Mathematical Models for Controlling Growing Biological Populations: A Survey

Mathematical models of growing biological populations have existed for many years, but only recently has theoretical and practical research effort been directed to the control and also to the optimal control of these models. Both deterministic and stochastic population models serve as the basis for applying the systems-analysis and control-theory approach of operations research to find optimal, or at least efficient, control strategies for ecological management. Applications of this decision-theory methodology have been made to finding controlling strategies for epidemic and pest populations, harvesting policies for forests, catch and regulation strategies of fisheries and wildlife, treatment strategies of the spread of infection, and even to finding control policies regulating human population. This paper reviews the important contributions to and future challenges in this field and includes a complete bibliography.