On Optimal Control of a Genotype-Structured Prey-Predator System for Ecological Rescue and Oscillation Restoration

Evolutionary changes impacts interactions among populations and can disrupt ecosystems by driving extinctions or by collapsing population oscillations, posing significant challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using optimal control method. To study this, we proposed a model which incorporates genotypically structured prey comprising of wild-type, heterozygous and mutant prey types and predator population. We proved that this model has both local and global existence and uniqueness of solutions ensuring the model robustness. Then, we applied optimal control method along with Pontryagin Maximum Principle by incorporating a control input in the model to minimize the mutant population and subsequently to stabilize the ecosystem. The numerical results clearly reveal that the undesired dynamics of the model can be controlled showing the suppression of the mutant, rescues the predator, and restores the oscillatory dynamics of the system. These findings demonstrate the efficacy of the control strategy and provide a mathematical framework for managing such ecological disruptions