Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management

In this study, we derive and study an additional food provided prey-predator model involving Holling type-III functional response among mutually interfering predators. This study investigates the effects of provision of additional food to natural enemies (predators) in altering pest (prey) dynamics. The preliminary results include positivity and boundedness of the solutions. We demonstrate the existence of equilibria, their local stability and bifurcation analysis. We also discuss the global dynamics and stability behavior with respect to crucial parameters using numerical methods. Our results show that the additional food influence the system dynamics and controlled provision of additional food is beneficial for pest management. Further, time optimal control problems are explored by considering the quality and quantity of additional food as control parameters. We framed and characterized the time optimal control problems using Pontryagin’s maximum principle and simulated using numerical optimization techniques. Our theoretical and numerical investigations reveal that the provision of suitable choice of additional food steers the system to a prey-elimination state, leading to a pest-regulated ecosystems. Our work uniquely integrates mutual interference among predators and slow predation dynamics with the provision of additional food, coupled with time optimal control strategies, offering a novel perspective on sustainable pest management and bio-control. MSC 2020 codes: 37A50; 60H10; 60J65; 60J70