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Spatiotemporal Dynamics of a Predator–Prey Model with Harvest and Disease in Prey

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  • Jingen Yang

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

  • Zhong Zhao

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

  • Yingying Kong

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

  • Jing Xu

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435000, China)

Abstract

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects.

Suggested Citation

  • Jingen Yang & Zhong Zhao & Yingying Kong & Jing Xu, 2025. "Spatiotemporal Dynamics of a Predator–Prey Model with Harvest and Disease in Prey," Mathematics, MDPI, vol. 13(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2474-:d:1714706
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    References listed on IDEAS

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    1. Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Manoj Kumar Singh & Arushi Sharma & Luis M. Sánchez-Ruiz, 2025. "Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense," Mathematics, MDPI, vol. 13(4), pages 1-19, February.
    3. 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.
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