Mathematical Structures Of Epidemic Systems
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Mathematical Structures Of Epidemic Systems
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Author : Vincenzo Capasso
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-06
Mathematical Structures Of Epidemic Systems written by Vincenzo Capasso and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Mathematics categories.
The dynamics of infectious diseases represents one of the oldest and ri- est areas of mathematical biology. From the classical work of Hamer (1906) and Ross (1911) to the spate of more modern developments associated with Anderson and May, Dietz, Hethcote, Castillo-Chavez and others, the subject has grown dramatically both in volume and in importance. Given the pace of development, the subject has become more and more di?use, and the need to provide a framework for organizing the diversity of mathematical approaches has become clear. Enzo Capasso, who has been a major contributor to the mathematical theory, has done that in the present volume, providing a system for organizing and analyzing a wide range of models, depending on the str- ture of the interaction matrix. The ?rst class, the quasi-monotone or positive feedback systems, can be analyzed e?ectively through the use of comparison theorems, that is the theory of order-preserving dynamical systems; the s- ond, the skew-symmetrizable systems, rely on Lyapunov methods. Capasso develops the general mathematical theory, and considers a broad range of - amples that can be treated within one or the other framework. In so doing, he has provided the ?rst steps towards the uni?cation of the subject, and made an invaluable contribution to the Lecture Notes in Biomathematics. Simon A. Levin Princeton, January 1993 Author’s Preface to Second Printing In the Preface to the First Printing of this volume I wrote: \ . .
Epidemic Models
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Author : Denis Mollison
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13
Epidemic Models written by Denis Mollison and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-13 with Mathematics categories.
Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.
Mathematics Applied To Biology And Medicine
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Author : Jacques Demongeot
language : en
Publisher: Wuerz Pub.
Release Date : 1993-01-01
Mathematics Applied To Biology And Medicine written by Jacques Demongeot and has been published by Wuerz Pub. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Biology categories.
Mathematics Of Epidemics On Networks
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Author : István Z. Kiss
language : en
Publisher: Springer
Release Date : 2017-06-08
Mathematics Of Epidemics On Networks written by István Z. Kiss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-08 with Mathematics categories.
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.
An Introduction To Mathematical Modeling Of Infectious Diseases
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Author : Michael Y. Li
language : en
Publisher: Springer
Release Date : 2018-01-30
An Introduction To Mathematical Modeling Of Infectious Diseases written by Michael Y. Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
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.
Mathematical Models In Epidemiology
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Author : Fred Brauer
language : en
Publisher: Springer Nature
Release Date : 2019-10-10
Mathematical Models In Epidemiology written by Fred Brauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-10 with Mathematics categories.
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.
Mathematical Epidemiology
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Author : Fred Brauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-30
Mathematical Epidemiology written by Fred Brauer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-30 with Medical categories.
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).
Age Structured Epidemic Modeling
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Author : Xue-Zhi Li
language : en
Publisher: Springer Nature
Release Date : 2020-05-28
Age Structured Epidemic Modeling written by Xue-Zhi Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-28 with Mathematics categories.
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.
Dynamical Modeling And Analysis Of Epidemics
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Author : Zhien Ma
language : en
Publisher: World Scientific
Release Date : 2009
Dynamical Modeling And Analysis Of Epidemics written by Zhien Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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.
Propagation Dynamics On Complex Networks
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Author : Xinchu Fu
language : en
Publisher: John Wiley & Sons
Release Date : 2013-12-17
Propagation Dynamics On Complex Networks written by Xinchu Fu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Mathematics categories.
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.