The impact of human shields in autonomous and non-autonomous prey–predator models with modified Cosner functional response

In this study, we investigate the complex interplay between prey and predators under varying human-mediated influences. Theoretical analyses explore the solution’s non-negativity and boundedness, existence of feasible equilibria and their stability behaviors, and various bifurcations including saddle–node and Hopf. Using a detailed numerical exploration, we identified distinct population distribution, demonstrating how different factors shape ecological systems in non-trivial ways. The results suggest that human interventions, whether through direct shielding of prey or indirect effects on predator–prey interactions, can significantly disrupt ecological dynamics. Our findings highlight the importance of sustainable strategies that conserve prey populations while supporting predators to maintain ecosystem balance. Furthermore, by adding seasonal changes to some key parameters, we extend our autonomous system to a nonautonomous framework. Simple periodic oscillations, higher periodic oscillations, bursting patterns, and the extinction of predators are observed due to seasonal changes in the parameters.