Predator-Prey Model with Sickness in Prey, Control Variables, and
Logarithmic Penalty Cost Function
Abstract
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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.