Mathematical Epidemiology
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Mathematical Epidemiology Of Infectious Diseases
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Author : O. Diekmann
language : en
Publisher: John Wiley & Sons
Release Date : 2000-04-07
Mathematical Epidemiology Of Infectious Diseases written by O. Diekmann 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 2000-04-07 with Mathematics categories.
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.
Mathematical Models In Epidemiology
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Author : Fred Brauer
language : en
Publisher: Springer Nature
Release Date : 2019-10-10
Mathematical Models In Epidemiology written by Fred Brauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-10 with Mathematics categories.
The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.
Mathematical Epidemiology
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Author : Fred Brauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-30
Mathematical Epidemiology written by Fred Brauer 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 2008-04-30 with Medical categories.
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).
An Introduction To Mathematical Epidemiology
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Author : Maia Martcheva
language : en
Publisher: Springer
Release Date : 2015-10-20
An Introduction To Mathematical Epidemiology written by Maia Martcheva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.
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 Modeling In Epidemiology
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Author : James C. Frauenthal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Modeling In Epidemiology written by James C. Frauenthal 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.
The text of this book is derived from courses taught by the author in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook. The audience for these courses was composed almost entirely of fourth year undergraduate students majoring in the mathematical sciences. The students had ordinarily completed four semesters of calculus and one of probability. Few had any prior experience with differential equations, stochastic processes, or epidemiology. It also seems prudent to mention that the author's background is in engineering and applied mathematics and not in epidemiology; it is hoped that this is not painfully obvious. The topics covered in this book have in some cases been modified from the way they were originally presented. However, care has been taken to include a suitable amount of material for a one semester course; the temptation to add gratuitous subject matter has been resisted. Similarly, when a choice between clarity and rigor was available, the more easily understood exposition was selected. By looking only at the table of contents, the casual reader could be easily misled into thinking that the main concern of this book is with epidemiology. This is not the case. The purpose of this book is to illustrate the process of formulating and solving mathematical models.
A Historical Introduction To Mathematical Modeling Of Infectious Diseases
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Author : Ivo M. Foppa
language : en
Publisher: Academic Press
Release Date : 2016-10-18
A Historical Introduction To Mathematical Modeling Of Infectious Diseases written by Ivo M. Foppa and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-18 with Mathematics categories.
A Historical Introduction to Mathematical Modeling of Infectious Diseases: Seminal Papers in Epidemiology offers step-by-step help on how to navigate the important historical papers on the subject, beginning in the 18th century. The book carefully, and critically, guides the reader through seminal writings that helped revolutionize the field. With pointed questions, prompts, and analysis, this book helps the non-mathematician develop their own perspective, relying purely on a basic knowledge of algebra, calculus, and statistics. By learning from the important moments in the field, from its conception to the 21st century, it enables readers to mature into competent practitioners of epidemiologic modeling. Presents a refreshing and in-depth look at key historical works of mathematical epidemiology Provides all the basic knowledge of mathematics readers need in order to understand the fundamentals of mathematical modeling of infectious diseases Includes questions, prompts, and answers to help apply historical solutions to modern day problems
An Introduction To Mathematical Epidemiology
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Author : Maia Martcheva
language : en
Publisher:
Release Date : 2015
An Introduction To Mathematical Epidemiology written by Maia Martcheva and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Biomathematics categories.
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
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Author : Harkaran Singh
language : en
Publisher: CRC Press
Release Date : 2018-12-07
Mathematical Population Dynamics And Epidemiology In Temporal And Spatio Temporal Domains written by Harkaran Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
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.
Mathematical Modeling For Epidemiology And Ecology
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Author : Glenn Ledder
language : en
Publisher: Springer Nature
Release Date : 2023-04-13
Mathematical Modeling For Epidemiology And Ecology written by Glenn Ledder and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-13 with Mathematics categories.
Mathematical Modeling for Epidemiology and Ecology provides readers with the mathematical tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents mathematics in biological contexts, focusing on the central mathematical ideas and the biological implications, with detailed explanations. The author assumes no mathematics background beyond elementary differential calculus. An introductory chapter on basic principles of mathematical modeling is followed by chapters on empirical modeling and mechanistic modeling. These chapters contain a thorough treatment of key ideas and techniques that are often neglected in mathematics books, such as the Akaike Information Criterion. The second half of the book focuses on analysis of dynamical systems, emphasizing tools to simplify analysis, such as the Routh-Hurwitz conditions and asymptotic analysis. Courses can be focused on either half of the book or thematically chosen material from both halves, such as a course on mathematical epidemiology. The biological content is self-contained and includes many topics in epidemiology and ecology. Some of this material appears in case studies that focus on a single detailed example, and some is based on recent research by the author on vaccination modeling and scenarios from the COVID-19 pandemic. The problem sets feature linked problems where one biological setting appears in multi-step problems that are sorted into the appropriate section, allowing readers to gradually develop complete investigations of topics such as HIV immunology and harvesting of natural resources. Some problems use programs written by the author for Matlab or Octave; these combine with more traditional mathematical exercises to give students a full set of tools for model analysis. Each chapter contains additional case studies in the form of projects with detailed directions. New appendices contain mathematical details on optimization, numerical solution of differential equations, scaling, linearization, and sophisticated use of elementary algebra to simplify problems.
Mathematical Tools For Understanding Infectious Disease Dynamics
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Author : Odo Diekmann
language : en
Publisher: Princeton University Press
Release Date : 2013
Mathematical Tools For Understanding Infectious Disease Dynamics written by Odo Diekmann and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This book 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.