Impact of Carrying Capacity on Species Competition in Optimization Strategies for Impulsive Releases

This work investigates the influence of carrying capacity on the replacement of species $S_1$ by species $S_2$, focusing on minimizing the intervention cost. We formulate the problem as an optimal control problem, where control actions consist of impulsive releases of individuals from species $S_2$. The objective is to determine optimal release strategies that ensures the eradication of $S_1$ and the successful establishment of $S_2$. Numerical results are presented to illustrate the control strategies and how carrying capacity affects the optimal release strategy.