Stochastic Epidemic Models And Their Statistical Analysis

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Stochastic Epidemic Models and Their Statistical Analysis

Author : Hakan Andersson
Publisher : Springer Science & Business Media
ISBN 13 : 1461211581
Total Pages : 140 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Epidemic Models and Their Statistical Analysis by : Hakan Andersson

Download or read book Stochastic Epidemic Models and Their Statistical Analysis written by Hakan Andersson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture notes describe stochastic epidemic models and methods for their statistical analysis. Our aim is to present ideas for such models, and methods for their analysis; along the way we make practical use of several probabilistic and statistical techniques. This will be done without focusing on any specific disease, and instead rigorously analyzing rather simple models. The reader of these lecture notes could thus have a two-fold purpose in mind: to learn about epidemic models and their statistical analysis, and/or to learn and apply techniques in probability and statistics. The lecture notes require an early graduate level knowledge of probability and They introduce several techniques which might be new to students, but our statistics. intention is to present these keeping the technical level at a minlmum. Techniques that are explained and applied in the lecture notes are, for example: coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm and MCMC methods. The aim is to introduce and apply these techniques, thus hopefully motivating their further theoretical treatment. A few sections, mainly in Chapter 5, assume some knowledge of weak convergence; we hope that readers not familiar with this theory can understand the these parts at a heuristic level. The text is divided into two distinct but related parts: modelling and estimation.

Stochastic Epidemic Models with Inference

Author : Tom Britton
Publisher : Springer Nature
ISBN 13 : 3030309002
Total Pages : 474 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Stochastic Epidemic Models with Inference by : Tom Britton

Download or read book Stochastic Epidemic Models with Inference written by Tom Britton and published by Springer Nature. This book was released on 2019-11-30 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.

Epidemic Modelling

Author : D. J. Daley
Publisher : Cambridge University Press
ISBN 13 : 9780521640794
Total Pages : 160 pages
Book Rating : 4.6/5 (47 download)

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Book Synopsis Epidemic Modelling by : D. J. Daley

Download or read book Epidemic Modelling written by D. J. Daley and published by Cambridge University Press. This book was released on 1999-04-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a general introduction to the mathematical modelling of diseases.

Epidemic Models

Author : Denis Mollison
Publisher : Cambridge University Press
ISBN 13 : 9780521475365
Total Pages : 458 pages
Book Rating : 4.4/5 (753 download)

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Book Synopsis Epidemic Models by : Denis Mollison

Download or read book Epidemic Models written by Denis Mollison and published by Cambridge University Press. This book was released on 1995-07-13 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.

Mathematical Tools for Understanding Infectious Disease Dynamics

Author : Odo Diekmann
Publisher : Princeton University Press
ISBN 13 : 0691155399
Total Pages : 516 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematical Tools for Understanding Infectious Disease Dynamics by : Odo Diekmann

Download or read book Mathematical Tools for Understanding Infectious Disease Dynamics written by Odo Diekmann and published by Princeton University Press. This book was released on 2013 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical and Statistical Estimation Approaches in Epidemiology

Author : Gerardo Chowell
Publisher : Springer Science & Business Media
ISBN 13 : 9048123135
Total Pages : 367 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Mathematical and Statistical Estimation Approaches in Epidemiology by : Gerardo Chowell

Download or read book Mathematical and Statistical Estimation Approaches in Epidemiology written by Gerardo Chowell and published by Springer Science & Business Media. This book was released on 2009-06-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and Statistical Estimation Approaches in Epidemiology compiles t- oretical and practical contributions of experts in the analysis of infectious disease epidemics in a single volume. Recent collections have focused in the analyses and simulation of deterministic and stochastic models whose aim is to identify and rank epidemiological and social mechanisms responsible for disease transmission. The contributions in this volume focus on the connections between models and disease data with emphasis on the application of mathematical and statistical approaches that quantify model and data uncertainty. The book is aimed at public health experts, applied mathematicians and sci- tists in the life and social sciences, particularly graduate or advanced undergraduate students, who are interested not only in building and connecting models to data but also in applying and developing methods that quantify uncertainty in the context of infectious diseases. Chowell and Brauer open this volume with an overview of the classical disease transmission models of Kermack-McKendrick including extensions that account for increased levels of epidemiological heterogeneity. Their theoretical tour is followed by the introduction of a simple methodology for the estimation of, the basic reproduction number,R . The use of this methodology 0 is illustrated, using regional data for 1918–1919 and 1968 in uenza pandemics.

