Stochastic Population Models
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Stochastic Population Models
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Author : James H. Matis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Population Models written by James H. Matis 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 Mathematics categories.
This monograph has been heavily influenced by two books. One is Ren shaw's [82] work on modeling biological populations in space and time. It was published as we were busily engaged in modeling African bee dispersal, and provided strong affirmation for the stochastic basis for our ecological modeling efforts. The other is the third edition of Jacquez' [28] classic book on compartmental analysis. He reviews stochastic compartmental analysis and utilizes generating functions in this edition to derive many useful re sults. We interpreted Jacquez' use of generating functions as a message that the day had come for modeling practioners to consider using this powerful approach as a model-building tool. We were inspired by the idea of using generating functions and related methods for two purposes. The first is to integrate seamlessly our previous research centering in stochastic com partmental modeling with our more recent research focusing on stochastic population modeling. The second, related purpose is to present some key research results of practical application in a natural, user-friendly way to the large user communities of compartmental and biological population modelers. One general goal of this monograph is to make a case for the practical utility of the various stochastic population models. In accordance with this objective, we have chosen to illustrate the various stochastic models, using four primary applications described in Chapter 2. In so doing, this mono graph is based largely on our own published work.
Stochastic Population And Epidemic Models
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Author : Linda J. S. Allen
language : en
Publisher: Springer
Release Date : 2015-08-20
Stochastic Population And Epidemic Models written by Linda J. S. Allen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-20 with Mathematics categories.
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.
Stochastic Population Models In Ecology And Epidemiology
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Author : Maurice Stevenson Bartlett
language : en
Publisher:
Release Date : 1960
Stochastic Population Models In Ecology And Epidemiology written by Maurice Stevenson Bartlett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Animal populations categories.
Stochastic Population Dynamics In Ecology And Conservation
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Author : Russell Lande
language : en
Publisher:
Release Date : 2003
Stochastic Population Dynamics In Ecology And Conservation written by Russell Lande and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides the most comprehensive introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including new and previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities.Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both deomgraphic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life history data. Metapopulation viability and the spatial scale of population fluctuations and extinction risk are analyzed. Stochastic dynamics and statistical uncertainty in population parameters are incorporated in Population Viability Analysis and strategies for sustainable harvesting.Statistics of species diversity measures and species abundance distributions are described, with implications for rapid assessments of biodiversity, and methods are developed for partitioning species diversity into additive components. Analysis of the stochastic dynamics of a tropical butterfly community in space and time indicates that most of the variance in the species abundance distribution is due to ecological heterogeneity among species, so that real communities are far from neutral.
Stochastic Differential Equations
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Author : Michael J. Panik
language : en
Publisher: John Wiley & Sons
Release Date : 2017-03-15
Stochastic Differential Equations written by Michael J. Panik and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-15 with Mathematics categories.
A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.
Stochastic Models In Biology
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Author : Narendra S. Goel
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Stochastic Models In Biology written by Narendra S. Goel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.
Probabilistic Models Of Population Evolution
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Author : Étienne Pardoux
language : en
Publisher: Springer
Release Date : 2016-06-17
Probabilistic Models Of Population Evolution written by Étienne Pardoux and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-17 with Mathematics categories.
This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications. Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, stochastic partial differential equations, and probabilistic models in evolutionary biology and population genetics. He obtained his PhD in 1975 at University of Paris-Sud.
Stochastic Abundance Models
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Author : S. Engen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Stochastic Abundance Models written by S. Engen 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 2013-03-07 with Social Science categories.
This monograph deals with the analysis of populations of elements. Each element is a member of one and only one class, and we shall mainly be concerned with populations with a large number of classes. No doubt the present theory has its outspring in ecology, where the elements symbolize the individual animals or plants, while the classes are the various species of the ecological community under consideration. Some basic ideas point back to a classical contribution by R.A. Fisher (1943, in collaboration with A.S. Corbet and c.B. Williams) representing a breakthrough for the theoretical analysis of diverse populations. Though most of the work in this field has been carried out by ecologists, statisticians and biometri cians have, over the past 15 years, shown an ever increasing interest in the topic. Besides being directed towards biometricians and statisticians, this monograph may hopefully be of interest for any research worker dealing with the classification of units into a large number of classes, in particular ecologists, sociologists and linguists. However, some background in statistics and probability theory is required. It would be unless to read the present book without some knowledge of the continuous and discrete probability distributions summarized in section 1.1, and the use of generating functions. In particular, a clear intuitive and formal understanding of the concept of condi tional probability and conditional distributions is required in order to interpret the various models correctly.
Stochastic Epidemic Models With Inference
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Author : Tom Britton
language : en
Publisher: Springer Nature
Release Date : 2019-11-30
Stochastic Epidemic Models With Inference written by Tom Britton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-30 with Mathematics categories.
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.
Stochastic Population Models
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Author : James H. Matis
language : en
Publisher: Taylor & Francis
Release Date : 2000-06-15
Stochastic Population Models written by James H. Matis and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-15 with Mathematics categories.
The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.