Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues

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Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues

Frederic Y M Wan
Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues Book PDF

Author : Frederic Y M Wan
Publisher : World Scientific Publishing Company
Page : 400 pages
File Size : 55,5 Mb
Release : 2017-08-16
Category : Mathematics
ISBN : 9789813143357

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Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues by Frederic Y M Wan Pdf

Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments). Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III. Request Inspection Copy Contents: Mathematical Models and the Modeling CycleGrowth of a Population:Evolution and EquilibriumStability and BifurcationInteracting Populations:Linear InteractionsNonlinear Autonomous InteractionsHIV Dynamics and Drug TreatmentsIndex Theory, Bistability and FeedbackOptimization:The Economics of GrowthOptimization over a Planning PeriodModifications of the Basic ProblemBoundary Value Problems are More ComplexConstraints and Control:"Do Your Best" and the Maximum PrincipleChlamydia TrachomatisGenetic Instability and CarcinogenesisMathematical Modeling RevisitedAppendices:First Order ODEBasic Numerical MethodsAssignments Readership: Undergraduates in mathematical biology, mathematical modeling of dynamical systems, optimization and control, viral dynamics (infectious diseases), oncology.

Mathematics for Life Science and Medicine

Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Mathematics for Life Science and Medicine Book PDF

Author : Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 41,6 Mb
Release : 2007-01-25
Category : Mathematics
ISBN : 9783540344261

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Mathematics for Life Science and Medicine by Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato Pdf

The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. It provides a fascinating survey of the theory of dynamical systems in biology and medicine. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine.

Spatial Dynamics Models In The Life Sciences And The Role Of Feedback In Robust Developments

Frederic Y M Wan
Spatial Dynamics Models In The Life Sciences And The Role Of Feedback In Robust Developments Book PDF

Author : Frederic Y M Wan
Publisher : World Scientific
Page : 496 pages
File Size : 47,8 Mb
Release : 2022-12-28
Category : Mathematics
ISBN : 9789811256585

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Spatial Dynamics Models In The Life Sciences And The Role Of Feedback In Robust Developments by Frederic Y M Wan Pdf

Basic mathematical techniques for partial differential equations (PDE) with applications to the life sciences form an integral part of the core curriculum for programs in mathematical biology. Yet, students in such a program with an undergraduate training in biology are typically deficient in any exposure to PDE. This volume starts with simple first order PDE and progresses through higher order equations and systems but with interesting applications, even at the level of a single first order PDE with constant coefficients.Similar to the two previous volumes by the author, another unique feature of the book is highlighting the scientific theme(s) of interest for the biological phenomena being modelled and analysed. In addition to temporal evolution of a biological phenomenon, its limiting equilibrium states and their stability, the possibility of locational variations leads to a study of additional themes such as (signal and wave) propagation, spatial patterning and robustness. The requirement that biological developments are relatively insensitive to sustained environmental changes provides an opportunity to examine the issue of feedback and robustness not encountered in the previous two volumes of this series.

Mathematics for the Life Sciences

Glenn Ledder
Mathematics for the Life Sciences Book PDF

Author : Glenn Ledder
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 41,5 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9781461472766

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Mathematics for the Life Sciences by Glenn Ledder Pdf

​ ​​ Mathematics for the Life Sciences provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents mathematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathematics background beyond algebra and precalculus. Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biological data and the basic principles of modeling. The remainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empirical modeling (using data to parameterize and select models). The modeling chapter contains a thorough treatment of key ideas and techniques that are often neglected in mathematics books. It also provides the reader with a sophisticated viewpoint and the essential background needed to make full use of the remainder of the book, which includes two chapters on probability and its applications to inferential statistics and three chapters on discrete and continuous dynamical systems. The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate section, allowing readers to gradually develop complete investigations from understanding the biological assumptions to a complete analysis.

