Stochastic Epidemic Models and Their Statistical Analysis
Title | Stochastic Epidemic Models and Their Statistical Analysis PDF eBook |
Author | Hakan Andersson |
Publisher | Springer Science & Business Media |
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.
Stochastic Epidemic Models and Their Statistical Analysis
Title | Stochastic Epidemic Models and Their Statistical Analysis PDF eBook |
Author | Hakan Andersson |
Publisher | Springer |
Pages | 156 |
Release | 2000-08-01 |
Genre | Medical |
ISBN | 0387950508 |
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.
Stochastic Epidemic Models with Inference
Title | Stochastic Epidemic Models with Inference PDF eBook |
Author | Tom Britton |
Publisher | Springer Nature |
Pages | 474 |
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.
Epidemic Modelling
Title | Epidemic Modelling PDF eBook |
Author | D. J. Daley |
Publisher | Cambridge University Press |
Pages | 160 |
Release | 1999-04-13 |
Genre | Mathematics |
ISBN | 9780521640794 |
This is a general introduction to the mathematical modelling of diseases.
Epidemic Models
Title | Epidemic Models PDF eBook |
Author | Denis Mollison |
Publisher | Cambridge University Press |
Pages | 458 |
Release | 1995-07-13 |
Genre | Mathematics |
ISBN | 9780521475365 |
Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.
Stochastic Modeling and Control
Title | Stochastic Modeling and Control PDF eBook |
Author | Ivan Ivanov |
Publisher | IntechOpen |
Pages | 286 |
Release | 2012-11-28 |
Genre | Mathematics |
ISBN | 9789535108306 |
Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.
Mathematical Tools for Understanding Infectious Disease Dynamics
Title | Mathematical Tools for Understanding Infectious Disease Dynamics PDF eBook |
Author | Odo Diekmann |
Publisher | Princeton University Press |
Pages | 517 |
Release | 2012-11-18 |
Genre | Science |
ISBN | 1400845629 |
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout