Theory of Nonlinear Age-Dependent Population Dynamics PDF Download
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Author: Glenn F. Webb
Publisher: CRC Press
ISBN: 9780824772901
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author: Glenn F. Webb
Publisher: CRC Press
ISBN: 9780824772901
Category : Mathematics
Languages : en
Pages : 312
Get Book Here
Book Description
Author: S. Anita
Publisher: Springer Science & Business Media
ISBN: 9780792366393
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This volume is devoted to some of the most biologically significant control problems governed by continuous age-dependent population dynamics. It investigates the existence, uniqueness, positivity, and asymptotic behaviour of the solutions of the continuous age-structured models. Some comparison results are also established. In the optimal control problems the emphasis is on first order necessary conditions of optimality. These conditions allow the determination of the optimal control or the approximation of the optimal control problem. The exact controllability for some models with diffusion and internal control is also studied. These subjects are treated using new concepts and techniques of modern optimal control theory, such as Clarke's generalized gradient, Ekeland's variational principle, Hamilton-Jacobi equations, and Carleman estimates. A background in advanced calculus and partial differential equations is required. Audience: This work will be of interest to students in mathematics, biology, and engineering, and researchers in applied mathematics, control theory, and biology.
Author: Mimmo Iannelli
Publisher: Springer
ISBN: 9402411461
Category : Mathematics
Languages : en
Pages : 357
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Book Description
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: 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: K.-H. Hoffmann
Publisher: Birkhäuser
ISBN: 3034876270
Category : Science
Languages : en
Pages : 227
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Book Description
This volume contains the contributions of participants of the conference "Optimal Control of Partial Differential Equations" which, under the chairmanship of the editors, took place at the Mathematisches Forschungsinstitut Oberwolfach from May 18 to May 24, 1986. The great variety of topics covered by the contributions strongly indicates that also in the future it will be impossible to develop a unifying control theory of partial differential equations. On the other hand, there is a strong tendency to treat prob lems which are directly connected to practical applications. So this volume contains real-world applications like optimal cooling laws for the production of rolled steel or concrete solutions for the problem of optimal shape design in mechanics and hydrody namics. Another main topic is the construction of numerical methods. This includes applications of the finite element method as well as of Quasi-Newton-methods to con strained and unconstrained control problems. Also, very complex problems arising in the theory of free boundary value problems are treated. ]~inally, some contribu tions show how practical problems stimulate the further development of the theory; in particular, this is the case for fields like suboptimal control, necessary optimality conditions and sensitivity analysis. As usual, the lectures and stimulating discussions took place in the pleasant at mosphere of the Mathematisches Forschungsinstitut Oberwolfach. Special thanks of the participants are returned to the Director as well as to the staff of the institute.
Author: Herbert Dawid
Publisher: Springer
ISBN: 3319391208
Category : Business & Economics
Languages : en
Pages : 518
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Book Description
This volume collects research papers addressing topical issues in economics and management with a particular focus on dynamic models which allow to analyze and foster the decision making of firms in dynamic complex environments. The scope of the contributions ranges from daily operational challenges firms face to strategic choices in dynamic industry environments and the analysis of optimal growth paths. The volume also highlights recent methodological developments in the areas of dynamic optimization, dynamic games and meta-heuristics, which help to improve our understanding of (optimal) decision making in a fast evolving economy.
Author: Diaraf Seck
Publisher: Springer Nature
ISBN: 3030573362
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.
Author: Carlos Castillo-Chavez
Publisher: Springer Science & Business Media
ISBN: 1461300657
Category : Medical
Languages : en
Pages : 375
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Book Description
This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.
Author: Robert F. Costantino
Publisher: Springer Science & Business Media
ISBN: 1461231701
Category : Science
Languages : en
Pages : 272
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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: Ovide Arino
Publisher: CRC Press
ISBN: 1000154254
Category : Mathematics
Languages : en
Pages : 812
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Book Description
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.
