Discrete Mathematical Models In Population Biology

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Mathematical Models in Population Biology and Epidemiology

Author : Fred Brauer
Publisher : Springer Science & Business Media
ISBN 13 : 1475735162
Total Pages : 432 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Mathematical Models in Population Biology and Epidemiology by : Fred Brauer

Download or read book Mathematical Models in Population Biology and Epidemiology written by Fred Brauer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Mathematical Models in Population Biology

Author : Saber N. Elaydi
Publisher : Springer
ISBN 13 : 9783031647949
Total Pages : 0 pages
Book Rating : 4.6/5 (479 download)

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Book Synopsis Discrete Mathematical Models in Population Biology by : Saber N. Elaydi

Download or read book Discrete Mathematical Models in Population Biology written by Saber N. Elaydi and published by Springer. This book was released on 2024-10-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text lays the foundation for understanding the beauty and power of discrete-time models. It covers rich mathematical modeling landscapes, each offering deep insights into the dynamics of biological systems. A harmonious balance is achieved between theoretical principles, mathematical rigor, and practical applications. Illustrative examples, numerical simulations, and empirical case studies are provided to enhance mastery of the subject and facilitate the translation of discrete-time mathematical biology into real-world challenges. Mainly geared to upper undergraduates, the text may also be used in graduate courses focusing on discrete-time modeling. Chapters 1–4 constitute the core of the text. Instructors will find the dependence chart quite useful when designing their particular course. This invaluable resource begins with an exploration of single-species models where frameworks for discrete-time modeling are established. Competition models and Predator-prey interactions are examined next followed by evolutionary models, structured population models, and models of infectious diseases. The consequences of periodic variations, seasonal changes, and cyclic environmental factors on population dynamics and ecological interactions are investigated within the realm of periodically forced biological models. This indispensable resource is structured to support educational settings: A first course in biomathematics, introducing students to the fundamental mathematical techniques essential for biological research. A modeling course with a concentration on developing and analyzing mathematical models that encapsulate biological phenomena. An advanced mathematical biology course that offers an in-depth exploration of complex models and sophisticated mathematical frameworks designed to tackle advanced problems in biology. With its clear exposition and methodical approach, this text educates and inspires students and professionals to apply mathematical biology to real-world situations. While minimal knowledge of calculus is required, the reader should have a solid mathematical background in linear algebra.

Mathematical Models in Biology

Author : Leah Edelstein-Keshet
Publisher : SIAM
ISBN 13 : 9780898719147
Total Pages : 629 pages
Book Rating : 4.7/5 (191 download)

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Book Synopsis Mathematical Models in Biology by : Leah Edelstein-Keshet

Download or read book Mathematical Models in Biology written by Leah Edelstein-Keshet and published by SIAM. This book was released on 1988-01-01 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic and Discrete Mathematical Methods for Modern Biology

Author : Raina Robeva
Publisher : Academic Press
ISBN 13 : 0128012714
Total Pages : 383 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Algebraic and Discrete Mathematical Methods for Modern Biology by : Raina Robeva

Download or read book Algebraic and Discrete Mathematical Methods for Modern Biology written by Raina Robeva and published by Academic Press. This book was released on 2015-05-09 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. Examines significant questions in modern biology and their mathematical treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Mathematical Models in Biology

Author : Elizabeth Spencer Allman
Publisher : Cambridge University Press
ISBN 13 : 9780521525862
Total Pages : 388 pages
Book Rating : 4.5/5 (258 download)

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Book Synopsis Mathematical Models in Biology by : Elizabeth Spencer Allman

Download or read book Mathematical Models in Biology written by Elizabeth Spencer Allman and published by Cambridge University Press. This book was released on 2004 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems

Author : Fred S. Roberts
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems by : Fred S. Roberts

Download or read book Discrete Mathematical Models, with Applications to Social, Biological, and Environmental Problems written by Fred S. Roberts and published by Prentice Hall. This book was released on 1976 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models; Graphs; Applications of graphs; Weighted digraphs and pulse processes; Markov chains; n-Person games; Group decisionmaking; Measurement and utility; Index.

