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

2017-08-16 Mathematics
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Release : 2017-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 355/5 ( reviews)

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Book Synopsis Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues by : Frederic Y M Wan

Download or read book Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues written by Frederic Y M Wan. This book was released on 2017-08-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical Models of Biology and Medicine

2019-10-04 Technology & Engineering
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Release : 2019-10-04
Genre : Technology & Engineering
Kind : eBook
Book Rating : 176/5 ( reviews)

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Book Synopsis Dynamical Models of Biology and Medicine by : Yang Kuang

Download or read book Dynamical Models of Biology and Medicine written by Yang Kuang. This book was released on 2019-10-04. Available in PDF, EPUB and Kindle. Book excerpt: 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

Stochastic Models In The Life Sciences And Their Methods Of Analysis

2019-08-29 Mathematics
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Release : 2019-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 62X/5 ( reviews)

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

Download or read book Stochastic Models In The Life Sciences And Their Methods Of Analysis written by Wan Frederic Y M. This book was released on 2019-08-29. Available in PDF, EPUB and Kindle. Book excerpt: 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

2001-06-15 Mathematics
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Release : 2001-06-15
Genre : Mathematics
Kind : eBook
Book Rating : 605/5 ( reviews)

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Book Synopsis Dynamical Models in Biology by : Miklós Farkas

Download or read book Dynamical Models in Biology written by Miklós Farkas. This book was released on 2001-06-15. Available in PDF, EPUB and Kindle. Book excerpt: 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

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

2022-12-28 Mathematics
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Release : 2022-12-28
Genre : Mathematics
Kind : eBook
Book Rating : 586/5 ( reviews)

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

Download or read book Spatial Dynamics Models In The Life Sciences And The Role Of Feedback In Robust Developments written by Frederic Y M Wan. This book was released on 2022-12-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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