[PDF] Optimal Control Applied To Population And Disease Models eBook

Author : Rachael Lynn Miller Neilan
Publisher :
Page : 205 pages
File Size : 38,29 MB
Release : 2009
Category :
ISBN :

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This dissertation considers the use of optimal control theory in population models for the purpose of characterizing strategies of control which minimize an invasive or infected population with the least cost. Three different models and optimal control problems are presented. Each model describes population dynamics via a system of differential equations and includes the effects of one or more control methods. The first model is a system of two ordinary differential equations describing dynamics between a native population and an invasive population. Population growth terms are functions of the control, constructed so that the value of the control may affect each population differently. A novel existence result is presented for the case of quadratic growth functions. With parameters chosen to mimic the competition between cottonwood and salt cedar plants, optimal schedules of controlled flooding are displayed. The second model, a system of six ordinary differential equations, describes the spread of cholera in a human population through ingestion of Vibrio cholerae. Equations track movement of susceptible individuals to either an asymptomatic infected class or a symptomatic infected class through ingestion of bacteria, both in a hyperinfectious state and a less-infectious state. Recovered individuals temporarily move to an immune class before being placed back in the susceptible class. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Within the model, three control functions represent rehydration and antibiotic treatment, vaccination, and sanitation. The cost-effective balance of multiple cholera intervention methods is compared for two endemic populations. The third model describes the spread of disease in both time and space using a system of three parabolic partial differential equations with convection-diffusion movement terms and no-flux boundary conditions. A control function representing vaccination is incorporated. State variables track the number of susceptible, infected, and immune individuals. Detailed analysis for the characterization of the optimal control is provided. The model and optimal control results are applied to the spread of rabies among raccoons with the control function determining the timing and placement of oral vaccine baits. Results illustrate cost-effective vaccine distribution strategies for both regular and irregular patterns of rabies propagation.

Author : Suzanne Lenhart
Publisher : CRC Press
Page : 272 pages
File Size : 19,87 MB
Release : 2007-05-07
Category : Mathematics
ISBN : 1420011413

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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 t

Author : Suzanne Lenhart
Publisher : Chapman and Hall/CRC
Page : 288 pages
File Size : 45,71 MB
Release : 2007
Category : Mathematics
ISBN :

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Author : Raouf Boucekkine
Publisher : Routledge
Page : 277 pages
File Size : 45,71 MB
Release : 2013-05-13
Category : Business & Economics
ISBN : 1136920927

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This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-standard decision variables into account. In addition, the contributions deal with the age structure of assets, resources, and populations under study. Interdisciplinary modelling has enormous potential for discovering new insights in global and regional development. Optimal Control of Age-structured Populations in Economy, Demography, and the Environment is a rich and excellent source of information on state-of-the-art modelling expertise and references. The book provides the necessary mathematical background for readers from different areas, such as applied sciences, management sciences and operations research, which helps guide the development of practical models. As well as this the book also surveys the current practice in applied modelling and looks at new research areas for a general mathematical audience. This book will be of interest primarily to researchers, postgraduate students, as well as a wider scientific community, including those focussing on the subjects of applied mathematics, environmental sciences, economics, demography, management, and operations research.

Author : Suzanne Lenhart
Publisher : CRC Press
Page : 272 pages
File Size : 17,94 MB
Release : 2007-05-07
Category : Mathematics
ISBN : 1584886404

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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.

Author : Maia Martcheva
Publisher : Springer
Page : 462 pages
File Size : 30,33 MB
Release : 2015-10-20
Category : Mathematics
ISBN : 1489976124

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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.

Author : Suresh P. Sethi
Publisher : Taylor & Francis US
Page : 536 pages
File Size : 10,50 MB
Release : 2006
Category : Business & Economics
ISBN : 9780387280929

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Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.

Author : Shah, Nita H.
Publisher : IGI Global
Page : 316 pages
File Size : 47,30 MB
Release : 2020-06-26
Category : Medical
ISBN : 1799837424

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When deadly illness spreads through a population at a rapid pace, time may be of the essence in order to save lives. Using mathematics as a language to interpret assumptions concerning the biological and population mechanics, one can make predictions by analyzing actual epidemiological data using mathematical tests and results. Mathematical models can help us understand the right disease status and predict the effects of the disease on populations, which can help limit the spread and devastation of the illness. Mathematical Models of Infectious Diseases and Social Issues is a collection of innovative research that examines the dynamics of diseases and their effect on populations. Featuring coverage of a broad range of topics including deterministic models, environmental pollution, and social issues, this book is ideally designed for diagnosticians, clinicians, healthcare providers, pharmacists, government health officials, policymakers, academicians, researchers, and students.

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 26,63 MB
Release : 2013-02-06
Category : Mathematics
ISBN : 1447148207

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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.