OPTIMAL CONTROL METHODS ON EPIDEMIOLOGICAL MODELS Understanding at a Glance

OPTIMAL CONTROL METHODS ON EPIDEMIOLOGICAL MODELS: Understanding at a Glance
English | May 14, 2026 | ASIN: B0GZJBPTSP | 57 pages | Epub | 1.82 MB
This book presents a structured introduction to mathematical modeling and optimal control, with an emphasis on the development, analysis, and interpretation of dynamical systems. It is written to provide readers with both the theoretical foundations and practical tools required to understand how mathematical models can be used to analyze complex real-world processes and inform decision-making. The motivation for this work stems from the growing need for quantitative approaches in addressing contemporary challenges. Mathematical models, particularly those based on systems of differential equations, offer a powerful framework for capturing dynamic interactions within complex systems. When combined with optimal control theory, these models allow for the systematic design and evaluation of strategies that balance performance objectives with practical constraints.The text is organized to guide the reader progressively from foundational concepts to more advanced analytical techniques. It begins with an overview of compartmental modeling frameworks and gradually introduces key ideas in optimal control theory, including the formulation of objective functionals, the construction of Hamiltonians, and the application of Pontryagin's Maximum Principle. Emphasis is placed not only on mathematical rigor butalso on interpretation, ensuring that the results are meaningful and applicable. In addition to theoretical development, the book incorporates computational approaches, particularly the use of numerical methods for solving optimal control problems. This book is intended for graduate students, researchers, and practitioners in applied mathematics, engineering, and related disciplines. A working knowledge of differential equations and basic calculus is assumed. Readers are encouraged to engage actively with the material, as the concepts presented are best understood through careful study and application. It is my hope that this work will serve as a useful resource for those seeking to understand and apply mathematical modeling and optimal control in advance and meaningful way.