Epidemics

Author : Ottar N. Bjørnstad
Publisher : Springer
ISBN 13 : 3319974874
Total Pages : 312 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Epidemics by : Ottar N. Bjørnstad

Download or read book Epidemics written by Ottar N. Bjørnstad and published by Springer. This book was released on 2018-10-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Epidemiology

Author : Fred Brauer
Publisher : Springer Science & Business Media
ISBN 13 : 3540789103
Total Pages : 415 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Mathematical Epidemiology by : Fred Brauer

Download or read book Mathematical Epidemiology written by Fred Brauer and published by Springer Science & Business Media. This book was released on 2008-04-30 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Mathematical Modeling of Random and Deterministic Phenomena

Author : Solym Mawaki Manou-Abi
Publisher : John Wiley & Sons
ISBN 13 : 1786304546
Total Pages : 308 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Mathematical Modeling of Random and Deterministic Phenomena by : Solym Mawaki Manou-Abi

Download or read book Mathematical Modeling of Random and Deterministic Phenomena written by Solym Mawaki Manou-Abi and published by John Wiley & Sons. This book was released on 2020-04-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.

Mathematical Models in Epidemiology

Author : Fred Brauer
Publisher : Springer Nature
ISBN 13 : 1493998285
Total Pages : 628 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Mathematical Models in Epidemiology by : Fred Brauer

Download or read book Mathematical Models in Epidemiology written by Fred Brauer and published by Springer Nature. This book was released on 2019-10-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention

Author : W. Y. Tan
Publisher : World Scientific
ISBN 13 : 9812561390
Total Pages : 610 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention by : W. Y. Tan

Download or read book Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention written by W. Y. Tan and published by World Scientific. This book was released on 2005 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Only book on extensive, deterministic models, statistic models, stochastic models and state space models and statistical methods for HIV epidemic involving IV drug usage and HIV epidemic in homosexual populations. - Provides most recent biological insights into HIV pathogenesis and HIV kinetics at the cellular level, and illustrates how to build up mathematical models based on these biological insights. - Only publication that provides in-depth analysis of HAART treatment protocols and discusses possible improvements to the HAART protocol. The book also provides connection between pharmacokinetics with treatment in HIV-infected individuals.

Mathematical Epidemiology of Infectious Diseases

Author : O. Diekmann
Publisher : John Wiley & Sons
ISBN 13 : 9780471492412
Total Pages : 324 pages
Book Rating : 4.4/5 (924 download)

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Book Synopsis Mathematical Epidemiology of Infectious Diseases by : O. Diekmann

Download or read book Mathematical Epidemiology of Infectious Diseases written by O. Diekmann and published by John Wiley & Sons. This book was released on 2000-04-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis

Author : W. Y. Tan
Publisher : World Scientific
ISBN 13 : 9789810241223
Total Pages : 458 pages
Book Rating : 4.2/5 (412 download)

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Book Synopsis Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis by : W. Y. Tan

Download or read book Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis written by W. Y. Tan and published by World Scientific. This book was released on 2000 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses systematically treatment on the development of stochastic, statistical and state space models of the HIV epidemic and of HIV pathogenesis in HIV-infected individuals, and presents the applications of these models. The book is unique in several ways: (1) it uses stochastic difference and differential equations to present the stochastic models of the HIV epidemic and HIV pathogenesis; in this sense, the deterministic models are considered as special cases when the numbers of different type of people or cells are very large (2) it provides, a critical analysis of deterministic and statistical models in the literature; (3) it develops state space models by combining stochastic models and statistical models; and (4) it provides a detailed discussion on the pros and cons of the different modeling approaches. This book is the first to introduce state space models for the HIV epidemic. It is also the first to develop stochastic models and state space models for the HIV pathogenesis in HIV-infected individuals.

An Introduction to Mathematical Modeling of Infectious Diseases

Author : Michael Y. Li
Publisher : Springer
ISBN 13 : 3319721224
Total Pages : 156 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis An Introduction to Mathematical Modeling of Infectious Diseases by : Michael Y. Li

Download or read book An Introduction to Mathematical Modeling of Infectious Diseases written by Michael Y. Li and published by Springer. This book was released on 2018-01-30 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Epidemic Models with Inference

Author : Tom Britton
Publisher :
ISBN 13 : 9783030309015
Total Pages : 477 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Stochastic Epidemic Models with Inference by : Tom Britton

Download or read book Stochastic Epidemic Models with Inference written by Tom Britton and published by . This book was released on 2019 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5-16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.

Mathematics of Epidemics on Networks

Author : István Z. Kiss
Publisher : Springer
ISBN 13 : 3319508067
Total Pages : 423 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Mathematics of Epidemics on Networks by : István Z. Kiss

Download or read book Mathematics of Epidemics on Networks written by István Z. Kiss and published by Springer. This book was released on 2017-06-08 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.