Epidemic Modelling

An Introduction

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Author: D. J. Daley,J. Gani

Publisher: Cambridge University Press

ISBN: 9780521014670

Category: Mathematics

Page: 213

View: 4056

This is a general introduction to the mathematical modelling of diseases.

An Introduction to Mathematical Physiology and Biology

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Author: J. Mazumdar

Publisher: Cambridge University Press

ISBN: 9780521646758

Category: Mathematics

Page: 226

View: 7897

A textbook about the mathematical modelling of biological and physiological phenomena for mathematically sophisticated students.

Modelling Biological Populations in Space and Time

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Author: Eric Renshaw

Publisher: Cambridge University Press

ISBN: 9780521448550

Category: Mathematics

Page: 403

View: 6033

This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.

An Introduction to Stochastic Processes with Applications to Biology, Second Edition

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Author: Linda J. S. Allen

Publisher: CRC Press

ISBN: 143989468X

Category: Mathematics

Page: 496

View: 9927

An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes. New to the Second Edition A new chapter on stochastic differential equations that extends the basic theory to multivariate processes, including multivariate forward and backward Kolmogorov differential equations and the multivariate Itô’s formula The inclusion of examples and exercises from cellular and molecular biology Double the number of exercises and MATLAB® programs at the end of each chapter Answers and hints to selected exercises in the appendix Additional references from the literature This edition continues to provide an excellent introduction to the fundamental theory of stochastic processes, along with a wide range of applications from the biological sciences. To better visualize the dynamics of stochastic processes, MATLAB programs are provided in the chapter appendices.

Math and Bio 2010

Linking Undergraduate Disciplines

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Author: Lynn Arthur Steen

Publisher: MAA

ISBN: 9780883858189

Category: Mathematics

Page: 161

View: 8732

Math & Bio 2010: Linking Undergraduate Disciplines envisages a new educational paradigm in which the disciplines of mathematics and biology, currently quite separate, will be productively linked in the undergraduate science programs of the 21st century. As a science, biology depends increasingly on data, algorithms, and models; in virtually every respect, it is becoming more quantitative, more computational, and more mathematical. While these trends are related, they are not the same; they represent, rather, three different perspectives on what many are calling the "new biology." All three methods---quantitative, computational, mathematical---are spreading across the entire landscape of biological science from molecular to cellular, organismic and ecological. The aim of this volume is to alert members of both communities---biological and mathematical---to the expanding and exciting challenges of interdisciplinary work in these fields.

Mathematical Epidemiology

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Author: Fred Brauer,Pauline van den Driessche,J. Wu

Publisher: Springer

ISBN: 3540789111

Category: Medical

Page: 414

View: 5273

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).

Stochastic Processes

Modelling and Simulation

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Author: D. N. Shanbhag,Calyampudi Radhakrishna Rao

Publisher: Gulf Professional Publishing

ISBN: 9780444500137

Category: Mathematics

Page: 1000

View: 6378

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

Human Biology

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Author: Raymond Pearl

Publisher: N.A

ISBN: N.A

Category: Anthropology

Page: N.A

View: 7088

Includes section "Recent literature useful in the study of human biology."

Epidemics and Rumours in Complex Networks

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Author: Moez Draief,Laurent Massoulié

Publisher: Cambridge University Press

ISBN: 9780521734431

Category: Mathematics

Page: 130

View: 8072

Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with network topology allows us to predict ultimate course, understand phase transitions and develop strategies to control and optimise dissemination. This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling methods, Poisson approximation (the Stein-Chen method), concentration inequalities (Chernoff bounds and Azuma-Hoeffding inequality) and branching processes. The authors examine the small-world phenomenon, preferential attachment, as well as classical epidemics. Each chapter ends with pointers to the wider literature. An ideal accompaniment for graduate courses, this book is also for researchers (statistical physicists, biologists, social scientists) who need an efficient guide to modern approaches to epidemic modelling on networks.

The Theoretical Biologist's Toolbox

Quantitative Methods for Ecology and Evolutionary Biology

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Author: Marc Mangel

Publisher: Cambridge University Press

ISBN: 1139455869

Category: Science

Page: N.A

View: 3818

Mathematical modelling is widely used in ecology and evolutionary biology and it is a topic that many biologists find difficult to grasp. In this new textbook Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Fundamental theories and applications are introduced using numerous examples from current biological research, complete with illustrations to highlight key points. Exercises are also included throughout the text to show how theory can be applied and to test knowledge gained so far. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.

Mathematical Models in Biology

An Introduction

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Author: Elizabeth S. Allman,John A. Rhodes

Publisher: Cambridge University Press

ISBN: 9780521525862

Category: Mathematics

Page: 370

View: 8847

Linear and non-linear models of populations, molecular evolution, phylogenetic tree construction, genetics, and infectious diseases are presented with minimal prerequisites.

Mathematical Biology

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Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 3662085429

Category: Mathematics

Page: 770

View: 9051

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.

Quasi-stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

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Author: Mats Gyllenberg,Dmitriĭ Sergeevich Silʹvestrov

Publisher: De Gruyter

ISBN: N.A

Category: Mathematics

Page: 579

View: 2642

This book is devoted to the mathematical studies of stochastic systems with quasi-stationary phenomena which have applications to population dynamics or epidemic models. In addition to its use for the research and reference purposes, the book can also be used in special courses on the subject and as a complementary reading in general courses on stochastic processes. In this respect, it may be useful for specialists as well as doctoral and advanced undergraduate students.

Biological Delay Systems

Linear Stability Theory

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Author: N. MacDonald

Publisher: Cambridge University Press

ISBN: 9780521340847

Category: Mathematics

Page: 235

View: 2886

In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for delays such as those due to gestation, maturation or transport. This book deals with a fundamental question in the analysis of the effects of delays, namely whether they affect the stability of steady states.

The Theory of the Chemostat

Dynamics of Microbial Competition

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Author: Hal L. Smith,Paul Waltman

Publisher: Cambridge University Press

ISBN: 9780521470278

Category: Mathematics

Page: 313

View: 4031

Basic modelling, analysis and simulation of systems that have proven effective in real ecological applications.

Mathematical Biology

An Introduction with Maple and Matlab

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Author: Ronald W. Shonkwiler,James Herod

Publisher: Springer Science & Business Media

ISBN: 0387709843

Category: Science

Page: 551

View: 8077

This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.

Mathematical Modelling of Zombies

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Author: Robert Smith?

Publisher: University of Ottawa Press

ISBN: 0776621688

Category: Mathematics

Page: 468

View: 8582

You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course. Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included). In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.). So if the zombies turn up, reach for this book. The future of the human race may depend on it.

Dynamical Processes on Complex Networks

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Author: Alain Barrat,Marc Barthélemy,Alessandro Vespignani

Publisher: Cambridge University Press

ISBN: 1107377420

Category: Science

Page: N.A

View: 9397

The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.

An Introduction to Mathematical Biology

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Author: Linda J. S. Allen

Publisher: Prentice Hall

ISBN: 9780130352163

Category: Mathematics

Page: 348

View: 8045

KEY BENEFIT: This reference introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Contains applications of mathematical theory to biological examples in each chapter. Focuses on deterministic mathematical models with an emphasis on predicting the qualitative solution behavior over time. Discusses classical mathematical models from population , including the Leslie matrix model, the Nicholson-Bailey model, and the Lotka-Volterra predator-prey model. Also discusses more recent models, such as a model for the Human Immunodeficiency Virus - HIV and a model for flour beetles. KEY MARKET: Readers seeking a solid background in the mathematics behind modeling in biology and exposure to a wide variety of mathematical models in biology.