Dynamic Models and Control of Biological Systems

Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao
Dynamic Models and Control of Biological Systems Book PDF

Author : Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 48,6 Mb
Release : 2009-07-30
Category : Science
ISBN : 9781441903594

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Dynamic Models and Control of Biological Systems by Vadrevu Sree Hari Rao,Ponnada Raja Sekhara Rao Pdf

Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.

Stochastic Models In The Life Sciences And Their Methods Of Analysis

Wan Frederic Y M
Stochastic Models In The Life Sciences And Their Methods Of Analysis Book PDF

Author : Wan Frederic Y M
Publisher : World Scientific
Page : 476 pages
File Size : 48,6 Mb
Release : 2019-08-29
Category : Mathematics
ISBN : 9789813274624

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Stochastic Models In The Life Sciences And Their Methods Of Analysis by Wan Frederic Y M Pdf

Biological processes are evolutionary in nature and often evolve in a noisy environment or in the presence of uncertainty. Such evolving phenomena are necessarily modeled mathematically by stochastic differential/difference equations (SDE), which have been recognized as essential for a true understanding of many biological phenomena. Yet, there is a dearth of teaching material in this area for interested students and researchers, notwithstanding the addition of some recent texts on stochastic modelling in the life sciences. The reason may well be the demanding mathematical pre-requisites needed to 'solve' SDE.A principal goal of this volume is to provide a working knowledge of SDE based on the premise that familiarity with the basic elements of a stochastic calculus for random processes is unavoidable. Through some SDE models of familiar biological phenomena, we show how stochastic methods developed for other areas of science and engineering are also useful in the life sciences. In the process, the volume introduces to biologists a collection of analytical and computational methods for research and applications in this emerging area of life science. The additions broaden the available tools for SDE models for biologists that have been limited by and large to stochastic simulations.

Dynamical Models in Biology

Miklós Farkas
Dynamical Models in Biology Book PDF

Author : Miklós Farkas
Publisher : Academic Press
Page : 187 pages
File Size : 53,6 Mb
Release : 2001-06-15
Category : Mathematics
ISBN : 0080530605

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Dynamical Models in Biology by Miklós Farkas Pdf

Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: Chaotic dynamics of populations The spread of sexually transmitted diseases Problems of the origin of life Models of immunology Formation of animal hide patterns The intuitive meaning of mathematical formulae explained with many figures Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. A 'down-to-earth' introduction to the growing field of modern mathematical biology Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

Dynamical Models of Biology and Medicine

Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma
Dynamical Models of Biology and Medicine Book PDF

Author : Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma
Publisher : MDPI
Page : 292 pages
File Size : 47,5 Mb
Release : 2019-10-04
Category : Technology & Engineering
ISBN : 9783039212170

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Dynamical Models of Biology and Medicine by Yang Kuang,Meng Fan,Shengqiang Liu,Wanbiao Ma Pdf

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

Mathematics for Life Science and Medicine

Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Mathematics for Life Science and Medicine Book PDF

Author : Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Publisher : Springer
Page : 228 pages
File Size : 51,9 Mb
Release : 2006-12-12
Category : Mathematics
ISBN : 354034425X

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Mathematics for Life Science and Medicine by Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato Pdf

The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. It provides a fascinating survey of the theory of dynamical systems in biology and medicine. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine.

The Dynamics of Biological Systems

Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi
The Dynamics of Biological Systems Book PDF

Author : Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi
Publisher : Springer Nature
Page : 267 pages
File Size : 50,5 Mb
Release : 2019-10-02
Category : Mathematics
ISBN : 9783030225834

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The Dynamics of Biological Systems by Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi Pdf

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

Modeling Dynamic Biological Systems

Bruce Hannon,Matthias Ruth
Modeling Dynamic Biological Systems Book PDF

Author : Bruce Hannon,Matthias Ruth
Publisher : Springer
Page : 434 pages
File Size : 45,6 Mb
Release : 2014-07-05
Category : Science
ISBN : 9783319056159

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Modeling Dynamic Biological Systems by Bruce Hannon,Matthias Ruth Pdf

