Author: Moez Draief
Publisher: Cambridge University Press
ISBN: 9780521734431
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Xinchu Fu
Publisher: John Wiley & Sons
ISBN: 1118762819
Category : Mathematics
Languages : en
Pages : 273
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Book Description
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.
Author: Moez Draief
Publisher:
ISBN: 9781316087299
Category : Computer security
Languages : en
Pages : 123
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Book Description
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.
Author: Alain Barrat
Publisher: Cambridge University Press
ISBN: 9781107626256
Category : Science
Languages : en
Pages : 361
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Book Description
The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.
Author: Mohammad Reza Sanatkar
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In this thesis, we propose a statistical model to predict disease dispersal in dynamic networks. We model the process of disease spreading using discrete time Markov chain. In this case, the vector of probability of infection is the state vector and every element of the state vector is a continuous variable between zero and one. In discrete time Markov chains, state probability vectors in each time step depends on state probability vector in the previous time step and one step transition probability matrix. The transition probability matrix can be time variant or time invariant. If this matrix's elements are functions of elements of vector state probability in previous step, the corresponding Markov chain is non linear dynamical system. However, if those elements are independent of vector state probability, the corresponding Markov chain is a linear dynamical system. We especially focus on the dispersal of soybean rust. In our problem, we have a network of US counties and we aim at predicting that which counties are more likely to get infected by soybean rust during a year based on observations of soybean rust up to that time as well as corresponding observations to previous years. Other data such as soybean and kudzu densities in each county, daily wind data, and distance between counties helps us to build the model. The rapid growth in the number of Internet users in recent years has led malware generators to exploit this potential to attack computer users around the word. Internet users are frequent targets of malicious software every day. The ability of malware to exploit the infrastructures of networks for propagation determines how detrimental they can be to the network's security. Malicious software can make large outbreaks if they are able to exploit the structure of the Internet and interactions between users to propagate. Epidemics typically start with some initial infected nodes. Infected nodes can cause their healthy neighbors to become infected with some probability. With time and in some cases with external intervention, infected nodes can be cured and go back to a healthy state. The study of epidemic dispersals on networks aims at explaining how epidemics evolve and spread in networks. One of the most interesting questions regarding an epidemic spread in a network is whether the epidemic dies out or results in a massive outbreak. Epidemic threshold is a parameter that addresses this question by considering both the network topology and epidemic strength.
Author: Romualdo Pastor-Satorras
Publisher: Springer Science & Business Media
ISBN: 9783540403722
Category : Science
Languages : en
Pages : 232
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Book Description
Networks can provide a useful model and graphic image useful for the description of a wide variety of web-like structures in the physical and man-made realms, e.g. protein networks, food webs and the Internet. The contributions gathered in the present volume provide both an introduction to, and an overview of, the multifaceted phenomenology of complex networks. Statistical Mechanics of Complex Networks also provides a state-of-the-art picture of current theoretical methods and approaches.
Author: Seyed Jalil Kazemitabar Amirkolaei
Publisher:
ISBN:
Category :
Languages : en
Pages : 87
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Book Description
In this PhD dissertation, we study epidemics on networks of contacts through the lens of statistical inference. The current work is an attempt to infer the propagation parameters following the outset of an epidemic spread. My contributions rely on the progress on mathematical modeling of infectious outbreak, information diffusion, and viral habit formation. These achievements paved the path to forecast and contain the spread of infectious diseases and to optimize viral marketing campaigns. What distinguishes this work is the forensics view that aims to infer the network or the propagation parameters from the final stage of an epidemic. We study here multiple problems of this kind including epidemic source identification and epidemic network reconstruction. Such problems are NP-hard by nature and previous contributions are ad-hoc and inconclusive for realistic networks, either in size or structure. This work proposes new methods that estimate the parameters of interest in polynomial time with arbitrary accuracy. We provide theoretical error bound guarantees for some of the solutions. We accompany the results with comparative simulations on popular networks from social media, urban infrastructure, and disease pandemics.
Author: Rosa M. Benito
Publisher: Springer Nature
ISBN: 3030653471
Category : Technology & Engineering
Languages : en
Pages : 702
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Book Description
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the IX International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2020). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks and technological networks.
Author:
Publisher:
ISBN: 9789461864116
Category :
Languages : en
Pages :
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Book Description
Author: István Z. Kiss
Publisher: Springer
ISBN: 3319508067
Category : Mathematics
Languages : en
Pages : 423
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Book Description
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.
