Mathematical Models In Biology

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Mathematical Models in Biology

Leah Edelstein-Keshet
Mathematical Models in Biology Book PDF

Author : Leah Edelstein-Keshet
Publisher : SIAM
Page : 629 pages
File Size : 42,9 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 0898719143

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Mathematical Models in Biology by Leah Edelstein-Keshet Pdf

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

Mathematical Modeling in Systems Biology

Brian P. Ingalls
Mathematical Modeling in Systems Biology Book PDF

Author : Brian P. Ingalls
Publisher : MIT Press
Page : 423 pages
File Size : 49,8 Mb
Release : 2022-06-07
Category : Science
ISBN : 9780262545822

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Mathematical Modeling in Systems Biology by Brian P. Ingalls Pdf

An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.

Mathematical Models in Biology

Elizabeth Spencer Allman,John A. Rhodes
Mathematical Models in Biology Book PDF

Author : Elizabeth Spencer Allman,John A. Rhodes
Publisher : Cambridge University Press
Page : 388 pages
File Size : 47,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0521525861

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Mathematical Models in Biology by Elizabeth Spencer Allman,John A. Rhodes Pdf

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Mathematical Models in Biology

Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino
Mathematical Models in Biology Book PDF

Author : Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino
Publisher : Springer
Page : 199 pages
File Size : 53,6 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319234977

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Mathematical Models in Biology by Valeria Zazzu,Maria Brigida Ferraro,Mario R. Guarracino Pdf

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

A Primer in Mathematical Models in Biology

Lee A. Segel,Leah Edelstein-Keshet
A Primer in Mathematical Models in Biology Book PDF

Author : Lee A. Segel,Leah Edelstein-Keshet
Publisher : SIAM
Page : 435 pages
File Size : 53,6 Mb
Release : 2013-05-09
Category : Science
ISBN : 9781611972498

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A Primer in Mathematical Models in Biology by Lee A. Segel,Leah Edelstein-Keshet Pdf

A textbook on mathematical modelling techniques with powerful applications to biology, combining theoretical exposition with exercises and examples.

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Sarah P. Otto,Troy Day
A Biologist s Guide to Mathematical Modeling in Ecology and Evolution Book PDF

Author : Sarah P. Otto,Troy Day
Publisher : Princeton University Press
Page : 745 pages
File Size : 47,7 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400840915

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A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Sarah P. Otto,Troy Day Pdf

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Methods and Models in Mathematical Biology

Johannes Müller,Christina Kuttler
Methods and Models in Mathematical Biology Book PDF

Author : Johannes Müller,Christina Kuttler
Publisher : Springer
Page : 711 pages
File Size : 53,9 Mb
Release : 2015-08-13
Category : Mathematics
ISBN : 9783642272516

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Methods and Models in Mathematical Biology by Johannes Müller,Christina Kuttler Pdf

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

Mathematical Modeling of Biological Processes

Avner Friedman,Chiu-Yen Kao
Mathematical Modeling of Biological Processes Book PDF

Author : Avner Friedman,Chiu-Yen Kao
Publisher : Springer
Page : 154 pages
File Size : 53,6 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9783319083148

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Mathematical Modeling of Biological Processes by Avner Friedman,Chiu-Yen Kao Pdf

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Mathematical Models for Biological Pattern Formation

Philip K. Maini,Hans G. Othmer
Mathematical Models for Biological Pattern Formation Book PDF

Author : Philip K. Maini,Hans G. Othmer
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301332

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Mathematical Models for Biological Pattern Formation by Philip K. Maini,Hans G. Othmer Pdf

This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

Explorations of Mathematical Models in Biology with MATLAB

Mazen Shahin
Explorations of Mathematical Models in Biology with MATLAB Book PDF

Author : Mazen Shahin
Publisher : John Wiley & Sons
Page : 304 pages
File Size : 47,6 Mb
Release : 2013-12-24
Category : Science
ISBN : 9781118548530