Many biologists and ecologists have developed models that find widespread use in theoretical investigations and in applications to organism behavior, disease control, population and metapopulation theory, ecosystem dynamics, and environmental management. This book captures and extends the process of model development by concentrating on the dynamic aspects of these processes and by providing the tools such that virtually anyone with basic knowledge in the Life Sciences can develop meaningful dynamic models. Examples of the systems modeled in the book range from models of cell development, the beating heart, the growth and spread of insects, spatial competition and extinction, to the spread and control of epidemics, including the conditions for the development of chaos. Key features: - easy-to-learn and easy-to-use software - examples from many subdisciplines of biology, covering models of cells, organisms, populations, and metapopulations - no prior computer or programming experience required Key benefits: - learn how to develop modeling skills and system thinking on your own rather than use models developed by others - be able to easily run models under alternative assumptions and investigate the implications of these assumptions for the dynamics of the biological system being modeled - develop skills to assess the dynamics of biological systems

Quantitative Elements of General Biology

Ivan Maly
Quantitative Elements of General Biology Book PDF

Author : Ivan Maly
Publisher : Springer Nature
Page : 200 pages
File Size : 51,8 Mb
Release : 2021-08-28
Category : Science
ISBN : 9783030791469

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Quantitative Elements of General Biology by Ivan Maly Pdf

This monograph sketches out a broad spectrum of problems (from evolution and metabolism to morphogenesis and biogeographical dynamics) whose solution has been impacted by mathematical models. Each of the selected examples has led to the recognition—and set direction to further study—of certain fundamental but unintuitive properties of biological systems, such as the making and breaking of specific symmetries that underlie morphogenesis. Whether they are long-established or only recently accepted, these models are selected for being thought-provoking and illuminating both the achievements and the gaps in our current understanding of the given area of biology. The selection of models is also meant to bring to the fore the existing degree of unity in the quantitative approach to diverse general-biological questions and in the systems-level properties that are discovered across the levels of biological organization. It is the thesis of this book that further cultivation of such unity is a way forward as we progress toward a general theory of living matter. This is an ideal book for students (in the broadest sense) of biology who wish to learn from this attempt to present the exemplary models, their methodological lessons, and the outline of a unified theory of living matter that is now beginning to emerge. In addition to a doctoral student preparing for quantitative biology research, this reader could also be an interdisciplinary scientist transitioning to biology. The latter—for example, a physicist or an engineer—may be comfortable with the mathematical apparatus and prepared to quickly enter the intended area of work, but desires a broader foundation in biology from the quantitative perspective.

Dynamic Systems Biology Modeling and Simulation

Joseph Distefano
Dynamic Systems Biology Modeling and Simulation Book PDF

Author : Joseph Distefano
Publisher : Academic Press
Page : 0 pages
File Size : 42,9 Mb
Release : 2015-01-10
Category : Science
ISBN : 0124104118

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Dynamic Systems Biology Modeling and Simulation by Joseph Distefano Pdf

Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems - from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial - with clearly spelled-out and unified nomenclature - derived from the author's own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications.

Dynamic Models in Biology

Stephen P. Ellner,John Guckenheimer
Dynamic Models in Biology Book PDF

Author : Stephen P. Ellner,John Guckenheimer
Publisher : Princeton University Press
Page : 352 pages
File Size : 45,9 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400840960

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Dynamic Models in Biology by Stephen P. Ellner,John Guckenheimer Pdf

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.

Current Trends in Dynamical Systems in Biology and Natural Sciences

Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino
Current Trends in Dynamical Systems in Biology and Natural Sciences Book PDF

Author : Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino
Publisher : Springer Nature
Page : 250 pages
File Size : 46,5 Mb
Release : 2020-05-06
Category : Mathematics
ISBN : 9783030411206

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Current Trends in Dynamical Systems in Biology and Natural Sciences by Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino Pdf

This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop “Dynamical Systems Applied to Biology and Natural Sciences – DSABNS”, held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.