A Short History Of Mathematical Population Dynamics

Author : Nicolas Bacaër
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 42,8 Mb
Release : 2011-02-01
Category : Mathematics
ISBN : 9780857291158

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A Short History of Mathematical Population Dynamics by Nicolas Bacaër Pdf

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.

Author : Ovide Arino
Publisher : CRC Press
Page : 812 pages
File Size : 52,9 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781000154252

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mathematical population dynamics by Ovide Arino Pdf

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.

Author : Harkaran Singh,Joydip Dhar
Publisher : CRC Press
Page : 274 pages
File Size : 44,7 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9781351251693

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Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains by Harkaran Singh,Joydip Dhar Pdf

Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.

Author : Hiromi Seno
Publisher : Springer Nature
Page : 471 pages
File Size : 49,6 Mb
Release : 2022-11-16
Category : Science
ISBN : 9789811960161

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A Primer on Population Dynamics Modeling by Hiromi Seno Pdf

This textbook provides an introduction to the mathematical models of population dynamics in mathematical biology. The focus of this book is on the biological meaning/translation of mathematical structures in mathematical models, rather than simply explaining mathematical details and literacies to analyze a model. In some recent usages of the mathematical model simply with computer numerical calculations, the model includes some inappropriate mathematical structure concerning the reasonability of modeling for the biological problem under investigation. For students and researchers who study or use mathematical models, it is important and helpful to understand what mathematical setup could be regarded as reasonable for the model with respect to the relation between the biological factors involved in the assumptions and the mathematical structure of the model. Topics covered in this book are; modeling with geometric progression, density effect in population dynamics, deriving continuous time models from discrete time models, basic modeling for birth-death stochastic processes, continuous time models, modeling interspecific reaction for the continuous time population dynamics model, competition and prey-predator dynamics, modeling for population dynamics with a heterogeneous structure of population, qualitative analysis on the discrete time dynamical system, necessary knowledge about fundamental mathematical theories to understand the dynamical nature of continuous time models. The book includes popular topics in ecology and mathematical biology, as well as classic theoretical topics. By understanding the biological meaning of modeling for simple models, readers will be able to derive a specific mathematical model for a biological problem by reasonable modeling. The contents of this book is made accessible for readers without strong Mathematical background.

Author : Utkir A Rozikov
Publisher : World Scientific
Page : 458 pages
File Size : 47,7 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811211249

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Population Dynamics: Algebraic And Probabilistic Approach by Utkir A Rozikov Pdf

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.

Author : J. M. Cushing
Publisher : SIAM
Page : 106 pages
File Size : 45,9 Mb
Release : 1998-01-01
Category : Science
ISBN : 1611970008

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An Introduction to Structured Population Dynamics by J. M. Cushing Pdf

Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Author : Roger Detels,Quarraisha Abdool Karim,Fran Baum
Publisher : Oxford University Press
Page : 1777 pages
File Size : 43,5 Mb
Release : 2022
Category : Medical
ISBN : 9780198816805

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Oxford Textbook of Global Public Health by Roger Detels,Quarraisha Abdool Karim,Fran Baum Pdf

"Public health is concerned with the process of mobilizing local, state/provincial, national, and international resources to assure the conditions in which all people can be healthy (Detels and Breslow 2002). To successfully implement this process and to make health for all achievable, public health must perform the functions listed in Box 1.1.1"--

Author : Stacey Smith?
Publisher : University of Ottawa Press
Page : 146 pages
File Size : 48,5 Mb
Release : 2023-10-24
Category : Medical
ISBN : 9780776640617

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The Top Ten Diseases of All Time by Stacey Smith? Pdf

Infectious diseases have been with us for millennia and continue to pose a threat, from the irritation of flu season to the potential extinction of our species. We instinctively fear them and alter our behaviour as a result. The reason we bury bodies six feet deep is because that was the depth that stopped plague transmission from the dead in the Middle Ages. Many religious practices, such as avoiding certain meats, were established because of foodborne disease transmission. In The Top Ten Diseases of All Time, Stacey Smith? presents the top ten deadliest diseases and their effects on society, providing a wealth of information about the trajectory and terrible impact of each disease, and humanity’s reaction to these diseases throughout the millennia. Did you know, for example, that: -The medical symbol evolved from the worms wrapped around a stick, because that was the only way to remove Guinea worms from the body, so having a stick meant you were a doctor. -Smallpox is the third-worst disease ever, yet it remains the only successfully eradicated human disease (but not for long!), thanks in part to a successful vaccine, in part to photographic recognition cards and in part due to helicopter-led forced vaccinations of whole villages in the former Yugoslavia. This brings up issues of individual rights versus public good that remain relevant today. -Four diseases were targeted for eradication in the 20th century; the failure to do so led directly to the creation of the environmental movement. -The inability of priests to explain how to stop the plague in the Middle Ages broke the back of the church as an all-powerful and all-knowing institution and led to colonialism and slavery. The Top Ten Diseases of All Time offers a fascinating overview of the deadliest diseases to spread throughout the world, including HIV/AIDS, Spanish Flu, Measles, The Black Death, Smallpox and others.

