Dynamics of squirrel populations competition model with the influence of fear effect and squirrel-pox virus

In this paper, we set up a model to consider the influence of fear effect on the competition between gray squirrels (Sciurus caroliinenss) and red squirrels (Sciurus vulgaris) with the transmission of squirrel-pox virus (SQRV). The positivity and boundedness of the system solutions were rigorously analyzed, while the existence and stability conditions of the equilibria were systematically investigated through stability theory. During stability analysis, a specific scenario was identified in which one species tended to become extinct. Consequently, the model was revised by implementing state feedback impulse control mechanisms designed to simulate ecological preservation measures. The existence of order-1 periodic solutions in the state feedback impulsive system was subsequently examined. All theoretical findings were validated through numerical simulations, and their ecological implications are comprehensively discussed.