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A Short History of Mathematical Population Dynamics

A Short History of Mathematical Population Dynamics Author Nicolas Bacaër
ISBN-10 0857291157
Release 2011-02-01
Pages 160
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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.

An Introduction to Mathematical Population Dynamics

An Introduction to Mathematical Population Dynamics Author Mimmo Iannelli
ISBN-10 9783319030265
Release 2015-01-23
Pages 346
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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.

Age Structured Population Dynamics in Demography and Epidemiology

Age Structured Population Dynamics in Demography and Epidemiology Author Hisashi Inaba
ISBN-10 9789811001888
Release 2017-04-13
Pages 555
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This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.

Population Dynamics and Laboratory Ecology

Population Dynamics and Laboratory Ecology Author Robert A. Desharnais
ISBN-10 0120139375
Release 2005
Pages 374
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Population Dynamics and Laboratory Ecology highlights the contributions laboratory studies are making to our understanding of the dynamics of ecological and evolutionary systems. Chapters address the scientific rationale for laboratory ecology, its historical role within the broader discipline, and recent advances in research. The book presents results from a wide range of laboratory systems including insects, mites, plankton, protists, and microbes. A common theme throughout the book is the value of microcosm studies in advancing our knowledge of ecological and evolutionary principles. Each chapter is authored by scientists who are leading experts in their fields. The book addresses fundamental questions that are of interest to biologists whether they work in the laboratory or field or whether they are primarily empiricists or theorists. Details a scientific rationale for laboratory systems in ecological and evolutionary studies Offers a view on historical role of laboratory studies Includes examples of recent research advances in ecology and evolution using laboratory systems, ranging from insects to microbes Integrates mathematics, statistics and experimental studies

Population Dynamics in Variable Environments

Population Dynamics in Variable Environments Author Shripad Tuljapurkar
ISBN-10 9783642516528
Release 2013-04-17
Pages 154
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Demography relates observable facts about individuals to the dynamics of populations. If the dynamics are linear and do not change over time, the classical theory of Lotka (1907) and Leslie (1945) is the central tool of demography. This book addresses the situation when the assumption of constancy is dropped. In many practical situations, a population will display unpredictable variation over time in its vital rates, which must then be described in statistical terms. Most of this book is concerned with the theory of populations which are subject to random temporal changes in their vital rates, although other kinds of variation (e. g. , cyclical) are also dealt with. The central questions are: how does temporal variation work its way into a population's future, and how does it affect our interpretation of a population's past. The results here are directed at demographers of humans and at popula tion biologists. The uneven mathematical level is dictated by the material, but the book should be accessible to readers interested in population the ory. (Readers looking for background or prerequisites will find much of it in Hal Caswell's Matrix population models: construction, analysis, and in terpretation (Sinauer 1989) ). This book is in essence a progress report and is deliberately brief; I hope that it is not mystifying. I have not attempted to be complete about either the history or the subject, although most sig nificant results and methods are presented.

Population Dynamics

Population Dynamics Author Naomi Cappuccino
ISBN-10 9780080539256
Release 1995-09-01
Pages 429
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An understanding of the dynamics of populations is critically important to ecologists, evolutionary biologists, wildlife managers, foresters, and many other biologists. This edited treatise brings together the latest research on how populations fluctuate in size, the factors that drive these changes, and the theories explaining how populations are regulated. The book also includes specific chapters dealing with insects of economic importance.

Mathematical Modeling in Economics Ecology and the Environment

Mathematical Modeling in Economics  Ecology and the Environment Author Natali Hritonenko
ISBN-10 9781461493112
Release 2014-01-08
Pages 296
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Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful. Core topics of this text are: · Economic growth and technological development · Population dynamics and human impact on the environment · Resource extraction and scarcity · Air and water contamination · Rational management of the economy and environment · Climate change and global dynamics The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order. Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.

Introduction to Population Modeling

Introduction to Population Modeling Author J.C. Frauenthal
ISBN-10 9781468473223
Release 2012-12-06
Pages 186
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The text of this monograph represents the author's lecture notes from a course taught in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook in the Spring of 1977. On account of its origin as lecture notes, some sections of the text are telegraphic in style while other portions are overly detailed. This stylistic foible has not been modified as it does not appear to detract seriously from the readability and it does help to indicate which topics were stressed. The audience for the course at Stony Brook was composed almost entirely of fourth year undergraduates majoring in the mathematical sciences. All of these students had studied at least four semesters of calculus and one of probability; few had any prior experience with either differential equations or ecology. It seems prudent to point out that the author's background is in engineering and applied mathematics and not in the biological sciences. It is hoped that this is not painfully obvious. -vii- The focus of the monograph is on the formulation and solution of mathematical models; it makes no pretense of being a text in ecology. The idea of a population is employed mainly as a pedagogic tool, providing unity and intuitive appeal to the varied mathematical ideas introduced. If the biological setting is stripped away, what remains can be interpreted as topics on the qualitative behavior of differential and difference equations.

