Allee and fear effects in prey-predator dynamics: stability analysis and optimal harvesting

Abstract

This study incorporates the Allee effect and the fear effect into a predator-prey model. We investigate how these factors, along with fishing pressure, influence the population dynamics of both predator and prey. The analysis begins by establishing the positivity and boundedness of solutions, ensuring the populations remain within realistic ranges. Stability analysis of the interior equilibrium point, where both populations coexist, reveals the system’s resilience to disturbances. Furthermore, we explore optimal fishing strategies that balance maximizing long-term profit with maintaining sustainable populations. Finally, numerical simulations conducted validate the theoretical predictions.