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Author : Mahya Aghaee
Publisher :
Page : 0 pages
File Size : 47,36 MB
Release : 2016
Category :
ISBN :
Author : Harkaran Singh
Publisher : CRC Press
Page : 338 pages
File Size : 50,81 MB
Release : 2018-12-07
Category : Mathematics
ISBN : 1351251686
Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.
Author : Maia Martcheva
Publisher : Springer
Page : 462 pages
File Size : 37,73 MB
Release : 2015-10-20
Category : Mathematics
ISBN : 1489976124
The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.
Author : Fred Brauer
Publisher : Springer Nature
Page : 628 pages
File Size : 14,61 MB
Release : 2019-10-10
Category : Mathematics
ISBN : 1493998285
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.
Author : Zhien Ma
Publisher : World Scientific
Page : 513 pages
File Size : 47,16 MB
Release : 2009
Category : Mathematics
ISBN : 9812797505
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 : Khalid Hattaf
Publisher : Springer Nature
Page : 348 pages
File Size : 22,31 MB
Release : 2020-07-30
Category : Technology & Engineering
ISBN : 3030498964
This book discusses significant research and study topics related to mathematical modelling and analysis of infectious diseases. It includes several models and modelling approaches with different aims, such as identifying and analysing causes of occurrence and re-occurrence, causes of spreading, treatments and control strategies. A valuable resource for researchers, students, educators, scientists, professionals and practitioners interested in gaining insights into various aspects of infectious diseases using mathematical modelling and mathematical analysis, the book will also appeal to general readers wanting to understand the dynamics of various diseases and related issues. Key Features Mathematical models that describe population prevalence or incidence of infectious diseases Mathematical tools and techniques to analyse data on the incidence of infectious diseases Early detection and risk estimate models of infectious diseases Mathematical models that describe the transmission of infectious diseases and analyse data Dynamical analysis and control strategies for infectious diseases Studies comparing the utility of particular models in describing infected diseases-related issues such as social, health and economic
Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 31,18 MB
Release : 2013-02-06
Category : Mathematics
ISBN : 1447148207
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
Author : Suzanne Lenhart
Publisher : CRC Press
Page : 272 pages
File Size : 25,91 MB
Release : 2007-05-07
Category : Mathematics
ISBN : 1420011413
From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t
Author : Abba B. Gumel
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 41,65 MB
Release : 2010
Category : Mathematics
ISBN : 0821843842
This volume stems from two DIMACS activities, the U.S.-Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.
Author : Hemen Dutta
Publisher : Elsevier
Page : 392 pages
File Size : 16,47 MB
Release : 2023-01-06
Category : Medical
ISBN : 0323995586
Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed. Includes models to describe global and local dynamics of various viruses Provides readers with control strategies for occurrence and reoccurrence of viruses Includes epidemic models under various effects and environments Provides readers with a robust set of mathematical tools and techniques for epidemiological modeling