Stability and Bifurcation in Age-dependent Population Dynamics PDF Download
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Author: K. E. Swick
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: K. E. Swick
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Glenn F. Webb
Publisher: CRC Press
ISBN: 9780824772901
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author: S. Anita
Publisher: Springer Science & Business Media
ISBN: 9401594368
Category : Mathematics
Languages : en
Pages : 207
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Book Description
The material of the present book is an extension of a graduate course given by the author at the University "Al.I. Cuza" Iasi and is intended for stu dents and researchers interested in the applications of optimal control and in mathematical biology. Age is one of the most important parameters in the evolution of a bi ological population. Even if for a very long period age structure has been considered only in demography, nowadays it is fundamental in epidemiology and ecology too. This is the first book devoted to the control of continuous age structured populationdynamics.It focuses on the basic properties ofthe solutions and on the control of age structured population dynamics with or without diffusion. The main goal of this work is to familiarize the reader with the most important problems, approaches and results in the mathematical theory of age-dependent models. Special attention is given to optimal harvesting and to exact controllability problems, which are very important from the econom ical or ecological points of view. We use some new concepts and techniques in modern control theory such as Clarke's generalized gradient, Ekeland's variational principle, and Carleman estimates. The methods and techniques we use can be applied to other control problems.
Author: J. M. Cushing
Publisher: SIAM
ISBN: 9781611970005
Category : Science
Languages : en
Pages : 106
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Book Description
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: Hisashi Inaba
Publisher: Springer
ISBN: 981100188X
Category : Social Science
Languages : en
Pages : 566
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Book Description
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: Robert Costantino
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 282
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Book Description
The study of populations is becoming increasingly focused on dynamics. We believe there are two reasons for this trend. The ftrst is the impactof nonlinear dynamics with its exciting ideas and colorful language: bifurcations, domains of attraction, chaos, fractals, strange attractors. Complexity, which is so very much a part of biology, now seems to be also a part of mathematics. A second trend is the accessibility of the new concepts. Thebarriers tocommunicationbetween theoristandexperimentalistseemless impenetrable. The active participationofthe experimentalist means that the theory will obtain substance. Our role is the application of the theory of dynamics to the analysis ofbiological populations. We began our work early in 1979 by writing an ordinary differential equation for the rateofchange in adult numbers which was based on an equilibrium model proposed adecadeearlier. Duringthenextfewmonths weftlledournotebookswithstraightforward deductions from the model and its associated biological implications. Slowly, some of the biological observations were explained and papers followed on a variety of topics: genetic and demographic stability, stationary probability distributions for population size,population growth asabirth-deathprocess, natural selectionanddensity-dependent population growth, genetic disequilibrium, and the stationary stochastic dynamics of adult numbers.
Author: Michel Chipot
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Author: Mimmo Iannelli
Publisher: Giardini
ISBN:
Category : Age distribution (Demography)
Languages : en
Pages : 196
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Book Description
Author: Glenn F. Webb
Publisher:
ISBN:
Category : Population
Languages : en
Pages :
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Book Description
Author: C. Y. Cyrus Chu
Publisher: Oxford University Press, USA
ISBN: 0195121589
Category : Family demography
Languages : en
Pages : 241
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Book Description
This book fills the gap between the classical supply-side theory of Malthus and the modern demand-side theory of economic demography. Specifically, it investigates the dynamic macroeconomic implications of various static microeconomic-family economic decisions. It is within this framework that Professor Chu studies the income distribution, the attitude composition, the job structure, and the savings (including pensions) of the population. Chu applies a mathematical apparatus, the theory of branching processes, to his problem, and supplies the reader with much detail and several discursive discussions on the topic. Graduate-level students, professors, and professional economists will be interested in Chu's efforts.
