of predators on prey and hunting cooperation among predators. We assume that fear can reduce the reproduction rate of the prey population and lower the activity of the prey population, which consequently lowers the disease transmission rate. Mathematical analysis of the model with regard to the non-negativity, boundedness of solutions, stability of equilibria, permanence of the model system are analyzed. The model undergoes backward bifurcation and bistability. We conduct extensive numerical simulations to explore the roles of fear effect, hunting cooperation and other biologically related parameters (e.g. disease transmission rate of prey, death rate of predators), it is found that low levels of fear and hunting cooperation can stabilize the eco-epidemiological system, however, relatively high levels of fear and hunting cooperation can induce limit cycles. Numerical simulations show the occurrence of multiple limit cycles. It is also observed that the system shows limit cycle oscillations for small disease transmission rate/death rate of predators, and the system becomes stable when the disease transmission rate/death rate of predators is high.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308869
    DOI: 10.1016/j.chaos.2020.110494
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    References listed on IDEAS

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    1. 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.
    2. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
    3. Evan L Preisser & Daniel I Bolnick, 2008. "The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-8, June.
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    Cited by:

    1. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
    2. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.

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