Models of Science Dynamics

Models of Science Dynamics Author Andrea Scharnhorst
ISBN-10 9783642230677
Release 2012-01-23
Pages 270
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Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of research. In order to capture the essence of phenomena as diverse as the structure of co-authorship networks or the evolution of citation diffusion patterns, such models can be represented by conceptual models based on historical and ethnographic observations, mathematical descriptions of measurable phenomena, or computational algorithms. Despite its evident importance, the mathematical modeling of science still lacks a unifying framework and a comprehensive study of the topic. This volume fills this gap, reviewing and describing major threads in the mathematical modeling of science dynamics for a wider academic and professional audience. The model classes presented cover stochastic and statistical models, system-dynamics approaches, agent-based simulations, population-dynamics models, and complex-network models. The book comprises an introduction and a foundational chapter that defines and operationalizes terminology used in the study of science, as well as a review chapter that discusses the history of mathematical approaches to modeling science from an algorithmic-historiography perspective. It concludes with a survey of remaining challenges for future science models and their relevance for science and science policy.

Stochastic Population Dynamics in Ecology and Conservation

Stochastic Population Dynamics in Ecology and Conservation Author Russell Lande
ISBN-10 0198525257
Release 2003
Pages 212
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All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides the most comprehensive introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including new and previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities. Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both deomgraphic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life historydata. Metapopulation viability and the spatial scale of population fluctuations and extinction risk are analyzed. Stochastic dynamics and statistical uncertainty in population parameters are incorporated in Population Viability Analysis and strategies for sustainable harvesting. Statistics of species diversity measures and species abundance distributions are described, with implications for rapid assessments of biodiversity, and methods are developed for partitioning species diversity intoadditive components. Analysis of the stochastic dynamics of a tropical butterfly community in space and time indicates that most of the variance in the species abundance distribution is due to ecological heterogeneity among species, so that real communities are far from neutral.

The Basic Approach to Age Structured Population Dynamics

The Basic Approach to Age Structured Population Dynamics Author Mimmo Iannelli
ISBN-10 9789402411461
Release 2017-09-29
Pages 350
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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.

The Prevention of Malaria

The Prevention of Malaria Author Sir Ronald Ross
ISBN-10 PRNC:32101001676947
Release 1910
Pages 669
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The Prevention of Malaria has been writing in one form or another for most of life. You can find so many inspiration from The Prevention of Malaria also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Prevention of Malaria book for free.

Complex Population Dynamics

Complex Population Dynamics Author Peter Turchin
ISBN-10 9781400847280
Release 2013-02-15
Pages 472
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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.

Essential Mathematical Biology

Essential Mathematical Biology Author Nicholas F. Britton
ISBN-10 9781447100492
Release 2012-12-06
Pages 335
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This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.

Oxford Textbook of Global Public Health

Oxford Textbook of Global Public Health Author Roger Detels
ISBN-10 9780199661756
Release 2015-02-26
Pages 1854
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The Oxford Textbook of Global Public Health is the ultimate resource on the subject of public health and epidemiology. The sixth edition has been thoroughly revised and updated, offering a global and comprehensive perspective on wide-ranging public health needs and priorities in modern health care. The sixth edition, available both in print and online, retains its approach of dividing the complex, dynamic subject of public health into three topics. 'The Scope of Public Health' discusses the development of the discipline, determinants of health and disease, public health policies, and law and ethics. Next, the textbook focuses on 'The Methods of Public Health,' including the main science behind the discipline - epidemiology. Finally, 'The Practice of Public Health' examines specific public health problems and the options for prevention and control. As well as identifying these issues by system or disease, there is also an awareness of the unique needs of particular population groups. New topics in this edition include: Climate change, genetic testing and epidemiology; new methods for measuring the burden of disease; life course approaches to epidemiology, behavioural economics; and physical activity, health and wellbeing. Two new editors, Quarraisha Abdool Karim (South Africa) and Chorh Chuan Tan (Singapore), join the established editor team of Roger Detels (USA), and Martin Gulliford (UK), representing a truly global outlook. The contributors are experts who have been drawn from around the world, offering perspectives from vastly different health systems with ranging public health needs and priorities. The Oxford Textbook of Global Public Health remains the most comprehensive, accessible text in the field, and is an essential reference for students and practitioners in public health and epidemiology.

Population Dynamics in Prehistory and Early History

Population Dynamics in Prehistory and Early History Author Elke Kaiser
ISBN-10 9783110266306
Release 2012-07-04
Pages 363
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The state of migration research has undergone rapid change since methods of analysis involving stable and radiogen isotopes and molecular genetics have started to be applied. At a conference held in Berlin in March 2010, groups whose research looks at population dynamics in pre and early, or in more recent history presented their insights about methodological approaches, research results and perspectives. The aim of this volume is to conduct a dialogue between archaeologists, geneticists and archaeometrists for the purpose of a reconstruction of (pre)historic population history.

Mathematical Modeling of Biological Processes

Mathematical Modeling of Biological Processes Author Avner Friedman
ISBN-10 9783319083148
Release 2014-09-19
Pages 154
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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.