optimal control applied to biological models chapman hall crc mathematical and computational biology

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Optimal Control Applied To Biological Models

Author : Suzanne Lenhart
ISBN : 9781584886402
Genre : Mathematics
File Size : 86. 77 MB
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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 the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

An Introduction To Systems Biology

Author : Uri Alon
ISBN : 9781584886426
Genre : Mathematics
File Size : 52. 11 MB
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Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The textavoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. An Introduction to Systems Biology: Design Principles of Biological Circuits builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.

An Introduction To Optimal Control Problems In Life Sciences And Economics

Author : Sebastian Aniţa
ISBN : 0817680985
Genre : Mathematics
File Size : 21. 74 MB
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Combining 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 ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

Advances In Computational Biology

Author : Luis F. Castillo
ISBN : 9783319015682
Genre : Computers
File Size : 68. 94 MB
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This volume compiles accepted contributions for the 2nd Edition of the Colombian Computational Biology and Bioinformatics Congress CCBCOL, after a rigorous review process in which 54 papers were accepted for publication from 119 submitted contributions. Bioinformatics and Computational Biology are areas of knowledge that have emerged due to advances that have taken place in the Biological Sciences and its integration with Information Sciences. The expansion of projects involving the study of genomes has led the way in the production of vast amounts of sequence data which needs to be organized, analyzed and stored to understand phenomena associated with living organisms related to their evolution, behavior in different ecosystems, and the development of applications that can be derived from this analysis.

Advances In Applied Mathematics

Author : Ali R. Ansari
ISBN : 9783319069234
Genre : Mathematics
File Size : 33. 26 MB
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This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was mathematical biology, including a keynote address by Professor Philip Maini. The second theme was computational science/numerical analysis, including a keynote address by Professor Grigorii Shishkin. The conference also addressed more general applications topics, with papers in business applications, fluid mechanics, optimization, scheduling problems and engineering applications, as well as a keynote by Professor Ali Nayfeh.

Optimization And Approximation

Author : Pablo Pedregal
ISBN : 9783319648439
Genre : Mathematics
File Size : 87. 52 MB
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This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

An Introduction To Mathematical Epidemiology

Author : Maia Martcheva
ISBN : 9781489976123
Genre : Mathematics
File Size : 88. 4 MB
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The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.

Nonlinear Systems Of Partial Differential Equations

Author :
ISBN : 9789814467476
Genre :
File Size : 64. 34 MB
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Geometric Optimal Control

Author : Heinz Schättler
ISBN : 9781461438342
Genre : Mathematics
File Size : 35. 54 MB
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This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Modeling Paradigms And Analysis Of Disease Transmission Models

Author : Abba B. Gumel
ISBN : 9780821843840
Genre : Mathematics
File Size : 38. 24 MB
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This volume stems from two DIMACS activities, the U.S.-Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.

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