Author : Fatih Yilmaz,Araceli Queiruga-Dios,María Jesús Santos Sánchez,Deolinda Rasteiro,Víctor Gayoso Martínez,Jesús Martín Vaquero
Publisher : Springer Nature
Page : 314 pages
File Size : 40,6 Mb
Release : 2022-04-15
Category : Mathematics
ISBN : 9783030964016

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Mathematical Methods for Engineering Applications by Fatih Yilmaz,Araceli Queiruga-Dios,María Jesús Santos Sánchez,Deolinda Rasteiro,Víctor Gayoso Martínez,Jesús Martín Vaquero Pdf

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering – ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain. Works included in this book cover applications of mathematics both in engineering research and in real-world problems, touching topics such as difference equations, number theory, optimization, and more. The list of applications includes the modeling of mechanical structures, the shape of machines, and the growth of a population, expanding to fields like information security and cryptography. Advances in teaching and learning mathematics in the context of engineering courses are also covered.This volume can be of special interest to researchers in applied mathematics and engineering fields, as well as practitioners seeking studies that address real-life problems in engineering.

Author : Matthias Ehrhardt,Michael Günther
Publisher : Springer Nature
Page : 518 pages
File Size : 50,9 Mb
Release : 2022-11-25
Category : Mathematics
ISBN : 9783031118180

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Progress in Industrial Mathematics at ECMI 2021 by Matthias Ehrhardt,Michael Günther Pdf

This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021. The works explore mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Topics covered include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation. The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

Author : Jianhong Wu,Xue Zhang
Publisher : Springer Nature
Page : 160 pages
File Size : 53,5 Mb
Release : 2020-11-14
Category : Mathematics
ISBN : 9783030540241

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Transmission Dynamics of Tick-Borne Diseases with Co-Feeding, Developmental and Behavioural Diapause by Jianhong Wu,Xue Zhang Pdf

This monograph introduces some current developments in the modelling of the spread of tick-borne diseases. Effective modelling requires the integration of multiple frameworks. Here, particular attention is given to the previously neglected issues of tick developmental and behavioral diapause, tick-borne pathogen co-feeding transmission, and their interactions. An introduction to the required basics of structured population formulations and delay differential equations is given, and topics for future study are suggested. The described techniques will also be useful in the study of other vector-borne diseases. The ultimate aim of this project is to develop a general qualitative framework leading to tick-borne disease risk predictive tools and a decision support system. The target audience is mathematical biologists interested in modelling tick population dynamics and tick-borne disease transmission, and developing computational tools for disease prevention and control.

Author : Arino
Publisher : CRC Press
Page : 808 pages
File Size : 43,7 Mb
Release : 1991-04-29
Category : Mathematics
ISBN : 0824784243

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mathematical population dynamics by Arino Pdf

Author : N. G. Cogan
Publisher : CRC Press
Page : 209 pages
File Size : 55,8 Mb
Release : 2022-09-09
Category : Mathematics
ISBN : 9781000646955

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Mathematical Modeling the Life Sciences by N. G. Cogan Pdf

The purpose of this unique textbook is to bridge the gap between the need for numerical solutions to modeling techniques through computer simulations to develop skill in employing sensitivity analysis to biological and life sciences applications. The underpinning mathematics is minimalized. The focus is on the consequences, implementation, and application. Historical context motivates the models. An understanding of the earliest models provides insight into more complicated ones. While the text avoids getting mired in the details of numerical analysis, it demonstrates how to use numerical methods and provides core codes that can be readily altered to fit a variety of situations. Numerical scripts in both Python and MATLAB® are included. Python is compiled in Jupyter Notebook to aid classroom use. Additionally, codes are organized and available online. One of the most important skills requiring the use of computer simulations is sensitivity analysis. Sensitivity analysis is increasingly used in biomathematics. There are numerous pitfalls to using sensitivity analysis and therefore a need for exposure to worked examples in order to successfully transfer their use from mathematicians to biologists. The interconnections between mathematics and the life sciences have an extensive history. This book offers a new approach to using mathematics to model applications using computers, to employ numerical methods, and takes students a step further into the realm of sensitivity analysis. With some guidance and practice, the reader will have a new and incredibly powerful tool to use. https://www.math.fsu.edu/~cogan/Book/Codes/Codes.html

Author : Natali Hritonenko,Yuri Yatsenko
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 47,9 Mb
Release : 2014-01-08
Category : Mathematics
ISBN : 9781461493112

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Mathematical Modeling in Economics, Ecology and the Environment by Natali Hritonenko,Yuri Yatsenko Pdf

Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful. Core topics of this text are: · Economic growth and technological development · Population dynamics and human impact on the environment · Resource extraction and scarcity · Air and water contamination · Rational management of the economy and environment · Climate change and global dynamics The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order. Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.

Author : Anonim
Publisher : Elsevier
Page : 278 pages
File Size : 51,8 Mb
Release : 2016-10-28
Category : Science
ISBN : 9780444636263

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Ecological Model Types by Anonim Pdf

Ecological Model Types brings an understanding on how to quantitatively analyze complex and dynamic ecosystems with the tools available today. Ecosystem studies widely use the notions of order, complexity, randomness, and organization, and are used interchangeably in literature, which causes much confusion. Better models synthesize our knowledge on ecosystems and their environmental problems, in contrast to statistical analysis, which only reveal the relationships between the data. This book brings together experts on ecological models to create a definitive work on how to understand our complex Earth. Bridges the gap between statistical analysis and synthesis of data, enhancing our understanding about ecosystems and their environmental problems Helps readers understand complex ecosystems by walking through the best modeling options to analyze and predict environmental effects Provides a detailed review of 14 model types, covering the breadth of options available for analysis at this time