From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t

Suzanne Lenhart, John T. Workman

Develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. This book examines the basic problem for continuous time ordinary differential equations (ODEs). It introduces the optimal control of discrete systems and of partial differential equations (PDEs).

Basic Optimal Control Problems. Existence and Other Solution Properties. State Conditions at the Final Time. Forward-Backward Sweep Method. Lab 1: Introductory Example. Lab 2: Mold and Fungicide. Lab 3: Bacteria. Bounded Controls. Lab 4: Bounded Case. Lab 5: Cancer. Lab 6: Fish Harvesting. Optimal Control of Several Variables. Lab 7: Epidemic Model. Lab 8: HIV Treatment. Lab 9: Bear Populations. Lab 10: Glucose Model. Linear Dependence on the Control. Lab 11: Timber Harvesting. Lab 12: Bioreactor. Free Terminal Time Problems. Adapted Forward-Backward Sweep. Lab 13: Predator-Prey Model. Discrete Time Models. Lab 14: Invasive Plant Species. Partial Differential Equation Models. Other Approaches and Extensions. References. Index.