Mathematical Epidemiology / Edition 1

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Overview

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).

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Product Details

Meet the Author

Fred Brauer is a professor emeritus at the University of Wisconsin – Madison, where he taught from 1960 to 1999, and has been an honorary professor at the University of British Columbia since 1997. He is the author or co-author of 115 papers on differential equations, mathematical population biology, and mathematical epidemiology as well as 10 books including undergraduate texts and a book on models in population biology and epidemiology jointly with Carlos Castillo – Chavez.

Pauline van den Driessche is a professor emerita in the Department of Mathematics and Statistics and an adjunct professor in the Department of Computer Science at the University of Victoria. Her research interests include mathematical biology, especially epidemiology, and matrix analysis. Recently she was awarded the 2007 Krieger – Nelson prize by the Canadian Mathematical Society, and gave the Olga Taussky Todd lecture at the International Conference in Industrial and Applied Mathematics in July 2007.

Jianhong Wu is a professor and a Senior Canada Research Chair in Applied Mathematics at York University. He is the author or coauthor of over 200 peer-reviewed publications and six monographs in the areas of nonlinear dynamical systems, delay differential equations, mathematical biology and epidemiology, neural networks, and pattern formation and recognition. He is the recipient of the Canadian Industrial and Applied Mathematics Research Prize (2003), the Alexander van Humboldt Fellowship (1996), the Paul Erdos Visiting Professorship (2000), and Cheung Kong/YangZi River Lecture Professorship (2006).

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Table of Contents

Part I: Introduction and General Framework.- A light introduction to modelling recurrent epidemics (David J.D. Earn).- Compartmental models in epidemiology (Fred Brauer).- An introduction to shastic epidemic models (Linda J.S. Allen).- Part II: Advanced Modeling and Heterogeneities.- An introduction to networks in epidemic modeling (Fred Brauer).- Deterministic compartmental models: Extensions of basic models (P. van den Driessche).- Further notes on the basic reproduction number (James Watmough and P. van den Driessche).- Spatial structure I: Patch models (P. van den Driessche).- Spatial structure II: Partial differential equation models (Jianhong Wu).- Continuous – time age – structured models in population dynamics and epidemiology (Jia Li and Fred Brauer).- Distribution theory, shastic processes and infectious disease modeling (Ping Yan).- Part III: Case Studies.- The role of mathematical models in explaining recurrent outbreaks of infectious childhood diseases (C.T. Bauch).- Modeling influenza: Pandemics and seasonal epidemics (Fred Brauer).- Mathematical models of influenza: The role of cross-immunity, quarantine and age structure (M. Nuno, C. Castillo – Chavez, Z. Feng, M. Martcheva).- A comparative analysis of models for West Nile virus (Marjorie J. Wonham, Mark A. Lewis).

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