Mathematical Population Dynamics

Author : Mimmo Iannelli,Andrea Pugliese
Publisher : Springer
Page : 346 pages
File Size : 54,7 Mb
Release : 2015-01-23
Category : Mathematics
ISBN : 9783319030265

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An Introduction to Mathematical Population Dynamics by Mimmo Iannelli,Andrea Pugliese Pdf

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.

Author : Nicolas Bacaër
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 50,9 Mb
Release : 2011-02-01
Category : Mathematics
ISBN : 9780857291158

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A Short History of Mathematical Population Dynamics by Nicolas Bacaër Pdf

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.

Author : Harkaran Singh,Joydip Dhar
Publisher : CRC Press
Page : 274 pages
File Size : 49,8 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9781351251693

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Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains by Harkaran Singh,Joydip Dhar Pdf

Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.

Author : Mimmo Iannelli,Fabio Milner
Publisher : Springer
Page : 350 pages
File Size : 54,6 Mb
Release : 2017-08-27
Category : Mathematics
ISBN : 9789402411461

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The Basic Approach to Age-Structured Population Dynamics by Mimmo Iannelli,Fabio Milner Pdf

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.

Author : J. M. Cushing
Publisher : SIAM
Page : 106 pages
File Size : 55,5 Mb
Release : 1998-01-01
Category : Science
ISBN : 1611970008

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An Introduction to Structured Population Dynamics by J. M. Cushing Pdf

Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Author : Ovide Arino
Publisher : CRC Press
Page : 128 pages
File Size : 48,8 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781000111163

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mathematical population dynamics by Ovide Arino Pdf

This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.

Author : Arino
Publisher : CRC Press
Page : 812 pages
File Size : 42,9 Mb
Release : 1991-04-29
Category : Mathematics
ISBN : 0824784243

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mathematical population dynamics by Arino Pdf

This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.

Author : T. Royama
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401129169

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Analytical Population Dynamics by T. Royama Pdf

A knowledge of animal population dynamics is essential for the proper management of natural resources and the environment. This book, now available in paperback, develops basic concepts and a rigorous methodology for the analysis of animal population dynamics to identify the underlying mechanisms.

Author : O Arino,David E Axelrod,Marek Kimmel
Publisher : World Scientific
Page : 910 pages
File Size : 50,6 Mb
Release : 1997-12-04
Category : Mathematics
ISBN : 9789814545976

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Advances In Mathematical Population Dynamics -- Molecules, Cells And Man - Proceedings Of The 4th International Conference On Mathematical Population Dynamics by O Arino,David E Axelrod,Marek Kimmel Pdf

This is a collection of refereed papers presented at the 4th International Conference on Mathematical Population Dynamics. The selection of papers and their organization were made by the following persons: O Arino, D Axelrod, V Capasso, W Fitzgibbon, P Jagers, M Kimmel, D Kirschner, C Mode, B Novak, R Sachs, W Stephan, A Swierniak and H Thieme.It features some of the new trends in cell and human population dynamics. The main link between the two traits is that human populations of concern here are essentially those subject to cell diseases, either the processes of anarchic proliferation or those by which some cell lines are killed by an infectious agent.The volume is divided into 3 main parts. Each part is subdivided into chapters, each chapter concentrating on a specific aspect. Each aspect is illustrated by one or several examples, developed in sections contributed by several authors. A detailed introduction for each part will enable the reader to refer to chapters of interest. An index and a bibliography for each part is also included for easy reference.This book will be useful for those interested in the subject matter.

Author : Richard Haberman
Publisher : SIAM
Page : 412 pages
File Size : 54,7 Mb
Release : 1998-12-01
Category : Mathematics
ISBN : 9780898714081

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Mathematical Models by Richard Haberman Pdf

The author uses mathematical techniques to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow.

Author : K. B. Newman,S. T. Buckland,B. J. T. Morgan,R. King,D. L. Borchers,D. J. Cole,P. Besbeas,O. Gimenez,L. Thomas
Publisher : Springer
Page : 215 pages
File Size : 51,5 Mb
Release : 2014-07-16
Category : Medical
ISBN : 9781493909773

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Modelling Population Dynamics by K. B. Newman,S. T. Buckland,B. J. T. Morgan,R. King,D. L. Borchers,D. J. Cole,P. Besbeas,O. Gimenez,L. Thomas Pdf

This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models). The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.

Author : Fred Brauer,Carlos Castillo-Chavez
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 43,6 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.

Author : Peter Turchin
Publisher : Princeton University Press
Page : 471 pages
File Size : 46,9 Mb
Release : 2013-02-15
Category : Science
ISBN : 9781400847280

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Complex Population Dynamics by Peter Turchin Pdf

Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

Author : Horst R. Thieme
Publisher : Princeton University Press
Page : 128 pages
File Size : 54,7 Mb
Release : 2018-06-05
Category : Science
ISBN : 9780691187655

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Mathematics in Population Biology by Horst R. Thieme Pdf

Author : Utkir A Rozikov
Publisher : World Scientific
Page : 458 pages
File Size : 48,5 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811211249

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Population Dynamics: Algebraic And Probabilistic Approach by Utkir A Rozikov Pdf

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.