Population Biology

Author : Alan Hastings
Publisher : Springer Science & Business Media
ISBN 13 : 1475727313
Total Pages : 228 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Population Biology by : Alan Hastings

Download or read book Population Biology written by Alan Hastings and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population biology has been investigated quantitatively for many decades, resulting in a rich body of scientific literature. Ecologists often avoid this literature, put off by its apparently formidable mathematics. This textbook provides an introduction to the biology and ecology of populations by emphasizing the roles of simple mathematical models in explaining the growth and behavior of populations. The author only assumes acquaintance with elementary calculus, and provides tutorial explanations where needed to develop mathematical concepts. Examples, problems, extensive marginal notes and numerous graphs enhance the book's value to students in classes ranging from population biology and population ecology to mathematical biology and mathematical ecology. The book will also be useful as a supplement to introductory courses in ecology.

Deterministic Mathematical Models in Population Ecology

Author : Herbert I. Freedman
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Deterministic Mathematical Models in Population Ecology by : Herbert I. Freedman

Download or read book Deterministic Mathematical Models in Population Ecology written by Herbert I. Freedman and published by . This book was released on 1980 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Single-species growth; Pedration and parasitism; Predador-prey systems; Lotka-volterra systems for predator-prey interactions; Intermediate predator-prey models; Continous models; Discrete models; The kolmogorov model; Related topics and applications; Related topics; Aplications; competition and cooperation (symbiosis); Lotka-volterra competition models; Higher-oder competition models; cooperation (symbiosis); Pertubation theory; The implicit function theorem; Existence and Uniqueness of solutions of ordinary differential equations; Stability and periodicity; The poincare-bendixon theorem; The hopf bifurcation theorem.

Mathematical Methods of Population Biology

Author : Frank Charles Hoppensteadt
Publisher : Cambridge University Press
ISBN 13 : 9780521282567
Total Pages : 162 pages
Book Rating : 4.2/5 (825 download)

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Book Synopsis Mathematical Methods of Population Biology by : Frank Charles Hoppensteadt

Download or read book Mathematical Methods of Population Biology written by Frank Charles Hoppensteadt and published by Cambridge University Press. This book was released on 1982-02-26 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to mathematical methods used in the study of population phenomena including models of total population and population age structure, models of random population events presented in terms of Markov chains, and methods used to uncover qualitative behavior of more complicated difference equations.

An Introduction to Mathematical Population Dynamics

Author : Mimmo Iannelli
Publisher : Springer
ISBN 13 : 3319030264
Total Pages : 346 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Introduction to Mathematical Population Dynamics by : Mimmo Iannelli

Download or read book An Introduction to Mathematical Population Dynamics written by Mimmo Iannelli and published by Springer. This book was released on 2015-01-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.

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

Author : Sarah P. Otto
Publisher : Princeton University Press
ISBN 13 : 1400840910
Total Pages : 745 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by : Sarah P. Otto

Download or read book A Biologist's Guide to Mathematical Modeling in Ecology and Evolution written by Sarah P. Otto and published by Princeton University Press. This book was released on 2011-09-19 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Mathematics in Population Biology

Author : Horst R. Thieme
Publisher : Princeton University Press
ISBN 13 : 0691187657
Total Pages : pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics in Population Biology by : Horst R. Thieme

Download or read book Mathematics in Population Biology written by Horst R. Thieme and published by Princeton University Press. This book was released on 2018-06-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Some Mathematical Questions in Biology

Author : Alan Hastings
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897157
Total Pages : 136 pages
Book Rating : 4.8/5 (971 download)

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Book Synopsis Some Mathematical Questions in Biology by : Alan Hastings

Download or read book Some Mathematical Questions in Biology written by Alan Hastings and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population biology has had a long history of mathematical modeling. The 1920s and 1930s saw major strides with the work of Lotka and Volterra in ecology and Fisher, Haldane, and Wright in genetics. In recent years, much more sophisticated mathematical techniques have been brought to bear on questions in population biology. Simultaneously, advances in experimental and field work have produced a wealth of new data. While this growth has tended to fragment the field, one unifying theme is that similar mathematical questions arise in a range of biological contexts. This volume contains the proceedings of a symposium on Some Mathematical Questions in Biology, held in Chicago in 1987. The papers all deal with different aspects of population biology, but there are overlaps in the mathematical techniques used; for example, dynamics of nonlinear differential and difference equations form a common theme. The topics covered are cultural evolution, multilocus population genetics, spatially structured population genetics, chaos and the dynamics of epidemics, and the dynamics of ecological communities.

