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Predator-Prey Model with Sickness in Prey, Control Variables, and Logarithmic Penalty Cost Function
  • Oukouomi Noutchie SC
Oukouomi Noutchie SC
North-West University - Vanderbijlpark Campus

Corresponding Author:[email protected]

Author Profile

Abstract

javascript:void(0) This study presents a novel predator-prey model that integrates disease dynamics within the prey population, using a Susceptible-Infected (SI) framework. The model introduces two control variables: one aimed at reducing disease transmission among prey and another focused on managing predator population levels. A logarithmic penalty cost function is employed to penalize reductions in prey and predator populations, reflecting the heightened ecological risks associated with low population sizes. The system is described by a set of differential equations that model the interactions between susceptible prey, infected prey, and predators under the influence of these control measures. The goal is to minimize the cost function over a specified time horizon, ensuring ecosystem stability while effectively managing disease spread and predator numbers. Our results provide insights into optimal control strategies that maintain ecological balance, offering a framework applicable to real-world wildlife management and conservation scenarios.
30 Aug 2024Submitted to Mathematical Methods in the Applied Sciences
02 Sep 2024Submission Checks Completed
02 Sep 2024Assigned to Editor
06 Sep 2024Review(s) Completed, Editorial Evaluation Pending
08 Sep 2024Reviewer(s) Assigned