Harvesting control in an integrodifference population model with concave growth term

We consider the harvest of a certain proportion of a population that is modeled by an integrodifference equation, which is discrete in time and continuous in the space variable. The dispersal of the population is modeled by an integral of the growth function evaluated at the current population density against a kernel function. A concave growth function is used. In our model, growth occurs first, then dispersal and lastly harvesting control before the next generation. With the goal of maximizing the discounted profit stream, the optimal control is characterized by an optimality system. Illustrative examples are computed numerically.