Optimal Control of a Genotype-Structured Prey–Predator Model: Strategies for Ecological Rescue and Oscillatory Dynamics Restoration

Evolutionary changes can significantly impact interactions among populations and disrupt ecosystems by driving extinctions or collapsing population oscillations, posing substantial challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using the optimal control method. To study this, we study a model that incorporates a genotypically structured prey population comprising wild-type, heterozygous, and mutant prey types, as well as the predator population. We prove that this model has both local and global existence and uniqueness of solutions, ensuring the model’s robustness. Then, we applied the optimal control method, incorporating Pontryagin’s Maximum Principle, to introduce a control input into the model and minimize the mutant population, thereby stabilizing the ecosystem. We utilize a reproduction number and a control efficacy measure to numerically demonstrate that the undesired dynamics of the model can be controlled, leading to the suppression of the mutant and the restoration of the oscillatory dynamics of the system. These findings demonstrate the applicability of optimal control strategies and provide a mathematical framework for managing such ecological disruptions.