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| Author | : Stephen Eric Tennenbaum |
| Publisher | : |
| Total Pages | : 258 |
| Release | : 2006 |
| Genre | : |
| ISBN | : |
| Author | : M. Iannelli |
| Publisher | : SIAM |
| Total Pages | : 186 |
| Release | : 2005-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898715776 |
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 | : Hisashi Inaba |
| Publisher | : Springer |
| Total Pages | : 555 |
| Release | : 2017-03-15 |
| Genre | : Social Science |
| ISBN | : 981100188X |
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 | : Horst R. Thieme |
| Publisher | : American Mathematical Society |
| Total Pages | : 357 |
| Release | : 2024-05-07 |
| Genre | : Mathematics |
| ISBN | : 1470474654 |
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.
| Author | : Brian Charlesworth |
| Publisher | : Cambridge University Press |
| Total Pages | : 325 |
| Release | : 1994-06-30 |
| Genre | : Mathematics |
| ISBN | : 0521459672 |
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.
| Author | : |
| Publisher | : Krishna Prakashan Media |
| Total Pages | : 252 |
| Release | : 1977 |
| Genre | : |
| ISBN | : 9788182830257 |
| Author | : Hal Caswell |
| Publisher | : Springer |
| Total Pages | : 308 |
| Release | : 2019-04-02 |
| Genre | : Social Science |
| ISBN | : 3030105342 |
This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.
| Author | : Saber Elaydi |
| Publisher | : Springer Nature |
| Total Pages | : 534 |
| Release | : 2023-03-25 |
| Genre | : Mathematics |
| ISBN | : 303125225X |
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.
| Author | : Mimmo Iannelli |
| Publisher | : Springer |
| Total Pages | : 350 |
| Release | : 2017-08-27 |
| Genre | : Mathematics |
| ISBN | : 9402411461 |
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 | : Mark Kot |
| Publisher | : Cambridge University Press |
| Total Pages | : 466 |
| Release | : 2001-07-19 |
| Genre | : Nature |
| ISBN | : 1316584054 |
Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.
