Download or read book Differential Equations Models in Biology Epidemiology and Ecology written by Stavros Busenberg and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

Download or read book Differential Equations and Applications in Ecology Epidemics and Population Problems written by Stavros Busenberg and published by Elsevier. This book was released on 2012-12-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations and Applications in Ecology, Epidemics, and Population Problems is composed of papers and abstracts presented at the 1981 research conference on Differential Equations and Applications to Ecology, Epidemics, and Population Problems held at Harvey Mudd College. The reported researches consist of mathematics that is either a direct outgrowth from questions in population biology and biomathematics, or applicable to such questions. The content of this volume are collected in four groups. The first group addresses aspects of population dynamics that involve the interaction between spatial and temporal effects. The second group covers other questions in population dynamics and some other areas of biomathematics. The third group deals with topics in differential and functional differential equations that are continuing to find important applications in mathematical biology. The last group comprises of work on various aspects of differential equations and dynamical systems, not essentially motivated by biological applications. This book is valuable to students and researchers in theoretical biology and biomathematics, as well as to those interested in modern applications of differential equations.

Download or read book Mathematical Modeling for Epidemiology and Ecology written by Glenn Ledder and published by Springer Nature. This book was released on 2023-04-13 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling for Epidemiology and Ecology provides readers with the mathematical 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 the biological implications, with detailed explanations. The author assumes no mathematics background beyond elementary differential calculus. An introductory chapter on basic principles of mathematical modeling is followed by chapters on empirical modeling and mechanistic modeling. These chapters contain a thorough treatment of key ideas and techniques that are often neglected in mathematics books, such as the Akaike Information Criterion. The second half of the book focuses on analysis of dynamical systems, emphasizing tools to simplify analysis, such as the Routh-Hurwitz conditions and asymptotic analysis. Courses can be focused on either half of the book or thematically chosen material from both halves, such as a course on mathematical epidemiology. The biological content is self-contained and includes many topics in epidemiology and ecology. Some of this material appears in case studies that focus on a single detailed example, and some is based on recent research by the author on vaccination modeling and scenarios from the COVID-19 pandemic. The problem sets feature linked problems where one biological setting appears in multi-step problems that are sorted into the appropriate section, allowing readers to gradually develop complete investigations of topics such as HIV immunology and harvesting of natural resources. Some problems use programs written by the author for Matlab or Octave; these combine with more traditional mathematical exercises to give students a full set of tools for model analysis. Each chapter contains additional case studies in the form of projects with detailed directions. New appendices contain mathematical details on optimization, numerical solution of differential equations, scaling, linearization, and sophisticated use of elementary algebra to simplify problems.

Download or read book Differential Equations Models in Biology Epidemiology and Ecology written by Stavros Busenberg and published by Springer. This book was released on 1991-09-25 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

Download or read book Structured Population Models in Biology and Epidemiology written by Pierre Magal and published by Springer. This book was released on 2008-04-12 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.

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.

Download or read book Differential Equations Models in Biology Epidemiology and Ecology written by Frederick W. Wiegel and published by . This book was released on 1974 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book A Course in Mathematical Biology written by Gerda de Vries and published by SIAM. This book was released on 2006-07-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?.

Download or read book Differential Equations with Applications to Biology written by Shigui Ruan and published by American Mathematical Soc.. This book was released on 1999 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.

Download or read book Methods and Models in Mathematical Biology written by Johannes Müller and published by Springer. This book was released on 2015-08-13 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Current Trends in Dynamical Systems in Biology and Natural Sciences written by Maira Aguiar and published by Springer Nature. This book was released on 2020-05-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Approaches to Mathematical Modeling of Biological Invasions written by Merlin C. Köhnke and published by . This book was released on 2020-08-21 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: With potentially dangerous biological invasions increasing due to rises in international trade and travel, research in invasion biology becomes increasingly relevant. Mathematical models form an integral part of this research. This book presents: research on mathematical modeling of biological invasions, different forms of differential equations such as ordinary differential equations, reaction-diffusion models, and stochastic differential equations, detailed investigations as well as a thorough introduction to dynamical systems. Subjects range from theoretical to applied models on fascinating case studies, including: investigating how phenomena such as inducible defense or group defense can be incorporated into mathematical models, investigating how selective infections can influence the dispersal of invasive species, investigating how invasive mammals in New Zealand can be controlled to rescue the national bird, the Kiwi. The book is well suited not only for accomplished researchers but also for students with limited quantitative background interested in studying biological invasions.

Download or read book An Introduction to Mathematical Epidemiology written by Maia Martcheva and published by Springer. This book was released on 2015-10-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book A Course in Mathematical Biology written by Gerda de Vries and published by SIAM. This book was released on 2006-07-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?.