Mathematical Modelling And Analysis Of Infectious Diseases

Author : Khalid Hattaf,Hemen Dutta
Publisher : Springer Nature
Page : 348 pages
File Size : 52,6 Mb
Release : 2020-07-30
Category : Technology & Engineering
ISBN : 9783030498962

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Mathematical Modelling and Analysis of Infectious Diseases by Khalid Hattaf,Hemen Dutta Pdf

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 : Michael Y. Li
Publisher : Springer
Page : 156 pages
File Size : 51,5 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319721224

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An Introduction to Mathematical Modeling of Infectious Diseases by Michael Y. Li Pdf

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 : Praveen Agarwal,Juan J. Nieto,Delfim F.M. Torres
Publisher : Academic Press
Page : 346 pages
File Size : 52,7 Mb
Release : 2022-06-01
Category : Science
ISBN : 9780323904582

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Mathematical Analysis of Infectious Diseases by Praveen Agarwal,Juan J. Nieto,Delfim F.M. Torres Pdf

Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases. Epidemic mathematical modeling and analysis is important, not only to understand disease progression, but also to provide predictions about the evolution of disease. One of the main focuses of the book is the transmission dynamics of the infectious diseases like COVID-19 and the intervention strategies. It also discusses optimal control strategies like vaccination and plasma transfusion and their potential effectiveness on infections using compartmental and mathematical models in epidemiology like SI, SIR, SICA, and SEIR. The book also covers topics like: biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of infectious diseases, mathematical modeling and analysis of diagnosis rate effects and prediction of viruses, data-driven graphical analysis of epidemic trends, dynamic simulation and scenario analysis of the spread of diseases, and the systematic review of the mathematical modeling of infectious disease like coronaviruses. Offers analytical and numerical techniques for virus models Discusses mathematical modeling and its applications in treating infectious diseases or analyzing their spreading rates Covers the application of differential equations for analyzing disease problems Examines probability distribution and bio-mathematical applications

Author : O. Diekmann,J. A. P. Heesterbeek
Publisher : John Wiley & Sons
Page : 324 pages
File Size : 43,6 Mb
Release : 2000-04-07
Category : Mathematics
ISBN : 0471492418

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Mathematical Epidemiology of Infectious Diseases by O. Diekmann,J. A. P. Heesterbeek Pdf

Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are unravelled. Conceptual clarity is attained, assumptions are stated clearly, hidden working hypotheses are attained and mechanistic links between different observables are exposed. Features: * Model construction, analysis and interpretation receive detailed attention * Uniquely covers both deterministic and stochastic viewpoints * Examples of applications given throughout * Extensive coverage of the latest research into the mathematical modelling of epidemics of infectious diseases * Provides a solid foundation of modelling skills The reader will learn to translate, model, analyse and interpret, with the help of the numerous exercises. In literally working through this text, the reader acquires modelling skills that are also valuable outside of epidemiology, certainly within population dynamics, but even beyond that. In addition, the reader receives training in mathematical argumentation. The text is aimed at applied mathematicians with an interest in population biology and epidemiology, at theoretical biologists and epidemiologists. Previous exposure to epidemic concepts is not required, as all background information is given. The book is primarily aimed at self-study and ideally suited for small discussion groups, or for use as a course text.

Author : Guri I. Marchuk
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 48,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401587983

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Mathematical Modelling of Immune Response in Infectious Diseases by Guri I. Marchuk Pdf

Beginning his work on the monograph to be published in English, this author tried to present more or less general notions of the possibilities of mathematics in the new and rapidly developing science of infectious immunology, describing the processes of an organism's defence against antigen invasions. The results presented in this monograph are based on the construc tion and application of closed models of immune response to infections which makes it possible to approach problems of optimizing the treat ment of chronic and hypertoxic forms of diseases. The author, being a mathematician, had creative long-Iasting con tacts with immunologists, geneticist, biologists, and clinicians. As far back as 1976 it resulted in the organization of a special seminar in the Computing Center of Siberian Branch of the USSR Academy of Sci ences on mathematical models in immunology. The seminar attracted the attention of a wide circle of leading specialists in various fields of science. All these made it possible to approach, from a more or less united stand point, the construction of models of immune response, the mathematical description of the models, and interpretation of results.

Author : Praveen Agarwal,Juan J. Nieto,Michael Ruzhansky,Delfim F. M. Torres
Publisher : Springer Nature
Page : 635 pages
File Size : 45,8 Mb
Release : 2021
Category : COVID-19 (Disease)
ISBN : 9789811624506

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Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact by Praveen Agarwal,Juan J. Nieto,Michael Ruzhansky,Delfim F. M. Torres Pdf

This edited volume is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and country-wise analysis of Covid-19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their bio-mathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.

