Optimal harvesting in an integrodifference population model

Abstract

We consider the harvest of a certain proportion of a population that is modelled by an integrodifference equation. This model is discrete in time and continuous in the space variable. The dispersal of the population is modelled 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. This paper gives the first optimal control result in integrodifference equations. Numerical results and interpretations are given for four different kernels. Copyright © 2005 John Wiley & Sons, Ltd.