Achieving Minimum-Time Biological Conservation and Pest Management for Additional Food provided Predator–Prey Systems involving Inhibitory Effect: A Qualitative Investigation

Abstract

Theoretical and experimental studies on prey-predator systems where predator is supplied with alternate sources of food have received significant attention over the years due to their relevance in achieving biological conservation and biological control. Some of the outcomes of these studies suggest that with appropriate quality and quantity of additional food, the system can be steered towards any desired state eventually with time. One of the limitations of previous studies is that the desired state is reached asymptotically, which makes the outcomes not easily applicable in practical scenarios. To overcome this limitation, in this work, we formulate and study optimal control problems to achieve the desired outcomes in minimum (finite) time.We consider two different models of additional food provided prey-predator systems involving Holling type IV functional response (with inhibitory effect of prey). In the first scenario, additional food is incorporated implicitly into the predator's functional response with a possibility of achieving biological conservation through co-existence of species and biological control by maintaining prey at a level that is least harmful to the system. In the second, the effect of additional food is incorporated explicitly into the predator's compartment with the goal of pest management by maintaining prey density at a very minimal damaging level. For both cases, appropriate optimal control strategies are derived and the theoretical findings are illustrated by numerical simulations. We also discuss the ecological significance of the theoretical findings for both models.

Bifurcation analysis of delayed predator–prey system with fear effect, additional food for predator, prey refuge and predator age structure

“…They found that in high-prey-refuge ecological systems, providing additional food to the predator population can prevent the extinction of the predator species. Ananth et al [22] formulated and studied optimal control problems with the objective of achieving desired outcomes in the shortest possible time. They consider two different models of supplemental additional food and also discuss the ecological implications of the theoretical findings for these two models.…”

Stochastic time-optimal control and sensitivity studies for additional food provided prey-predator systems involving Holling type-IV functional response

“…The authors in Srinivasu et al [14] have studied an additional food provided deterministic prey-predator systems involving Holling type-IV functional response. In Ananth and Vamsi and May [17,19], the authors studied the optimal control problems of deterministic prey-predator systems involving Holling type-IV functional response with the quality of additional food and the quantity of additional food as the control parameters respectively. As in earlier mentioned works the authors in the works [15,17,19] also considered the provision of additional food to predators both in the complimentary and supplementary sense.…”

“…The authors in Srinivasu et al [14] have studied an additional food provided deterministic prey-predator systems involving Holling type-IV functional response. In Ananth and Vamsi and May [17,19], the authors studied the optimal control problems of deterministic prey-predator systems involving Holling type-IV functional response with the quality of additional food and the quantity of additional food as the control parameters respectively. It is important to note that the specific influence of additional food in a Holling type-IV prey-predator model depends on various factors, including the parameters of the model, the relative availability of primary prey and additional food, and the ecological context.…”