Mathematics Of Epidemics On Networks

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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 : 50,9 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.

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 : 53,9 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.

Epidemics and Rumours in Complex Networks

Moez Draief,Laurent Massoulié
Epidemics and Rumours in Complex Networks Book PDF

Author : Moez Draief,Laurent Massoulié
Publisher : Cambridge University Press
Page : 0 pages
File Size : 47,9 Mb
Release : 2009-12-03
Category : Mathematics
ISBN : 0521734436

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Epidemics and Rumours in Complex Networks by Moez Draief,Laurent Massoulié Pdf

Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with network topology allows us to predict ultimate course, understand phase transitions and develop strategies to control and optimise dissemination. This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling methods, Poisson approximation (the Stein-Chen method), concentration inequalities (Chernoff bounds and Azuma-Hoeffding inequality) and branching processes. The authors examine the small-world phenomenon, preferential attachment, as well as classical epidemics. Each chapter ends with pointers to the wider literature. An ideal accompaniment for graduate courses, this book is also for researchers (statistical physicists, biologists, social scientists) who need an efficient guide to modern approaches to epidemic modelling on networks.

Epidemics

Ottar N. Bjørnstad
Epidemics Book PDF

Author : Ottar N. Bjørnstad
Publisher : Springer
Page : 312 pages
File Size : 50,9 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.

Temporal Network Epidemiology

Naoki Masuda,Petter Holme
Temporal Network Epidemiology Book PDF

Author : Naoki Masuda,Petter Holme
Publisher : Springer
Page : 342 pages
File Size : 44,8 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9789811052873

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Temporal Network Epidemiology by Naoki Masuda,Petter Holme Pdf

This book covers recent developments in epidemic process models and related data on temporally varying networks. It is widely recognized that contact networks are indispensable for describing, understanding, and intervening to stop the spread of infectious diseases in human and animal populations; “network epidemiology” is an umbrella term to describe this research field. More recently, contact networks have been recognized as being highly dynamic. This observation, also supported by an increasing amount of new data, has led to research on temporal networks, a rapidly growing area. Changes in network structure are often informed by epidemic (or other) dynamics, in which case they are referred to as adaptive networks. This volume gathers contributions by prominent authors working in temporal and adaptive network epidemiology, a field essential to understanding infectious diseases in real society.

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 : 47,5 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.

Propagation Dynamics on Complex Networks

Xinchu Fu,Michael Small,Guanrong Chen
Propagation Dynamics on Complex Networks Book PDF

Author : Xinchu Fu,Michael Small,Guanrong Chen
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 54,8 Mb
Release : 2013-12-17
Category : Mathematics
ISBN : 9781118762813

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Propagation Dynamics on Complex Networks by Xinchu Fu,Michael Small,Guanrong Chen Pdf

Explores the emerging subject of epidemic dynamics on complex networks, including theories, methods, and real-world applications Throughout history epidemic diseases have presented a serious threat to human life, and in recent years the spread of infectious diseases such as dengue, malaria, HIV, and SARS has captured global attention; and in the modern technological age, the proliferation of virus attacks on the Internet highlights the emergent need for knowledge about modeling, analysis, and control in epidemic dynamics on complex networks. For advancement of techniques, it has become clear that more fundamental knowledge will be needed in mathematical and numerical context about how epidemic dynamical networks can be modelled, analyzed, and controlled. This book explores recent progress in these topics and looks at issues relating to various epidemic systems. Propagation Dynamics on Complex Networks covers most key topics in the field, and will provide a valuable resource for graduate students and researchers interested in network science and dynamical systems, and related interdisciplinary fields. Key Features: Includes a brief history of mathematical epidemiology and epidemic modeling on complex networks. Explores how information, opinion, and rumor spread via the Internet and social networks. Presents plausible models for propagation of SARS and avian influenza outbreaks, providing a reality check for otherwise abstract mathematical modeling. Considers various infectivity functions, including constant, piecewise-linear, saturated, and nonlinear cases. Examines information transmission on complex networks, and investigates the difference between information and epidemic spreading.

Mathematical Epidemiology

Fred Brauer,Pauline van den Driessche,J. Wu
Mathematical Epidemiology Book PDF

Author : Fred Brauer,Pauline van den Driessche,J. Wu
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 41,5 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).

