Deterministic Models In Mathematical Demography
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| Author | : J. Impagliazzo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 195 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364282319X |
Mathematical Demography, the study of population and its analysis through mathematical models, has received increased interest in the mathematical com munity in recent years. It was not until the twentieth century, however, that the study of population, predominantly human population, achieved its math ematical character. The subject of mathematical demography can be viewed from either a deterministic viewpoint or from a stochastic viewpoint. For the sake of brevity, stochastic models are not included in this work. It is, therefore, my intention to consider only established deterministic models in this discussion, starting with the life table as the earliest model, to a generalized matrix model which is developed in this treatise. These deterministic models provide sufficient de velopment and conclusions to formulate sound mathematical population analy sis and estimates of population projections. It should be noted that although the subject of mathematical demography focuses on human populations, the development and results may be applied to any population as long as the preconditions that make the model valid are maintained. Information concerning mathematical demography is at best fragmented.
| Author | : John Impagliazzo |
| Publisher | : |
| Total Pages | : 204 |
| Release | : 1985-06-01 |
| Genre | : Denmark |
| ISBN | : 9783642823206 |
| Author | : John Impagliazzo |
| Publisher | : |
| Total Pages | : 630 |
| Release | : 1980 |
| Genre | : Demography |
| 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 | : J. H. Pollard |
| Publisher | : Cambridge University Press |
| Total Pages | : 200 |
| Release | : 1979-02-01 |
| Genre | : Social Science |
| ISBN | : 9780521294423 |
First published in 1973, this book gives an account of some of the more important models which have been proposed for studying the growth of human populations, with a particular emphasis on stochastic models. Despite the practical importance of the subject, at the time of original publication there had been little connection between these models and their possible applications. The book drew together, for the first time, the theoretical analysis of the mathematician and the practical problems of the actuary. Exercises are set at the end of each chapter and brief solutions appear at the back of the text. This book will be of value to anyone with an interest mathematical models and statistics.
| Author | : Randall J. Swift |
| Publisher | : Chapman and Hall/CRC |
| Total Pages | : 480 |
| Release | : 2015-05-26 |
| Genre | : Mathematics |
| ISBN | : 9781420066456 |
A self-contained resource, this book develops fully the mathematical methods and techniques used in population modeling. It begins with an examination of deterministic models, then uses them as a foundation for the formulation of the stochastic models. In three distinct parts, the book covers the modeling of single populations and applications, develops models for multiple and large populations with applications, and examines recent applications of the methods being discussed in the earlier parts of the book. Lastly, the use of MATLAB and Mathematica is included for many simulations and to help with the solution of the more difficult problems posed.
| Author | : Solym Mawaki Manou-Abi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 308 |
| Release | : 2020-04-28 |
| Genre | : Mathematics |
| ISBN | : 1786304546 |
This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.
| Author | : David P. Smith |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2013-07-23 |
| Genre | : Social Science |
| ISBN | : 3642358586 |
Mathematical demography is the centerpiece of quantitative social science. The founding works of this field from Roman times to the late Twentieth Century are collected here, in a new edition of a classic work by David R. Smith and Nathan Keyfitz. Commentaries by Smith and Keyfitz have been brought up to date and extended by Kenneth Wachter and Hervé Le Bras, giving a synoptic picture of the leading achievements in formal population studies. Like the original collection, this new edition constitutes an indispensable source for students and scientists alike, and illustrates the deep roots and continuing vitality of mathematical demography.
| Author | : Sylvie Meleard |
| Publisher | : Springer |
| Total Pages | : 111 |
| Release | : 2015-09-03 |
| Genre | : Mathematics |
| ISBN | : 3319217119 |
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
| Author | : Nicolas Bacaër |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 160 |
| Release | : 2011-02-01 |
| Genre | : Mathematics |
| ISBN | : 0857291157 |
As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.
