Mathematical Models in Population Biology and Epidemiology

Author: Fred Brauer,Dawn Bies

Publisher: Springer Science & Business Media

ISBN: 1475735162

Category: Science

Page: 417

View: 2204

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

Mathematical Models in Population Biology and Epidemiology

Author: Fred Brauer,Carlos Castillo-Chavez

Publisher: Springer Science & Business Media

ISBN: 1461416868

Category: Mathematics

Page: 508

View: 4420

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

Mathematical Models in Population Biology and Epidemiology

Author: Fred Brauer,Carlos Castillo-Chavez

Publisher: Springer Science & Business Media

ISBN: 9780387989020

Category: Science

Page: 417

View: 7259

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

Modeling Infectious Diseases in Humans and Animals

Author: Matt J. Keeling,Pejman Rohani

Publisher: Princeton University Press

ISBN: 1400841038

Category: Science

Page: 408

View: 3524

For epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recent developments as well as more traditional approaches. Matt Keeling and Pejman Rohani move from modeling with simple differential equations to more recent, complex models, where spatial structure, seasonal "forcing," or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory. In each of the eight chapters, they deal with a specific modeling approach or set of techniques designed to capture a particular biological factor. They illustrate the methodology used with examples from recent research literature on human and infectious disease modeling, showing how such techniques can be used in practice. Diseases considered include BSE, foot-and-mouth, HIV, measles, rubella, smallpox, and West Nile virus, among others. Particular attention is given throughout the book to the development of practical models, useful both as predictive tools and as a means to understand fundamental epidemiological processes. To emphasize this approach, the last chapter is dedicated to modeling and understanding the control of diseases through vaccination, quarantine, or culling. Comprehensive, practical introduction to infectious disease modeling Builds from simple to complex predictive models Models and methodology fully supported by examples drawn from research literature Practical models aid students' understanding of fundamental epidemiological processes For many of the models presented, the authors provide accompanying programs written in Java, C, Fortran, and MATLAB In-depth treatment of role of modeling in understanding disease control

Structured Population Models in Biology and Epidemiology

Author: Pierre Magal,Shigui Ruan

Publisher: Springer

ISBN: 3540782737

Category: Mathematics

Page: 302

View: 1412

In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.

An Introduction to Mathematical Modeling of Infectious Diseases

Author: Michael Y. Li

Publisher: Springer

ISBN: 3319721224

Category: Mathematics

Page: 156

View: 1617

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Dynamical Models in Biology

Author: Miklós Farkas

Publisher: Academic Press

ISBN: 9780080530604

Category: Mathematics

Page: 187

View: 594

Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: Chaotic dynamics of populations The spread of sexually transmitted diseases Problems of the origin of life Models of immunology Formation of animal hide patterns The intuitive meaning of mathematical formulae explained with many figures Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. A 'down-to-earth' introduction to the growing field of modern mathematical biology Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

Mathematical Epidemiology of Infectious Diseases

Model Building, Analysis and Interpretation

Author: O. Diekmann,J. A. P. Heesterbeek

Publisher: John Wiley & Sons

ISBN: 9780471492412

Category: Mathematics

Page: 303

View: 4686

Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are unravelled. Conceptual clarity is attained, assumptions are stated clearly, hidden working hypotheses are attained and mechanistic links between different observables are exposed. Features: * Model construction, analysis and interpretation receive detailed attention * Uniquely covers both deterministic and stochastic viewpoints * Examples of applications given throughout * Extensive coverage of the latest research into the mathematical modelling of epidemics of infectious diseases * Provides a solid foundation of modelling skills The reader will learn to translate, model, analyse and interpret, with the help of the numerous exercises. In literally working through this text, the reader acquires modelling skills that are also valuable outside of epidemiology, certainly within population dynamics, but even beyond that. In addition, the reader receives training in mathematical argumentation. The text is aimed at applied mathematicians with an interest in population biology and epidemiology, at theoretical biologists and epidemiologists. Previous exposure to epidemic concepts is not required, as all background information is given. The book is primarily aimed at self-study and ideally suited for small discussion groups, or for use as a course text.

Dynamical Systems in Population Biology

Author: Xiao-Qiang Zhao

Publisher: Springer

ISBN: 3319564331

Category: Mathematics

Page: 406

View: 4727

This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 100 papers, and his research has played an important role in the development of the theory and applications of monotone dynamical systems, periodic and almost periodic semiflows, uniform persistence, and basic reproduction ratios.

An Introduction to Mathematical Epidemiology

Author: Maia Martcheva

Publisher: Springer

ISBN: 1489976124

Category: Mathematics

Page: 453

View: 5507

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.

Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains

Author: Harkaran Singh,Joydip Dhar

Publisher: Apple Academic Press

ISBN: 9781771886710

Category:

Page: 350

View: 8103

In today's era, the spread of diseases happens very quickly as a large population migrates from one part to another of the world with the readily available transportation facilities. In this century, mankind faces even more challenging environment- and health-related problems than ever before. Therefore, the 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 in making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, devising control strategies, and much more. This new volume, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, focuses on the study of population dynamics with special emphasis on the migration of populations in a heterogeneous patchy habitat, the human and animal population, and the spreading of epidemics, an important area of research in mathematical biology dealing with the survival of different species. The volume 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. The studies presented here on the prey-predator models can be helpful for conservation strategies in forestry habitats, and the epidemic model studies can helpful to the public health policymakers in determining how to control the rapid outbreak of infectious diseases. In this book, the authors have proposed eleven different models in order to facilitate understanding: Two models with different prey-predator interactions Four population models with diffusion in two-patch environment One prey-predator model with disease in the prey Four epidemic models with different control strategies. This book will be of interest to interdisciplinary researchers and policymakers, especially mathematical biologists, biologists, physicists, and epidemiologists. The book can be useful as textbook or reference book for graduate and postgraduate advanced level mathematical biology courses.

Mathematical Biology

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 3662085429

Category: Mathematics

Page: 770

View: 4135

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

Mathematical Methods and Models in Biomedicine

Author: Urszula Ledzewicz,Heinz Schättler,Avner Friedman,Eugene Kashdan

Publisher: Springer Science & Business Media

ISBN: 1461441781

Category: Mathematics

Page: 427

View: 6301

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.

Some Mathematical Questions in Biology

Models in Population Biology

Author: Alan Hastings

Publisher: American Mathematical Soc.

ISBN: 9780821897157

Category: Science

Page: 123

View: 892

Population biology has had a long history of mathematical modeling. The 1920s and 1930s saw major strides with the work of Lotka and Volterra in ecology and Fisher, Haldane, and Wright in genetics. In recent years, much more sophisticated mathematical techniques have been brought to bear on questions in population biology. Simultaneously, advances in experimental and field work have produced a wealth of new data. While this growth has tended to fragment the field, one unifying theme is that similar mathematical questions arise in a range of biological contexts. This volume contains the proceedings of a symposium on Some Mathematical Questions in Biology, held in Chicago in 1987. The papers all deal with different aspects of population biology, but there are overlaps in the mathematical techniques used; for example, dynamics of nonlinear differential and difference equations form a common theme. The topics covered are cultural evolution, multilocus population genetics, spatially structured population genetics, chaos and the dynamics of epidemics, and the dynamics of ecological communities.

Game-Theoretical Models in Biology

Author: Mark Broom,Jan Rychtar

Publisher: CRC Press

ISBN: 1439853215

Category: Mathematics

Page: 520

View: 1702

Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well. The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use MATLAB® to solve various games. Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behavior, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modeling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modeling of these diverse biological phenomena.

A Short History of Mathematical Population Dynamics

Author: Nicolas Bacaër

Publisher: Springer Science & Business Media

ISBN: 9780857291158

Category: Mathematics

Page: 160

View: 717

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.

Forecasting Product Liability Claims

Epidemiology and Modeling in the Manville Asbestos Case

Author: Eric Stallard,Kenneth G. Manton,Joel E. Cohen

Publisher: Springer Science & Business Media

ISBN: 9780387949871

Category: Business & Economics

Page: 394

View: 6735

The Johns-Manville asbestos litigation took 12 years to reach settlement and is expected to generate nearly 500,000 claims at a value of over $34 billion. This book describes the tasks of forecasting the number, timing, and nature of claims from a set of exposed persons of unknown size. The models will be of use in other product liability cases. Written for a broad audience of actuaries, biostatisticans, health scientists, financial analysts, and statisticians.

Mathematical Tools for Understanding Infectious Disease Dynamics

Author: Odo Diekmann,Hans Heesterbeek,Tom Britton

Publisher: Princeton University Press

ISBN: 0691155399

Category: Mathematics

Page: 502

View: 5524

Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout

Mathematical and Statistical Methods for Genetic Analysis

Author: Kenneth Lange

Publisher: Springer Science & Business Media

ISBN: 1475727399

Category: Mathematics

Page: 265

View: 3641

Geneticists now stand on the threshold of sequencing the genome in its entirety. The unprecedented insights into human disease and evolution offered by mapping and sequencing are transforming medicine and agriculture. This revolution depends vitally on the contributions made by applied mathematicians, statisticians, and computer scientists. Kenneth Lange has written a book to enable graduate students in the mathematical sciences to understand and model the epidemiological and experimental data encountered in genetics research. Mathematical, statistical, and computational principles relevant to this task are developed hand-in-hand with applications to gene mapping, risk prediction, and the testing of epidemiological hypotheses. The book covers many topics previously only accessible in journal articles, such as pedigree analysis algorithms, Markov chain, Monte Carlo methods, reconstruction of evolutionary trees, radiation hybrid mapping, and models of recombination. The whole is backed by numerous exercise sets.