<p>Patch dynamics form a fundamental theoretical framework in population dynamics studies. The dispersal behavior of prey across habitat patches is a key driver maintaining population resilience and community integrity. In this work, we explore an eco-epidemiological predator-prey model featuring two spatially segregated prey habitats. The impacts of saturated fear cost, special radio-dependent functional response and harvesting in the predator with environmental perturbations are evaluated in the model. The model admits a globally positive and ultimately bounded solution. And sufficient conditions are obtained for guaranteeing disease extinction and persistence in the mean, along with the existence of an ergodic stationary distribution by constructing appropriate Lyapunov functions. Numerical simulations are implemented to quantitatively validate the principal theoretical conclusions of the model. Some interesting conclusions can be drawn: Higher noise intensities can accelerate the extinction process; Fear effects serve as a crucial regulatory mechanism in population dynamics, maintaining ecological balance while introducing complex nonlinear behaviors to predator-prey systems. While escalating fear intensity suppresses the prey population’s birth rate, it does not precipitate prey extinction. Crucially, even under extreme fear levels, the prey population persists due to the saturation effect of fear-induced costs; Cross-patch dispersal acts as an ecological stabilizer, simultaneously decreasing extinction vulnerability and maintaining viable population levels.</p>

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Mathematical analysis of a two-patch eco-epidemiological predator-prey model with fear effects and a generalized ratio-dependent functional response

  • Yan Zhang,
  • Nanfeng Wei,
  • Feng Lai,
  • Shujing Gao,
  • Youquan Luo

摘要

Patch dynamics form a fundamental theoretical framework in population dynamics studies. The dispersal behavior of prey across habitat patches is a key driver maintaining population resilience and community integrity. In this work, we explore an eco-epidemiological predator-prey model featuring two spatially segregated prey habitats. The impacts of saturated fear cost, special radio-dependent functional response and harvesting in the predator with environmental perturbations are evaluated in the model. The model admits a globally positive and ultimately bounded solution. And sufficient conditions are obtained for guaranteeing disease extinction and persistence in the mean, along with the existence of an ergodic stationary distribution by constructing appropriate Lyapunov functions. Numerical simulations are implemented to quantitatively validate the principal theoretical conclusions of the model. Some interesting conclusions can be drawn: Higher noise intensities can accelerate the extinction process; Fear effects serve as a crucial regulatory mechanism in population dynamics, maintaining ecological balance while introducing complex nonlinear behaviors to predator-prey systems. While escalating fear intensity suppresses the prey population’s birth rate, it does not precipitate prey extinction. Crucially, even under extreme fear levels, the prey population persists due to the saturation effect of fear-induced costs; Cross-patch dispersal acts as an ecological stabilizer, simultaneously decreasing extinction vulnerability and maintaining viable population levels.