Optimal Control Applied to Biological Models by Suzanne Lenhart and John T. Workman is a comprehensive textbook that introduces the mathematical theory of optimal control and its applications to biological systems. The book is designed for advanced undergraduate or beginning graduate students and provides a thorough development of the mathematical aspects of optimal control theory. It covers a wide range of topics, including the basic optimal control problems, existence and solution properties, state conditions at the final time, and the forward-backward sweep method. The text also includes practical examples and exercises, as well as interactive "lab" sections that allow readers to apply optimal control theory to biological models. The book begins with an introduction to optimal control theory, explaining the concept of optimal control as a method for finding a control that optimizes some objective functional. It then moves on to discuss the necessary conditions for optimal control, including the use of adjoint functions and the Hamiltonian. The authors also explore the application of optimal control theory to various biological models, such as disease models, harvesting models, and population dynamics. The text includes detailed examples and exercises that help readers understand the theory and its applications. The book is structured into chapters that cover different aspects of optimal control theory, including the basic problem, existence and solution properties, state conditions at the final time, and the forward-backward sweep method. Each chapter includes a set of exercises that allow readers to practice the concepts discussed. The text also includes a section on the application of optimal control theory to biological models, with examples that illustrate how the theory can be used to solve real-world problems in biology. The authors emphasize the importance of understanding the mathematical foundations of optimal control theory and its application to biological systems. They also highlight the role of numerical methods in solving optimal control problems, particularly in the context of biological models. The book is written in a clear and accessible manner, making it suitable for students and researchers who are new to the field of optimal control theory and its applications to biology. The text is supported by a variety of references and resources, making it a valuable resource for anyone interested in the application of optimal control theory to biological systems.Optimal Control Applied to Biological Models by Suzanne Lenhart and John T. Workman is a comprehensive textbook that introduces the mathematical theory of optimal control and its applications to biological systems. The book is designed for advanced undergraduate or beginning graduate students and provides a thorough development of the mathematical aspects of optimal control theory. It covers a wide range of topics, including the basic optimal control problems, existence and solution properties, state conditions at the final time, and the forward-backward sweep method. The text also includes practical examples and exercises, as well as interactive "lab" sections that allow readers to apply optimal control theory to biological models. The book begins with an introduction to optimal control theory, explaining the concept of optimal control as a method for finding a control that optimizes some objective functional. It then moves on to discuss the necessary conditions for optimal control, including the use of adjoint functions and the Hamiltonian. The authors also explore the application of optimal control theory to various biological models, such as disease models, harvesting models, and population dynamics. The text includes detailed examples and exercises that help readers understand the theory and its applications. The book is structured into chapters that cover different aspects of optimal control theory, including the basic problem, existence and solution properties, state conditions at the final time, and the forward-backward sweep method. Each chapter includes a set of exercises that allow readers to practice the concepts discussed. The text also includes a section on the application of optimal control theory to biological models, with examples that illustrate how the theory can be used to solve real-world problems in biology. The authors emphasize the importance of understanding the mathematical foundations of optimal control theory and its application to biological systems. They also highlight the role of numerical methods in solving optimal control problems, particularly in the context of biological models. The book is written in a clear and accessible manner, making it suitable for students and researchers who are new to the field of optimal control theory and its applications to biology. The text is supported by a variety of references and resources, making it a valuable resource for anyone interested in the application of optimal control theory to biological systems.