The Basic Approach To Age Structured Population Dynamics

Author : Mimmo Iannelli,Fabio Milner
Publisher : Springer
Page : 350 pages
File Size : 55,5 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 : Hisashi Inaba
Publisher : Springer
Page : 555 pages
File Size : 42,8 Mb
Release : 2017-03-15
Category : Social Science
ISBN : 9789811001888

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Age-Structured Population Dynamics in Demography and Epidemiology by Hisashi Inaba Pdf

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.

Author : Utkir A Rozikov
Publisher : World Scientific
Page : 458 pages
File Size : 44,6 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.

Author : Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft
Publisher : Springer Nature
Page : 663 pages
File Size : 51,8 Mb
Release : 2022-10-03
Category : Mathematics
ISBN : 9783030875022

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Current Trends in Analysis, its Applications and Computation by Paula Cerejeiras,Michael Reissig,Irene Sabadini,Joachim Toft Pdf

This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.

Author : Mimmo Iannelli
Publisher : Giardini
Page : 196 pages
File Size : 47,5 Mb
Release : 1995
Category : Age distribution (Demography)
ISBN : CHI:46889805

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Mathematical Theory of Age-structured Population Dynamics by Mimmo Iannelli Pdf

Author : Shripad Tuljapurkar,Hal Caswell
Publisher : Springer Science & Business Media
Page : 660 pages
File Size : 48,9 Mb
Release : 1997-01-31
Category : Mathematics
ISBN : 0412072718

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Structured-Population Models in Marine, Terrestrial, and Freshwater Systems by Shripad Tuljapurkar,Hal Caswell Pdf

Providing many examples of how models can be implemented and interpreted, this book describes the biology of the life cycle and follows the transitions of individuals through stages in the life cycle. The focus is on models as tools.

Author : M. Iannelli,M. Martcheva,F. A. Milner
Publisher : SIAM
Page : 186 pages
File Size : 47,9 Mb
Release : 2005-04-01
Category : Mathematics
ISBN : 9780898715774

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Gender-structured Population Modeling by M. Iannelli,M. Martcheva,F. A. Milner Pdf

This book gives a unified presentation of, and mathematical framework for, modeling population growth by couple formation, summarizing both past and present modeling results. It provides results on model analysis, gives an up-to-date review of mathematical demography, discusses numerical methods, and puts deterministic modeling of human populations into historical perspective.

Author : Xue-Zhi Li,Junyuan Yang,Maia Martcheva
Publisher : Springer Nature
Page : 386 pages
File Size : 46,5 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9783030424961

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Age Structured Epidemic Modeling by Xue-Zhi Li,Junyuan Yang,Maia Martcheva Pdf

This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology. Chronological age and class-age play an important role in the description of infectious diseases and this text provides the tools for the analysis of this type of partial differential equation models. This book presents general theoretical tools as well as large number of specific examples to guide the reader to develop their own tools that they may then apply to study structured models in mathematical epidemiology. The book will be a valuable addition to the arsenal of all researchers interested in developing theory or studying specific models with age structure.

Author : Sebastian Aniţa
Publisher : Springer Nature
Page : 284 pages
File Size : 41,6 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9783031499715

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Mathematical Modeling and Control in Life and Environmental Sciences by Sebastian Aniţa Pdf

Author : Johan A. Metz,Odo Diekmann
Publisher : Springer
Page : 526 pages
File Size : 51,9 Mb
Release : 2014-03-11
Category : Mathematics
ISBN : 9783662131596

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The Dynamics of Physiologically Structured Populations by Johan A. Metz,Odo Diekmann Pdf

Author : Louis W. Botsford,J. Wilson White,Alan Hastings
Publisher : Oxford University Press
Page : 352 pages
File Size : 51,8 Mb
Release : 2019-09-26
Category : Science
ISBN : 9780191075919

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Population Dynamics for Conservation by Louis W. Botsford,J. Wilson White,Alan Hastings Pdf

The management and conservation of natural populations relies heavily on concepts and results generated from models of population dynamics. Yet this is the first book to present a unified and coherent explanation of the underlying theory. This novel text begins with a consideration of what makes a good state variable, progressing from the simplest models (those with a single variable such as abundance or biomass) to more complex models with other key variables of population structure (including age, size, life history stage, and space). Throughout the book, attention is paid to concepts such as population variability, population stability, population viability/persistence, and harvest yield. Later chapters address specific applications to conservation such as recovery planning for species at risk, fishery management, and the spatial management of marine resources. Population Dynamics for Conservation is suitable for graduate-level students. It will also be valuable to academic and applied researchers in population biology. This overview of population dynamic theory can serve to further their population research, as well as to improve their understanding of population management.

Author : Raouf Boucekkine,Natali Hritonenko,Yuri Yatsenko
Publisher : Routledge
Page : 321 pages
File Size : 55,9 Mb
Release : 2013-05-13
Category : Business & Economics
ISBN : 9781136920936

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Optimal Control of Age-structured Populations in Economy, Demography, and the Environment by Raouf Boucekkine,Natali Hritonenko,Yuri Yatsenko Pdf

This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-standard decision variables into account. In addition, the contributions deal with the age structure of assets, resources, and populations under study. Interdisciplinary modelling has enormous potential for discovering new insights in global and regional development. Optimal Control of Age-structured Populations in Economy, Demography, and the Environment is a rich and excellent source of information on state-of-the-art modelling expertise and references. The book provides the necessary mathematical background for readers from different areas, such as applied sciences, management sciences and operations research, which helps guide the development of practical models. As well as this the book also surveys the current practice in applied modelling and looks at new research areas for a general mathematical audience. This book will be of interest primarily to researchers, postgraduate students, as well as a wider scientific community, including those focussing on the subjects of applied mathematics, environmental sciences, economics, demography, management, and operations research.

Author : J. M. Cushing
Publisher : SIAM
Page : 106 pages
File Size : 42,9 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 : Louis W. Botsford,J. Wilson White,Alan Hastings
Publisher : Oxford University Press, USA
Page : 353 pages
File Size : 40,7 Mb
Release : 2019-10
Category : Science
ISBN : 9780198758365

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Population Dynamics for Conservation by Louis W. Botsford,J. Wilson White,Alan Hastings Pdf

This book outlines concepts such as population variability, population stability, population viability and persistance, and harvest yield. Also addressed are specific applications to conservation such as managing species at risk, fishery management, and the spatial manageement of marine resources.--Adapted from back cover.

Author : Oswald J. Schmitz
Publisher : Island Press
Page : 184 pages
File Size : 53,7 Mb
Release : 2013-03-19
Category : Science
ISBN : 1597265985

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Ecology and Ecosystem Conservation by Oswald J. Schmitz Pdf

Meeting today’s environmental challenges requires a new way of thinking about the intricate dependencies between humans and nature. Ecology and Ecosystem Conservation provides students and other readers with a basic understanding of the fundamental principles of ecological science and their applications, offering an essential overview of the way ecology can be used to devise strategies to conserve the health and functioning of ecosystems. The book begins by exploring the need for ecological science in understanding current environmental issues and briefly discussing what ecology is and isn’t. Subsequent chapters address critical issues in conservation and show how ecological science can be applied to them. The book explores questions such as: • What is the role of ecological science in decision making? • What factors govern the assembly of ecosystems and determine their response to various stressors? • How does Earth’s climate system function and determine the distribution of life on Earth? • What factors control the size of populations? • How does fragmentation of the landscape affect the persistence of species on the landscape? • How does biological diversity influence ecosystem processes? The book closes with a final chapter that addresses the need not only to understand ecological science, but to put that science into an ecosystem conservation ethics perspective.