Optimal Harvesting in an Integro-difference Population Model

We consider the harvest of a certain proportion of a population that is modeled by an integro-difference equation. This model is discrete in time and continuous in the space variable. The dispersal of the population is modeled by an integral of the population density against a kernel function. The control is the harvest, and the goal is to maximize the profit. The optimal control is characterized by introducing an adjoint function. Numerical results and interpretations are given for four different kernels