Mathematical Models in Population Biology and Epidemiology

Author : Fred Brauer
Publisher : Springer
ISBN 13 : 9781461416876
Total Pages : 508 pages
Book Rating : 4.4/5 (168 download)

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Book Synopsis Mathematical Models in Population Biology and Epidemiology by : Fred Brauer

Download or read book Mathematical Models in Population Biology and Epidemiology written by Fred Brauer and published by Springer. This book was released on 2011-11-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaos in Ecology

Author : J. M. Cushing
Publisher : Elsevier
ISBN 13 : 9780121988760
Total Pages : 248 pages
Book Rating : 4.9/5 (887 download)

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Book Synopsis Chaos in Ecology by : J. M. Cushing

Download or read book Chaos in Ecology written by J. M. Cushing and published by Elsevier. This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos in Ecology is a convincing demonstration of chaos in a biological population. The book synthesizes an ecologically focused interdisciplinary blend of non-linear dynamics theory, statistics, and experimentation yielding results of uncommon clarity and rigor. Topics include fundamental issues that are of general and widespread importance to population biology and ecology. Detailed descriptions are included of the mathematical, statistical, and experimental steps they used to explore nonlinear dynamics in ecology. Beginning with a brief overview of chaos theory and its implications for ecology. The book continues by deriving and rigorously testing a mathematical model that is closely wedded to biological mechanisms of their research organism. Therefrom were generated a variety of predictions that are fundamental to chaos theory and experiments were designed and analyzed to test those predictions. Discussion of patterns in chaos and how they can be investigated using real data follows and book ends with a discussion of the salient lessons learned from this research program Book jacket.

A Short History of Mathematical Population Dynamics

Author : Nicolas Bacaër
Publisher : Springer Science & Business Media
ISBN 13 : 0857291157
Total Pages : 160 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis A Short History of Mathematical Population Dynamics by : Nicolas Bacaër

Download or read book A Short History of Mathematical Population Dynamics written by Nicolas Bacaër and published by Springer Science & Business Media. This book was released on 2011-02-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.

A Primer on Population Dynamics Modeling

Author : Hiromi Seno
Publisher : Springer Nature
ISBN 13 : 981196016X
Total Pages : 471 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis A Primer on Population Dynamics Modeling by : Hiromi Seno

Download or read book A Primer on Population Dynamics Modeling written by Hiromi Seno and published by Springer Nature. This book was released on 2022-11-16 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to the mathematical models of population dynamics in mathematical biology. The focus of this book is on the biological meaning/translation of mathematical structures in mathematical models, rather than simply explaining mathematical details and literacies to analyze a model. In some recent usages of the mathematical model simply with computer numerical calculations, the model includes some inappropriate mathematical structure concerning the reasonability of modeling for the biological problem under investigation. For students and researchers who study or use mathematical models, it is important and helpful to understand what mathematical setup could be regarded as reasonable for the model with respect to the relation between the biological factors involved in the assumptions and the mathematical structure of the model. Topics covered in this book are; modeling with geometric progression, density effect in population dynamics, deriving continuous time models from discrete time models, basic modeling for birth-death stochastic processes, continuous time models, modeling interspecific reaction for the continuous time population dynamics model, competition and prey-predator dynamics, modeling for population dynamics with a heterogeneous structure of population, qualitative analysis on the discrete time dynamical system, necessary knowledge about fundamental mathematical theories to understand the dynamical nature of continuous time models. The book includes popular topics in ecology and mathematical biology, as well as classic theoretical topics. By understanding the biological meaning of modeling for simple models, readers will be able to derive a specific mathematical model for a biological problem by reasonable modeling. The contents of this book is made accessible for readers without strong Mathematical background.