A Two Sex Age Structured Population Model In Discrete Time

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A Two Sex Age Structured Population Model In Discrete Time

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Author : Stephen Eric Tennenbaum
language : en
Publisher:
Release Date : 2006

A Two Sex Age Structured Population Model In Discrete Time written by Stephen Eric Tennenbaum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Gender Structured Population Modeling

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Author : M. Iannelli
language : en
Publisher: SIAM
Release Date : 2005-04-01

Gender Structured Population Modeling written by M. Iannelli and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-01 with Mathematics categories.

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.

Age Structured Population Dynamics In Demography And Epidemiology

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Author : Hisashi Inaba
language : en
Publisher: Springer
Release Date : 2017-03-15

Age Structured Population Dynamics In Demography And Epidemiology written by Hisashi Inaba and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-15 with Social Science categories.

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.

Discrete Time Dynamics Of Structured Populations And Homogeneous Order Preserving Operators

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Author : Horst R. Thieme
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-07

Discrete Time Dynamics Of Structured Populations And Homogeneous Order Preserving Operators written by Horst R. Thieme and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-07 with Mathematics categories.

A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Evolution In Age Structured Populations

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Author : Brian Charlesworth
language : en
Publisher: Cambridge University Press
Release Date : 1994-06-30

Evolution In Age Structured Populations written by Brian Charlesworth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-30 with Mathematics categories.

The populations of many species of animals and plants are age-structured, i.e. the individuals present at any one time were born over a range of different times, and their fertility and survival depend on age. The properties of such populations are important for interpreting experiments and observations on the genetics of populations for animal and plant breeding, and for understanding the evolution of features of life-histories such as senescence and time of reproduction. In this new edition Brian Charlesworth provides a comprehensive review of the basic mathematical theory of the demography and genetics of age-structured populations. The mathematical level of the book is such that it will be accessible to anyone with a knowledge of basic calculus and linear algebra.

Advances In Discrete Dynamical Systems Difference Equations And Applications

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Author : Saber Elaydi
language : en
Publisher: Springer Nature
Release Date : 2023-03-25

Advances In Discrete Dynamical Systems Difference Equations And Applications written by Saber Elaydi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-25 with Mathematics categories.

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Structured Population Models In Marine Terrestrial And Freshwater Systems

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Author : Shripad Tuljapurkar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Structured Population Models In Marine Terrestrial And Freshwater Systems written by Shripad Tuljapurkar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

In the summer of 1993, twenty-six graduate and postdoctoral stu dents and fourteen lecturers converged on Cornell University for a summer school devoted to structured-population models. This school was one of a series to address concepts cutting across the traditional boundaries separating terrestrial, marine, and freshwa ter ecology. Earlier schools resulted in the books Patch Dynamics (S. A. Levin, T. M. Powell & J. H. Steele, eds., Springer-Verlag, Berlin, 1993) and Ecological Time Series (T. M. Powell & J. H. Steele, eds., Chapman and Hall, New York, 1995); a book on food webs is in preparation. Models of population structure (differences among individuals due to age, size, developmental stage, spatial location, or genotype) have an important place in studies of all three kinds of ecosystem. In choosing the participants and lecturers for the school, we se lected for diversity-biologists who knew some mathematics and mathematicians who knew some biology, field biologists sobered by encounters with messy data and theoreticians intoxicated by the elegance of the underlying mathematics, people concerned with long-term evolutionary problems and people concerned with the acute crises of conservation biology. For four weeks, these perspec tives swirled in discussions that started in the lecture hall and carried on into the sweltering Ithaca night. Diversity mayor may not increase stability, but it surely makes things interesting.

Wildlife Demography

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Author : John R. Skalski
language : en
Publisher: Elsevier
Release Date : 2010-07-20

Wildlife Demography written by John R. Skalski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-20 with Science categories.

Wildlife Demography compiles the multitude of available estimation techniques based on sex and age data, and presents these varying techniques in one organized, unified volume. Designed to guide researchers to the most appropriate estimator based upon their particular data set and the desired level of study precision, this book provides quantitative consideration, statistical models, estimator variance, assumptions and examples of use. The authors focus on estimation techniques using sex and age ratios because this data is relatively easy to collect and commonly used by wildlife management. - Applicable to a wide array of wildlife species, including game and non-game birds and mammals - Features more than 100 annotated examples illustrating application of statistical methods - Includes more than 640 references of the analysis of nontagging data and the factors that may influence interpretation - Derives historical and ad hoc demographic methods in a modern statistical framework

Modeling Biological Systems

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Author : James W. Haefner
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05

Modeling Biological Systems written by James W. Haefner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Science categories.

I Principles 1 1 Models of Systems 3 1. 1 Systems. Models. and Modeling . . . . . . . . . . . . . . . . . . . . 3 1. 2 Uses of Scientific Models . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3 Example: Island Biogeography . . . . . . . . . . . . . . . . . . . . . 6 1. 4 Classifications of Models . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Constraints on Model Structure . . . . . . . . . . . . . . . . . . . . . 12 1. 6 Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 7 Misuses of Models: The Dark Side . . . . . . . . . . . . . . . . . . . 13 1. 8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 The Modeling Process 17 2. 1 Models Are Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. 2 Two Alternative Approaches . . . . . . . . . . . . . . . . . . . . . . 18 2. 3 An Example: Population Doubling Time . . . . . . . . . . . . . . . . 24 2. 4 Model Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Qualitative Model Formulation 32 3. 1 How to Eat an Elephant . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 2 Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 4 Errors in Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . 44 3. 5 Advantages and Disadvantages of Forrester Diagrams . . . . . . . . . 44 3. 6 Principles of Qualitative Formulation . . . . . . . . . . . . . . . . . . 45 3. 7 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 8 Other Modeling Problems . . . . . . . . . . . . . . . . . . . . . . . . 49 viii Contents . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 9 Exercises 53 4 Quantitative Model Formulation: I 4. 1 From Qualitative to Quantitative . . . . . . . . . . . . . . . . . Finite Difference Equations and Differential Equations 4. 2 . . . . . . . . . . . . . . . . 4. 3 Biological Feedback in Quantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5 Exercises 5 Quantitative Model Formulation: I1 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 1 Physical Processes 81 . . . . . . . . . . . . . . . 5. 2 Using the Toolbox of Biological Processes 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 3 Useful Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 4 Examples 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 5 Exercises 104 6 Numerical Techniques 107 . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Mistakes Computers Make 107 . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Numerical Integration 110 . . . . . . . . . . . . . . . . 6. 3 Numerical Instability and Stiff Equations 115 . . . . . . . . . . . . . .

An Introduction To Mathematical Epidemiology

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Author : Maia Martcheva
language : en
Publisher: Springer
Release Date : 2015-10-20

An Introduction To Mathematical Epidemiology written by Maia Martcheva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.