Age Structured Epidemic Modeling

Author : Xue-Zhi Li,Junyuan Yang,Maia Martcheva
Publisher : Springer Nature
Page : 386 pages
File Size : 53,9 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9783030424961

Get Book

Age Structured Epidemic Modeling by Xue-Zhi Li,Junyuan Yang,Maia Martcheva Pdf

This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology. Chronological age and class-age play an important role in the description of infectious diseases and this text provides the tools for the analysis of this type of partial differential equation models. This book presents general theoretical tools as well as large number of specific examples to guide the reader to develop their own tools that they may then apply to study structured models in mathematical epidemiology. The book will be a valuable addition to the arsenal of all researchers interested in developing theory or studying specific models with age structure.

Author : Hisashi Inaba
Publisher : Springer
Page : 555 pages
File Size : 46,7 Mb
Release : 2017-03-15
Category : Social Science
ISBN : 9789811001888

Get Book

Age-Structured Population Dynamics in Demography and Epidemiology by Hisashi Inaba Pdf

This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.

Author : Zhien Ma
Publisher : World Scientific
Page : 513 pages
File Size : 47,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812797506

Get Book

Dynamical Modeling and Analysis of Epidemics by Zhien Ma Pdf

This timely book covers the basic concepts of the dynamics of epidemic disease, presenting various kinds of models as well as typical research methods and results. It introduces the latest results in the current literature, especially those obtained by highly rated Chinese scholars. A lot of attention is paid to the qualitative analysis of models, the sheer variety of models, and the frontiers of mathematical epidemiology. The process and key steps in epidemiological modeling and prediction are highlighted, using transmission models of HIV/AIDS, SARS, and tuberculosis as application examples.

Author : Denis Mollison
Publisher : Cambridge University Press
Page : 458 pages
File Size : 43,5 Mb
Release : 1995-07-13
Category : Mathematics
ISBN : 0521475368

Get Book

Epidemic Models by Denis Mollison Pdf

Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.

Author : Fred Brauer,Pauline van den Driessche,J. Wu
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 48,9 Mb
Release : 2008-04-30
Category : Medical
ISBN : 9783540789109

Get Book

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 : Maia Martcheva
Publisher : Springer
Page : 453 pages
File Size : 44,6 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9781489976123

Get Book

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 : Raouf Boucekkine,Natali Hritonenko,Yuri Yatsenko
Publisher : Routledge
Page : 277 pages
File Size : 53,6 Mb
Release : 2013-05-13
Category : Business & Economics
ISBN : 9781136920929

Get Book

Optimal Control of Age-structured Populations in Economy, Demography, and the Environment by Raouf Boucekkine,Natali Hritonenko,Yuri Yatsenko Pdf

This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-standard decision variables into account. In addition, the contributions deal with the age structure of assets, resources, and populations under study. Interdisciplinary modelling has enormous potential for discovering new insights in global and regional development. Optimal Control of Age-structured Populations in Economy, Demography, and the Environment is a rich and excellent source of information on state-of-the-art modelling expertise and references. The book provides the necessary mathematical background for readers from different areas, such as applied sciences, management sciences and operations research, which helps guide the development of practical models. As well as this the book also surveys the current practice in applied modelling and looks at new research areas for a general mathematical audience. This book will be of interest primarily to researchers, postgraduate students, as well as a wider scientific community, including those focussing on the subjects of applied mathematics, environmental sciences, economics, demography, management, and operations research.

Author : Mimmo Iannelli,Fabio Milner
Publisher : Springer
Page : 350 pages
File Size : 46,7 Mb
Release : 2017-08-27
Category : Mathematics
ISBN : 9789402411461

Get Book

The Basic Approach to Age-Structured Population Dynamics by Mimmo Iannelli,Fabio Milner Pdf

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 2024-06-01
Category : Electronic
ISBN : 9789814471428

Get Book

Dynamical Modeling and Analysis of Epidemics by Anonim Pdf

Author : Pierre Magal,Shigui Ruan
Publisher : Springer
Page : 314 pages
File Size : 52,5 Mb
Release : 2008-04-12
Category : Mathematics
ISBN : 9783540782735

Get Book

Structured Population Models in Biology and Epidemiology by Pierre Magal,Shigui Ruan Pdf

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.

Author : Ottar N. Bjørnstad
Publisher : Springer
Page : 312 pages
File Size : 43,7 Mb
Release : 2018-10-30
Category : Medical
ISBN : 9783319974873

Get Book

Epidemics by Ottar N. Bjørnstad Pdf

This book is designed to be a practical study in infectious disease dynamics. The book offers an easy to follow implementation and analysis of mathematical epidemiology. The book focuses on recent case studies in order to explore various conceptual, mathematical, and statistical issues. The dynamics of infectious diseases shows a wide diversity of pattern. Some have locally persistent chains-of-transmission, others persist spatially in ‘consumer-resource metapopulations’. Some infections are prevalent among the young, some among the old and some are age-invariant. Temporally, some diseases have little variation in prevalence, some have predictable seasonal shifts and others exhibit violent epidemics that may be regular or irregular in their timing. Models and ‘models-with-data’ have proved invaluable for understanding and predicting this diversity, and thence help improve intervention and control. Using mathematical models to understand infectious disease dynamics has a very rich history in epidemiology. The field has seen broad expansions of theories as well as a surge in real-life application of mathematics to dynamics and control of infectious disease. The chapters of Epidemics: Models and Data using R have been organized in a reasonably logical way: Chapters 1-10 is a mix and match of models, data and statistics pertaining to local disease dynamics; Chapters 11-13 pertains to spatial and spatiotemporal dynamics; Chapter 14 highlights similarities between the dynamics of infectious disease and parasitoid-host dynamics; Finally, Chapters 15 and 16 overview additional statistical methodology useful in studies of infectious disease dynamics. This book can be used as a guide for working with data, models and ‘models-and-data’ to understand epidemics and infectious disease dynamics in space and time.

Author : D. J. Daley,J. Gani
Publisher : Cambridge University Press
Page : 160 pages
File Size : 54,9 Mb
Release : 1999-04-13
Category : Mathematics
ISBN : 0521640792

Get Book

Epidemic Modelling by D. J. Daley,J. Gani Pdf

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

Author : Stefan Ma,Yingcun Xia
Publisher : World Scientific
Page : 240 pages
File Size : 45,5 Mb
Release : 2009
Category : Technology & Engineering
ISBN : 9789812834829

Get Book

Mathematical Understanding of Infectious Disease Dynamics by Stefan Ma,Yingcun Xia Pdf

An Original book with a comprehensive collection of many significant topics of the frontiers in applied presentation of many epidemic models with many real-life examples. presents an integration of interesting ideas from the well-mixed fields of statistics and mathematics. A valuable resource for researchers in wide range of disciplines to solve problems of practical interest.

Author : Xuezhi Li,Geni Gupur,Guangtian Zhu
Publisher : Unknown
Page : 228 pages
File Size : 41,9 Mb
Release : 2002
Category : Epidemiology
ISBN : 1900184117

Get Book

Mathematical Theory of Age-structured Epidemic Dynamics by Xuezhi Li,Geni Gupur,Guangtian Zhu Pdf

Author : Odo Diekmann,Hans Heesterbeek,Tom Britton
Publisher : Princeton University Press
Page : 517 pages
File Size : 55,6 Mb
Release : 2012-11-18
Category : Science
ISBN : 9781400845620

Get Book

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

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