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Author : D. J. Daley,J. Gani
Publisher : Cambridge University Press
Page : 160 pages
File Size : 55,7 Mb
Release : 1999-04-13
Category : Mathematics
ISBN : 0521640792
This is a general introduction to the mathematical modelling of diseases.
Author : George Christakos,Ricardo A. Olea,Marc L. Serre,Hwa-Lung Yu,Lin-Lin Wang
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 43,7 Mb
Release : 2006-09-24
Category : Science
ISBN : 9783540281658
This multidisciplinary reference takes the reader through all four major phases of interdisciplinary inquiry: adequate conceptualization, rigorous formulation, substantive interpretation, and innovative implementation. The text introduces a novel synthetic paradigm of public health reasoning and epidemic modelling, and implements it with a study of the infamous 14th century AD Black Death disaster that killed at least one-fourth of the European population.
Author : Tom Britton,Etienne Pardoux
Publisher : Springer Nature
Page : 474 pages
File Size : 55,8 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030309008
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.
Author : Denis Mollison
Publisher : Cambridge University Press
Page : 458 pages
File Size : 48,7 Mb
Release : 1995-07-13
Category : Mathematics
ISBN : 0521475368
Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.
Author : D. J. Daley,J. Gani
Publisher : Cambridge University Press
Page : 230 pages
File Size : 40,9 Mb
Release : 2001-05-28
Category : Mathematics
ISBN : 0521014670
This is a general introduction to the mathematical modelling of diseases.
Author : Xue-Zhi Li,Junyuan Yang,Maia Martcheva
Publisher : Springer Nature
Page : 386 pages
File Size : 44,6 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9783030424961
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.
Author : Xinzhi Liu,Peter Stechlinski
Publisher : Springer
Page : 271 pages
File Size : 49,8 Mb
Release : 2017-02-25
Category : Mathematics
ISBN : 9783319532080
This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.
Author : Ottar N. Bjørnstad
Publisher : Springer
Page : 312 pages
File Size : 50,8 Mb
Release : 2018-10-30
Category : Medical
ISBN : 9783319974873
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.
Author : Zhien Ma
Publisher : World Scientific
Page : 513 pages
File Size : 40,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812797506
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.
Author : István Z. Kiss,Joel C. Miller,Péter L. Simon
Publisher : Springer
Page : 423 pages
File Size : 49,5 Mb
Release : 2017-06-08
Category : Mathematics
ISBN : 9783319508061
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.
Author : Hakan Andersson,Tom Britton
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211587
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.
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 : 53,5 Mb
Release : 2003-08-25
Category : Medical
ISBN : 9780309185547
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.
Author : Michael Y. Li
Publisher : Springer
Page : 156 pages
File Size : 40,6 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319721224
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.
Author : Simon Dobson
Publisher : Unknown
Page : 190 pages
File Size : 54,7 Mb
Release : 2020-07-22
Category : Computers
ISBN : 1838535659
Science is based on models that we construct to help us to better understand the world. This is especially true for epidemic diseases, where we want to know the effects of different sorts of transmission, different control strategies, and so forth. But what is a model of disease? How are they built, and what questions can we ask of them? This book tries to explain network-based epidemic modelling through a unique combination of accessible text, introductory mathematics, and all the Python code needed to perform computational experiments that explore different disease models and countermeasures. Written at the height of the 2020 covid-19 pandemic, the book aims to demystify the science that underlies many of the policy responses we can make to disease outbreaks, and make the necessary experimental and analytical tools more accessible to anyone with an interest in science.
Author : D. J. Daley,J. Gani
Publisher : Cambridge University Press
Page : 0 pages
File Size : 52,6 Mb
Release : 2001-05-28
Category : Mathematics
ISBN : 0521014670
This general introduction to the mathematical techniques needed to understand epidemiology begins with an historical outline of some disease statistics dating from Daniel Bernoulli's smallpox data of 1760. The authors then go on to describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (nonhomogeneous) populations. They offer a range of methods for constructing and analyzing models, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumors and macro-parasitic diseases. Questions of fitting data to models, and the use of models to understand methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text.