Optimal Direct Control Programs for a Prey-Predator System

Abstract

Numerous biological systems involve species acting out the roles of prey and predators. In this paper, it is assumed that the prey feed upon resources of value to humans and that the predators only food supply is the prey. An often used control program for such a situation is a direct one in which the prey are controlled by destroying them outright. Such programs often times also involve the predators resulting in side effects which can be both unexpected and unpleasant. In this paper, the influence of direct human control is added to a known model for a prey-predator system. Optimal control programs are determined for a cost function dependent upon both resource damage due to the prey and economic (including environmental) costs of control. The basic characteristics of a direct optimal pest management program are illustrated with several figures and discussion.