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Explorations of Mathematical Models in Biology with MATLAB by Mazen Shahin Pdf

Explore and analyze the solutions of mathematical models from diverse disciplines As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MATLAB, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with MATLAB provides an introduction to model creation using MATLAB, followed by the translation, analysis, interpretation, and observation of the models. With an integrated and interdisciplinary approach that embeds mathematical modeling into biological applications, the book illustrates numerous applications of mathematical techniques within biology, ecology, and environmental sciences. Featuring a quantitative, computational, and mathematical approach, the book includes: Examples of real-world applications, such as population dynamics, genetics, drug administration, interacting species, and the spread of contagious diseases, to showcase the relevancy and wide applicability of abstract mathematical techniques Discussion of various mathematical concepts, such as Markov chains, matrix algebra, eigenvalues, eigenvectors, first-order linear difference equations, and nonlinear first-order difference equations Coverage of difference equations to model a wide range of real-life discrete time situations in diverse areas as well as discussions on matrices to model linear problems Solutions to selected exercises and additional MATLAB codes Explorations of Mathematical Models in Biology with MATLAB is an ideal textbook for upper-undergraduate courses in mathematical models in biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science. The book is also an excellent reference for biologists, ecologists, mathematicians, biomathematicians, and environmental and resource economists.

Mathematical Models for Society and Biology

Edward Beltrami
Mathematical Models for Society and Biology Book PDF

Author : Edward Beltrami
Publisher : Academic Press
Page : 288 pages
File Size : 53,6 Mb
Release : 2013-06-19
Category : Social Science
ISBN : 9780124046931

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Mathematical Models for Society and Biology by Edward Beltrami Pdf

Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book

A Course in Mathematical Biology

Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch
A Course in Mathematical Biology Book PDF

Author : Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch
Publisher : SIAM
Page : 307 pages
File Size : 55,9 Mb
Release : 2006-07-01
Category : Mathematics
ISBN : 9780898716122

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A Course in Mathematical Biology by Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch Pdf

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

Mathematical Models in Population Biology and Epidemiology

Fred Brauer,Carlos Castillo-Chavez
Mathematical Models in Population Biology and Epidemiology Book PDF

Author : Fred Brauer,Carlos Castillo-Chavez
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 55,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475735161

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Mathematical Models in Population Biology and Epidemiology by Fred Brauer,Carlos Castillo-Chavez Pdf

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

Single-Cell-Based Models in Biology and Medicine

Alexander Anderson,Katarzyna Rejniak
Single Cell Based Models in Biology and Medicine Book PDF

Author : Alexander Anderson,Katarzyna Rejniak
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 45,9 Mb
Release : 2007-08-08
Category : Mathematics
ISBN : 9783764381233

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Single-Cell-Based Models in Biology and Medicine by Alexander Anderson,Katarzyna Rejniak Pdf

Aimed at postgraduate students in a variety of biology-related disciplines, this volume presents a collection of mathematical and computational single-cell-based models and their application. The main sections cover four general model groupings: hybrid cellular automata, cellular potts, lattice-free cells, and viscoelastic cells. Each section is introduced by a discussion of the applicability of the particular modelling approach and its advantages and disadvantages, which will make the book suitable for students starting research in mathematical biology as well as scientists modelling multicellular processes.

Mathematical Tools for Understanding Infectious Disease Dynamics

Odo Diekmann,Hans Heesterbeek,Tom Britton
Mathematical Tools for Understanding Infectious Disease Dynamics Book PDF

Author : Odo Diekmann,Hans Heesterbeek,Tom Britton
Publisher : Princeton University Press
Page : 516 pages
File Size : 41,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9780691155395

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Mathematical Tools for Understanding Infectious Disease Dynamics by Odo Diekmann,Hans Heesterbeek,Tom Britton Pdf

This book explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology.