Optimal Control for Predator-Prey Systems Involving Inhibitory Effect

Identifying the Issue

• While there are many predator-prey models developed to study the dynamics of populations of species, there are very few works done to study the controllability aspects to reach the desired state in finite time. None of the current models have developed control strategies based on the quality of additional food for predator-prey systems with type IV response (inhibitory effect f prey). Furthermore, we have considered two models for covering the various approaches in providing food supplements
• In this work, we have also examined the role of the inhibitory effect of prey species in achieving the desired outcome

Objective of the Research

• We consider two different models of the additional food provided prey-predator systems involving Holling type IV functional response (with the inhibitory effect of prey)
• The main objective is to drive the system to a desired state in minimum (finite) time. We wish to achieve bio-conservation and bio-control by providing optimal quality of additional food as a control
• Both the models are relevant

Who should read this?

Academicians, Mathematics, Bio-Mathematics, Mathematical Modelling, Eco-Managers, Experimental Ecologists

Solution

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 the 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 the 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 simulation.

Key Features and Benefits

• When additional food supplements are provided to the predators, the quantity of additional food is generally determined by the gut volume of the species. Thus, it is important to ensure that the quality of additional food is monitored regularly. In this work, we provide strategies to the eco-managers based on the quality of additional food.
• Both biological conservation and bio-control can be achieved in finite time.

Impact

• The work presented in this paper provides a minimum-time approach to drive predator-prey systems towards biological conservation and pest management
• Eco-Managers could benefit from the findings of this work in supplying appropriate quality of additional food provided to achieve the desired outcome

Team

• Sri Ananth V S, Department of Mathematics and Computer Science, SSSIHL
• Dr. D K K Vamsi, Department of Mathematics and Computer Science, SSSIHL

Paper Published in: Acta Biotheoretica, Volume 70, Article Number5 (2022) (Impact Factor: 1.74, SCI Indexed)

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

Read Paper Here: https://doi.org/10.1007/s10441-021-09430-2