Mathematical Analysis of Predators in Shaping Prey Species: A Study of a Biological Ecosystem

This study analyzes critical threats to wildlife species' extinction, focusing on human activities, climatic challenges, and the Allee effect within ecological frameworks. We investigate the dynamics of two interacting reaction–diffusion models, particularly examining the harvesting of prey species proportional to their intrinsic growth rates. Our findings reveal significant depletion of prey populations, especially under intense predation pressure, leading to potential extinction. While coexistence between species is possible in the absence of harvesting, one species may drive the other to extinction under certain conditions. The analytical results are supported by numerical examples, emphasizing the need for sustainable harvesting practices to maintain ecological balance and prevent species endangerment.