Stochastic Epidemic Models And Their Statistical Analysis

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Stochastic Epidemic Models and Their Statistical Analysis

Hakan Andersson,Tom Britton
Stochastic Epidemic Models and Their Statistical Analysis Book PDF

Author : Hakan Andersson,Tom Britton
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211587

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Stochastic Epidemic Models and Their Statistical Analysis by Hakan Andersson,Tom Britton Pdf

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.

Epidemic Models

Denis Mollison
Epidemic Models Book PDF

Author : Denis Mollison
Publisher : Cambridge University Press
Page : 458 pages
File Size : 55,8 Mb
Release : 1995-07-13
Category : Mathematics
ISBN : 0521475368

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Epidemic Models by Denis Mollison Pdf

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

Stochastic Epidemic Models with Inference

Tom Britton,Etienne Pardoux
Stochastic Epidemic Models with Inference Book PDF

Author : Tom Britton,Etienne Pardoux
Publisher : Springer Nature
Page : 474 pages
File Size : 47,9 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030309008

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Stochastic Epidemic Models with Inference by Tom Britton,Etienne Pardoux Pdf

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

D. J. Daley,J. Gani
Epidemic Modelling Book PDF

Author : D. J. Daley,J. Gani
Publisher : Cambridge University Press
Page : 160 pages
File Size : 55,9 Mb
Release : 1999-04-13
Category : Mathematics
ISBN : 0521640792

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

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

Epidemics

Ottar N. Bjørnstad
Epidemics Book PDF

Author : Ottar N. Bjørnstad
Publisher : Springer
Page : 312 pages
File Size : 44,7 Mb
Release : 2018-10-30
Category : Medical
ISBN : 9783319974873

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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.

Mathematical Tools for Understanding Infectious Disease Dynamics

Odo Diekmann,Hans Heesterbeek,Tom Britton
Mathematical Tools for Understanding Infectious Disease Dynamics Book PDF

Author : Odo Diekmann,Hans Heesterbeek,Tom Britton
Publisher : Princeton University Press
Page : 516 pages
File Size : 43,8 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.

Mathematical and Statistical Estimation Approaches in Epidemiology

Gerardo Chowell,James M. Hayman,Luís M. A. Bettencourt,Carlos Castillo-Chavez
Mathematical and Statistical Estimation Approaches in Epidemiology Book PDF

Author : Gerardo Chowell,James M. Hayman,Luís M. A. Bettencourt,Carlos Castillo-Chavez
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 42,8 Mb
Release : 2009-06-06
Category : Mathematics
ISBN : 9789048123131

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Mathematical and Statistical Estimation Approaches in Epidemiology by Gerardo Chowell,James M. Hayman,Luís M. A. Bettencourt,Carlos Castillo-Chavez Pdf

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.

Stochastic Epidemic Models with Inference

Tom Britton,Etienne Pardoux
Stochastic Epidemic Models with Inference Book PDF

Author : Tom Britton,Etienne Pardoux
Publisher : Unknown
Page : 477 pages
File Size : 47,7 Mb
Release : 2019
Category : Biomathematics
ISBN : 3030309010

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Stochastic Epidemic Models with Inference by Tom Britton,Etienne Pardoux Pdf

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

Daryl J. Daley,Joseph Mark Gani
Epidemic Modelling Book PDF

Author : Daryl J. Daley,Joseph Mark Gani
Publisher : Cambridge University Press
Page : 230 pages
File Size : 53,6 Mb
Release : 1999
Category : Epidemics
ISBN : 0521014670

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Epidemic Modelling by Daryl J. Daley,Joseph Mark Gani Pdf

This is a general introduction to the mathematical techniques needed to understand epidemiology. It begins with an historical outline of some disease statistics, before describing simple deterministic and stochastic models.

Dynamical Modeling and Analysis of Epidemics

Zhien Ma
Dynamical Modeling and Analysis of Epidemics Book PDF

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

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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.

Stochastic Processes in Epidemic Theory

Jean-Pierre Gabriel,Claude Lefevre,Philippe Picard
Stochastic Processes in Epidemic Theory Book PDF

Author : Jean-Pierre Gabriel,Claude Lefevre,Philippe Picard
Publisher : Springer
Page : 208 pages
File Size : 48,5 Mb
Release : 2014-03-11
Category : Mathematics
ISBN : 9783662100677

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Stochastic Processes in Epidemic Theory by Jean-Pierre Gabriel,Claude Lefevre,Philippe Picard Pdf

This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.

Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

Gerardo Chowell,James M. Hyman
Mathematical and Statistical Modeling for Emerging and Re emerging Infectious Diseases Book PDF

Author : Gerardo Chowell,James M. Hyman
Publisher : Springer
Page : 356 pages
File Size : 46,9 Mb
Release : 2016-07-27
Category : Mathematics
ISBN : 9783319404134

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Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases by Gerardo Chowell,James M. Hyman Pdf

The contributions by epidemic modeling experts describe how mathematical models and statistical forecasting are created to capture the most important aspects of an emerging epidemic.Readers will discover a broad range of approaches to address questions, such as Can we control Ebola via ring vaccination strategies? How quickly should we detect Ebola cases to ensure epidemic control? What is the likelihood that an Ebola epidemic in West Africa leads to secondary outbreaks in other parts of the world? When does it matter to incorporate the role of disease-induced mortality on epidemic models? What is the role of behavior changes on Ebola dynamics? How can we better understand the control of cholera or Ebola using optimal control theory? How should a population be structured in order to mimic the transmission dynamics of diseases such as chlamydia, Ebola, or cholera? How can we objectively determine the end of an epidemic? How can we use metapopulation models to understand the role of movement restrictions and migration patterns on the spread of infectious diseases? How can we capture the impact of household transmission using compartmental epidemic models? How could behavior-dependent vaccination affect the dynamical outcomes of epidemic models? The derivation and analysis of the mathematical models addressing these questions provides a wide-ranging overview of the new approaches being created to better forecast and mitigate emerging epidemics. This book will be of interest to researchers in the field of mathematical epidemiology, as well as public health workers.

Mathematical Modeling of Random and Deterministic Phenomena

Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Mathematical Modeling of Random and Deterministic Phenomena Book PDF

Author : Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Publisher : John Wiley & Sons
Page : 308 pages
File Size : 52,8 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9781786304544

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Mathematical Modeling of Random and Deterministic Phenomena by Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone Pdf

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.

Stochastic Modeling and Control

Ivan Ivanov
Stochastic Modeling and Control Book PDF

Author : Ivan Ivanov
Publisher : BoD – Books on Demand
Page : 288 pages
File Size : 40,7 Mb
Release : 2012-11-28
Category : Mathematics
ISBN : 9789535108306

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Stochastic Modeling and Control by Ivan Ivanov Pdf

Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.

Mathematics of Epidemics on Networks

István Z. Kiss,Joel C. Miller,Péter L. Simon
Mathematics of Epidemics on Networks Book PDF

Author : István Z. Kiss,Joel C. Miller,Péter L. Simon
Publisher : Springer
Page : 423 pages
File Size : 54,5 Mb
Release : 2017-06-08
Category : Mathematics
ISBN : 9783319508061

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Mathematics of Epidemics on Networks by István Z. Kiss,Joel C. Miller,Péter L. Simon Pdf

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.