Mathematical Modeling In Epidemiology

Author : Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng
Publisher : Springer Nature
Page : 628 pages
File Size : 54,8 Mb
Release : 2019-10-10
Category : Mathematics
ISBN : 9781493998289

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Mathematical Models in Epidemiology by Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng Pdf

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.

Author : James C. Frauenthal
Publisher : Springer Science & Business Media
Page : 128 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642677953

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Mathematical Modeling in Epidemiology by James C. Frauenthal Pdf

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.

Author : Jyoti Mishra,Ritu Agarwal,Abdon Atangana
Publisher : CRC Press
Page : 441 pages
File Size : 47,9 Mb
Release : 2020-12-28
Category : Mathematics
ISBN : 9781000226942

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Mathematical Modeling and Soft Computing in Epidemiology by Jyoti Mishra,Ritu Agarwal,Abdon Atangana Pdf

This book describes the uses of different mathematical modeling and soft computing techniques used in epidemiology for experiential research in projects such as how infectious diseases progress to show the likely outcome of an epidemic, and to contribute to public health interventions. This book covers mathematical modeling and soft computing techniques used to study the spread of diseases, predict the future course of an outbreak, and evaluate epidemic control strategies. This book explores the applications covering numerical and analytical solutions, presents basic and advanced concepts for beginners and industry professionals, and incorporates the latest methodologies and challenges using mathematical modeling and soft computing techniques in epidemiology. Primary users of this book include researchers, academicians, postgraduate students, and specialists.

Author : Maia Martcheva
Publisher : Springer
Page : 453 pages
File Size : 45,9 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9781489976123

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An Introduction to Mathematical Epidemiology by Maia Martcheva Pdf

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.

Author : O. Diekmann,J. A. P. Heesterbeek
Publisher : John Wiley & Sons
Page : 324 pages
File Size : 55,5 Mb
Release : 2000-04-07
Category : Mathematics
ISBN : 0471492418

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Mathematical Epidemiology of Infectious Diseases by O. Diekmann,J. A. P. Heesterbeek Pdf

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.

Author : Ivo M. Foppa
Publisher : Academic Press
Page : 214 pages
File Size : 47,5 Mb
Release : 2016-10-18
Category : Mathematics
ISBN : 9780128024997

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A Historical Introduction to Mathematical Modeling of Infectious Diseases by Ivo M. Foppa Pdf

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

Author : Michael Y. Li
Publisher : Springer
Page : 156 pages
File Size : 47,7 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319721224

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An Introduction to Mathematical Modeling of Infectious Diseases by Michael Y. Li Pdf

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.

Author : Fred Brauer,Carlos Castillo-Chavez
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 41,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475735161

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Mathematical Models in Population Biology and Epidemiology by Fred Brauer,Carlos Castillo-Chavez Pdf

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.

Author : Fred Brauer,Pauline van den Driessche,J. Wu
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 45,5 Mb
Release : 2008-04-30
Category : Medical
ISBN : 9783540789109

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Mathematical Epidemiology by Fred Brauer,Pauline van den Driessche,J. Wu Pdf

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).

Author : Alexander Krämer,Mirjam Kretzschmar,Klaus Krickeberg
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 55,8 Mb
Release : 2010-01-23
Category : Medical
ISBN : 9780387938356

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Modern Infectious Disease Epidemiology by Alexander Krämer,Mirjam Kretzschmar,Klaus Krickeberg Pdf

Hardly a day goes by without news headlines concerning infectious disease threats. Currently the spectre of a pandemic of influenza A|H1N1 is raising its head, and heated debates are taking place about the pro’s and con’s of vaccinating young girls against human papilloma virus. For an evidence-based and responsible communication of infectious disease topics to avoid misunderstandings and overreaction of the public, we need solid scientific knowledge and an understanding of all aspects of infectious diseases and their control. The aim of our book is to present the reader with the general picture and the main ideas of the subject. The book introduces the reader to methodological aspects of epidemiology that are specific for infectious diseases and provides insight into the epidemiology of some classes of infectious diseases characterized by their main modes of transmission. This choice of topics bridges the gap between scientific research on the clinical, biological, mathematical, social and economic aspects of infectious diseases and their applications in public health. The book will help the reader to understand the impact of infectious diseases on modern society and the instruments that policy makers have at their disposal to deal with these challenges. It is written for students of the health sciences, both of curative medicine and public health, and for experts that are active in these and related domains, and it may be of interest for the educated layman since the technical level is kept relatively low.

Author : Schiesser William E
Publisher : World Scientific
Page : 460 pages
File Size : 53,5 Mb
Release : 2018-06-27
Category : Technology & Engineering
ISBN : 9789813238800

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Mathematical Modeling Approach To Infectious Diseases, A: Cross Diffusion Pde Models For Epidemiology by Schiesser William E Pdf

Author : Odo Diekmann,Hans Heesterbeek,Tom Britton
Publisher : Princeton University Press
Page : 516 pages
File Size : 43,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780691155395

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Mathematical Tools for Understanding Infectious Disease Dynamics by Odo Diekmann,Hans Heesterbeek,Tom Britton Pdf

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.

Author : Fred Brauer,Carlos Castillo-Chavez
Publisher : SIAM
Page : 279 pages
File Size : 52,5 Mb
Release : 2013-02-07
Category : Mathematics
ISBN : 9781611972412

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Mathematical Models for Communicable Diseases by Fred Brauer,Carlos Castillo-Chavez Pdf

A self-contained and comprehensive guide to the mathematical modeling of disease transmission, appropriate for graduate students.

Author : Stefan Ma
Publisher : World Scientific
Page : 240 pages
File Size : 43,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812834836

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Mathematical Understanding of Infectious Disease Dynamics by Stefan Ma Pdf

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Mathematical Modeling of Infectious Diseases: Dynamics and Control from 15 August to 9 October 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.

Author : Matt J. Keeling,Pejman Rohani
Publisher : Princeton University Press
Page : 385 pages
File Size : 41,7 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400841035

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Modeling Infectious Diseases in Humans and Animals by Matt J. Keeling,Pejman Rohani Pdf

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