Mathematical Models in Epidemiology

Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng
Mathematical Models in Epidemiology Book PDF

Author : Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng
Publisher : Springer Nature
Page : 628 pages
File Size : 52,6 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.

Temporal Networks

Petter Holme,Jari Saramäki
Temporal Networks Book PDF

Author : Petter Holme,Jari Saramäki
Publisher : Springer
Page : 352 pages
File Size : 43,8 Mb
Release : 2013-05-23
Category : Science
ISBN : 9783642364617

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Temporal Networks by Petter Holme,Jari Saramäki Pdf

The concept of temporal networks is an extension of complex networks as a modeling framework to include information on when interactions between nodes happen. Many studies of the last decade examine how the static network structure affect dynamic systems on the network. In this traditional approach the temporal aspects are pre-encoded in the dynamic system model. Temporal-network methods, on the other hand, lift the temporal information from the level of system dynamics to the mathematical representation of the contact network itself. This framework becomes particularly useful for cases where there is a lot of structure and heterogeneity both in the timings of interaction events and the network topology. The advantage compared to common static network approaches is the ability to design more accurate models in order to explain and predict large-scale dynamic phenomena (such as, e.g., epidemic outbreaks and other spreading phenomena). On the other hand, temporal network methods are mathematically and conceptually more challenging. This book is intended as a first introduction and state-of-the art overview of this rapidly emerging field.

Age Structured Epidemic Modeling

Xue-Zhi Li,Junyuan Yang,Maia Martcheva
Age Structured Epidemic Modeling Book PDF

Author : Xue-Zhi Li,Junyuan Yang,Maia Martcheva
Publisher : Springer Nature
Page : 386 pages
File Size : 46,8 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9783030424961

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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.

Microbial Threats to Health

Institute of Medicine,Board on Global Health,Committee on Emerging Microbial Threats to Health in the 21st Century
Microbial Threats to Health Book PDF

Author : Institute of Medicine,Board on Global Health,Committee on Emerging Microbial Threats to Health in the 21st Century
Publisher : National Academies Press
Page : 397 pages
File Size : 50,6 Mb
Release : 2003-08-25
Category : Medical
ISBN : 9780309185547

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Microbial Threats to Health by Institute of Medicine,Board on Global Health,Committee on Emerging Microbial Threats to Health in the 21st Century Pdf

Infectious diseases are a global hazard that puts every nation and every person at risk. The recent SARS outbreak is a prime example. Knowing neither geographic nor political borders, often arriving silently and lethally, microbial pathogens constitute a grave threat to the health of humans. Indeed, a majority of countries recently identified the spread of infectious disease as the greatest global problem they confront. Throughout history, humans have struggled to control both the causes and consequences of infectious diseases and we will continue to do so into the foreseeable future. Following up on a high-profile 1992 report from the Institute of Medicine, Microbial Threats to Health examines the current state of knowledge and policy pertaining to emerging and re-emerging infectious diseases from around the globe. It examines the spectrum of microbial threats, factors in disease emergence, and the ultimate capacity of the United States to meet the challenges posed by microbial threats to human health. From the impact of war or technology on disease emergence to the development of enhanced disease surveillance and vaccine strategies, Microbial Threats to Health contains valuable information for researchers, students, health care providers, policymakers, public health officials. and the interested public.

Mathematical Epidemiology of Infectious Diseases

O. Diekmann,J. A. P. Heesterbeek
Mathematical Epidemiology of Infectious Diseases Book PDF

Author : O. Diekmann,J. A. P. Heesterbeek
Publisher : John Wiley & Sons
Page : 324 pages
File Size : 55,9 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.

Graph Theoretic Methods in Multiagent Networks

Mehran Mesbahi,Magnus Egerstedt
Graph Theoretic Methods in Multiagent Networks Book PDF

Author : Mehran Mesbahi,Magnus Egerstedt
Publisher : Princeton University Press
Page : 424 pages
File Size : 41,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835355

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Graph Theoretic Methods in Multiagent Networks by Mehran Mesbahi,Magnus Egerstedt Pdf

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA

Dynamical Modeling and Analysis of Epidemics

Zhien Ma,Jia Li
Dynamical Modeling and Analysis of Epidemics Book PDF

Author : Zhien Ma,Jia Li
Publisher : World Scientific
Page : 513 pages
File Size : 45,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812797490

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Dynamical Modeling and Analysis of Epidemics by Zhien Ma,Jia Li 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.