Most all agricultural crops suffer damage to some extent dtie to certaiin insects that eat or otherwise damage the crop. Attempts to control pests directly through the utse of insecticides are often made by generously applying insecticides whenever pests appear in numbers above some arbitrary level. If a mathematical model for a biological system is available, then not only can the effects of such direct control be examined, but the methods of optimal control theory may be used to determinle rational control programs for minimizing control costs as well as ecological and crop damage costs. In this paper, the influence of human control is added to a known model for a prey-predator system. Optimal control for this system subject to selective insecticide control, general insecticide control, and biological control is then determined for a cost ftunction dependent upoIn both crop damage and economic costs of control.
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Thomas L. Vincent (1975) studied this question.