Sebastian Aniţa - Böcker

Combining two important and growing areas of applied mathematics—control theory and modeling—this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences.Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new concepts, and carefully presented MATLAB® programs guide the reader through methods in optimal control and related models. This approach not only fosters an understanding of the basic topics, but also leads the way to new, independent research.With minimal prerequisites and exercises in each chapter, An Introduction to Optimal Control Problems in Life Sciences and Economics, serves as an excellent textbook for graduate and advanced undergraduate courses in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance. The work is also a useful reference for researchers and practitioners working with optimal control theory in the above areas.

This monograph explores the use of mathematical modeling and control theory in a variety of contemporary challenges in mathematical biology and environmental sciences.  Emphasizing an approach of learning by doing, the authors focus on a set of significant case studies emerging from real-world problems and illustrate how mathematical techniques and computational experiments can be employed in the search for sustainable solutions.The following topics are extensively discussed:Eradicability and control of a paradigmatic epidemic model, with a view to the existence of endemic states, their stability, and the existence of travelling wavesA spatially structured epidemic model concerning malaria as an example of vector-borne epidemicsOptimal harvesting problems for space-structured and age-structured population dynamicsControlling epidemics in agriculture due to pest insectsThe role of predators as a possible biocontrol agent of epidemics in agricultureControl by taxation of the environmental pollution produced by human activitiesThe originality of this text is in its leitmotif – regional control – along the principle of “Think Globally, Act Locally.” Indeed, for example, in many real spatially structured ecosystems, it is practically impossible to control the relevant system by global interventions in the whole habitat.Proofs are given whenever they may serve as a guide to the introduction of new concepts. Each chapter includes a comprehensive description of the numerical methods used for the computational experiments, and MATLAB© codes for many of the numerical simulations are available for download.  Several challenging open problems are also provided to stimulate future research.This text is aimed at mathematicians, engineers, and other scientists working in areas such as biology, medicine, and economics. Graduate and advanced undergraduate students of a quantitative subject related to the analysis and applications of dynamical systems and their control will also find it to be a valuable resource.