Epidemic Modelling

Epidemic Modelling
Author: D. J. Daley
Publisher: Cambridge University Press
Total Pages: 160
Release: 1999-04-13
Genre: Mathematics
ISBN: 9780521640794

This is a general introduction to the mathematical modelling of diseases.

Epidemics

Epidemics
Author: Ottar N. Bjørnstad
Publisher: Springer
Total Pages: 318
Release: 2018-10-30
Genre: Medical
ISBN: 3319974874

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.

Stochastic Epidemic Models with Inference

Stochastic Epidemic Models with Inference
Author: Tom Britton
Publisher: Springer Nature
Total Pages: 477
Release: 2019-11-30
Genre: Mathematics
ISBN: 3030309002

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.

Mathematical Epidemiology

Mathematical Epidemiology
Author: Fred Brauer
Publisher: Springer Science & Business Media
Total Pages: 415
Release: 2008-04-30
Genre: Medical
ISBN: 3540789103

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).

Stochastic Epidemic Models and Their Statistical Analysis

Stochastic Epidemic Models and Their Statistical Analysis
Author: Hakan Andersson
Publisher: Springer Science & Business Media
Total Pages: 140
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461211581

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.

Age Structured Epidemic Modeling

Age Structured Epidemic Modeling
Author: Xue-Zhi Li
Publisher: Springer
Total Pages: 383
Release: 2021-05-29
Genre: Mathematics
ISBN: 9783030424985

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.

Stochastic Population and Epidemic Models

Stochastic Population and Epidemic Models
Author: Linda J. S. Allen
Publisher: Springer
Total Pages: 55
Release: 2015-08-20
Genre: Mathematics
ISBN: 331921554X

This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.

Mathematics of Epidemics on Networks

Mathematics of Epidemics on Networks
Author: István Z. Kiss
Publisher: Springer
Total Pages: 423
Release: 2017-06-08
Genre: Mathematics
ISBN: 3319508067

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.

Applications Of Epidemiological Models To Public Health Policymaking: The Role Of Heterogeneity In Model Predictions

Applications Of Epidemiological Models To Public Health Policymaking: The Role Of Heterogeneity In Model Predictions
Author: Zhilan Feng
Publisher: World Scientific
Total Pages: 306
Release: 2014-04-16
Genre: Mathematics
ISBN: 9814522368

Mathematical models can be very helpful to understand the transmission dynamics of infectious diseases. This book presents examples of epidemiological models and modeling tools that can assist policymakers to assess and evaluate disease control strategies.

Deterministic Threshold Models in the Theory of Epidemics

Deterministic Threshold Models in the Theory of Epidemics
Author: P. Waltman
Publisher: Springer Science & Business Media
Total Pages: 108
Release: 2013-03-08
Genre: Mathematics
ISBN: 3642808204

These notes correspond to a set of lectures given at the Univer sity of Alberta during the spring semester, 1973. The first four sec tions present a systematic development of a deterministic, threshold model for the spraad of an infection. Section 5 presents some compu tational results and attempts to tie the model with other mathematics. In each of the last three sections a separate, specialized topic is presented. The author wishes to thank Professor F. Hoppensteadt for making available preprints of two of his papers and for reading and comment ing on a preliminary version of these notes. He also wishes to thank Professor J. Mosevich for providing the graphs in Section 5. The visit at the University of Alberta was a very pleasant one and the author wishes to express his appreciation to Professors S. Ghurye and J. Macki for the invitation to visit there. Finally, thanks are due to the very competent secretarial staff at the University of Alberta for typing the original draft of the lecture notes and to Mrs. Ada Burns of the University of Iowa for her excellent typescript of the final version. TABLE OF CONTENTS 1. A Simple Epidemic Model with Permanent Removal . . . • . . . 1 2. A More General Model and the Determination of the Intensity of an Epidemic. 10 21 3. A Threshold Model. 4. A Threshold Model with Temporary Immunity. 34 5. Some Special Cases and Some Numerical Examples 48 A Two Population Threshold Model . 62 6.