Author : Schiesser William E
Publisher : World Scientific
Page : 460 pages
File Size : 48,5 Mb
Release : 2018-06-27
Category : Technology & Engineering
ISBN : 9789813238800

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Mathematical Modeling Approach To Infectious Diseases, A: Cross Diffusion Pde Models For Epidemiology by Schiesser William E Pdf

Author : Shah, Nita H.,Mittal, Mandeep
Publisher : IGI Global
Page : 316 pages
File Size : 45,8 Mb
Release : 2020-06-26
Category : Medical
ISBN : 9781799837428

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Mathematical Models of Infectious Diseases and Social Issues by Shah, Nita H.,Mittal, Mandeep Pdf

When deadly illness spreads through a population at a rapid pace, time may be of the essence in order to save lives. Using mathematics as a language to interpret assumptions concerning the biological and population mechanics, one can make predictions by analyzing actual epidemiological data using mathematical tests and results. Mathematical models can help us understand the right disease status and predict the effects of the disease on populations, which can help limit the spread and devastation of the illness. Mathematical Models of Infectious Diseases and Social Issues is a collection of innovative research that examines the dynamics of diseases and their effect on populations. Featuring coverage of a broad range of topics including deterministic models, environmental pollution, and social issues, this book is ideally designed for diagnosticians, clinicians, healthcare providers, pharmacists, government health officials, policymakers, academicians, researchers, and students.

Author : Zhien Ma
Publisher : World Scientific
Page : 513 pages
File Size : 44,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812797506

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Dynamical Modeling and Analysis of Epidemics by Zhien Ma Pdf

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 : Zhien Ma,Yicang Zhou,Jianhong Wu
Publisher : World Scientific
Page : 355 pages
File Size : 54,8 Mb
Release : 2009
Category : Medical
ISBN : 9789814261258

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Modeling and Dynamics of Infectious Diseases by Zhien Ma,Yicang Zhou,Jianhong Wu Pdf

This book provides a systematic introduction to the fundamental methods and techniques and the frontiers of ? along with many new ideas and results on ? infectious disease modeling, parameter estimation and transmission dynamics. It provides complementary approaches, from deterministic to statistical to network modeling; and it seeks viewpoints of the same issues from different angles, from mathematical modeling to statistical analysis to computer simulations and finally to concrete applications.

Author : Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng
Publisher : Springer Nature
Page : 628 pages
File Size : 48,5 Mb
Release : 2019-10-10
Category : Mathematics
ISBN : 9781493998289

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Mathematical Models in Epidemiology by Fred Brauer,Carlos Castillo-Chavez,Zhilan Feng Pdf

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 : Fred Brauer,Carlos Castillo-Chavez
Publisher : SIAM
Page : 279 pages
File Size : 51,9 Mb
Release : 2013-02-07
Category : Mathematics
ISBN : 9781611972412

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Mathematical Models for Communicable Diseases by Fred Brauer,Carlos Castillo-Chavez Pdf

A self-contained and comprehensive guide to the mathematical modeling of disease transmission, appropriate for graduate students.

Author : Maia Martcheva
Publisher : Springer
Page : 453 pages
File Size : 50,5 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9781489976123

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An Introduction to Mathematical Epidemiology by Maia Martcheva Pdf

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 : Matt J. Keeling,Pejman Rohani
Publisher : Princeton University Press
Page : 385 pages
File Size : 55,8 Mb
Release : 2011-09-19
Category : Science
ISBN : 9781400841035

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Modeling Infectious Diseases in Humans and Animals by Matt J. Keeling,Pejman Rohani Pdf

For epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recent developments as well as more traditional approaches. Matt Keeling and Pejman Rohani move from modeling with simple differential equations to more recent, complex models, where spatial structure, seasonal "forcing," or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory. In each of the eight chapters, they deal with a specific modeling approach or set of techniques designed to capture a particular biological factor. They illustrate the methodology used with examples from recent research literature on human and infectious disease modeling, showing how such techniques can be used in practice. Diseases considered include BSE, foot-and-mouth, HIV, measles, rubella, smallpox, and West Nile virus, among others. Particular attention is given throughout the book to the development of practical models, useful both as predictive tools and as a means to understand fundamental epidemiological processes. To emphasize this approach, the last chapter is dedicated to modeling and understanding the control of diseases through vaccination, quarantine, or culling. Comprehensive, practical introduction to infectious disease modeling Builds from simple to complex predictive models Models and methodology fully supported by examples drawn from research literature Practical models aid students' understanding of fundamental epidemiological processes For many of the models presented, the authors provide accompanying programs written in Java, C, Fortran, and MATLAB In-depth treatment of role of modeling in understanding disease control

Author : Xinzhi Liu,Peter Stechlinski
Publisher : Springer
Page : 271 pages
File Size : 48,7 Mb
Release : 2017-02-25
Category : Mathematics
ISBN : 9783319532080

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Infectious Disease Modeling by Xinzhi Liu,Peter Stechlinski Pdf

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.