Deterministic and Stochastic Studies on Additional Food Provided Prey-Predator Systems with Group Defence among Prey and Mutual Interference among Predators

The influence of competition and additional food on prey-predator dynamics has attracted considerable interest from mathematical biology researchers in recent times. In this study, we consider an additional food provided prey-predator model exhibiting Holling type-IV functional response among mutually interferring predators. We prove the existence and uniqueness of global positive solutions for the proposed model. We study the existence and stability of equilibrium points and further explored bifurcations with respect to the additional food and competition. We further study the global dynamics of the system and discuss the consequences of providing additional food. Later, we do the time-optimal control studies with respect to the quality and quantity of additional food as control variables by transforming the independent variable in the control system. Making use of the Pontraygin maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. We further enhanced the model by incorpoating both continuous and discrete noise. We further characterized and numerically simulated the stochastic optimal controls through Sufficient Stochastic Maximum Principle. We show that the findings of these dynamics and control studies have the potential to be applied to a variety of problems in pest management.