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

Jingen Yang (), Zhong Zhao, Yingying Kong and Jing Xu
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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

Mathematics, 2025, vol. 13, issue 15, 1-22

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.

Keywords: predator-prey model; eco-epidemic; non-constant positive steady state; harvest; bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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