Mathematical Modeling Of Virus Infection

Author : William E Schiesser
Publisher : World Scientific
ISBN 13 : 9811236658
Total Pages : 178 pages
Book Rating : 4.55/5 ( download)

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Download or read book Mathematical Modeling Of Virus Infection: Ode/pde Analysis In R written by William E Schiesser and published by World Scientific. This book was released on 2021-03-17 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two models for the spread and control of a virus are detailed in this book: The Lung/Respiratory System Model (LSM) and the SVIR (Susceptible-Vaccinated-Infected-Recovered) Model.The LSM gives the spatiotemporal distribution of four viral-related proteins: virus population density along the lung air passage, host cell primary infection protein (viral genetic material (VGM)) concentration, host cell secondary infection protein (VGM) concentration, and air stream virion population density.The model is executed for a single inhalation, and a series of inhalation/exhalation cycles. For the latter, the progression of the viral infection into the lung is a principal result.The SVIR is first formulated as a system of ordinary differential equations (ODEs) in time, then extended to a system of PDEs to account for spatial effects (spatiotemporal modeling).Principal outputs from the ODE/PDE models are the levels of vaccinations and infections. For the latter, the efficacy of the vaccine is a parameter that can be varied in a computer-based analysis of a vaccine therapy.The coding of the models is in R, a quality, open-source scientific computing system, and can be executed on modest computers. The R routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the ODE/PDE models, such as changes in the parameters and the form of the model equations.

Author : Gennady Bocharov
Publisher : Springer
ISBN 13 : 3319723170
Total Pages : 256 pages
Book Rating : 4.74/5 ( download)

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Download or read book Mathematical Immunology of Virus Infections written by Gennady Bocharov and published by Springer. This book was released on 2018-06-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph concisely but thoroughly introduces the reader to the field of mathematical immunology. The book covers first basic principles of formulating a mathematical model, and an outline on data-driven parameter estimation and model selection. The authors then introduce the modeling of experimental and human infections and provide the reader with helpful exercises. The target audience primarily comprises researchers and graduate students in the field of mathematical biology who wish to be concisely introduced into mathematical immunology.

Author : William E. Schiesser
Publisher :
ISBN 13 : 9789811236648
Total Pages : 178 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Mathematical Modeling of Virus Infection written by William E. Schiesser and published by . This book was released on 1901 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Martin Nowak
Publisher : Oxford University Press, UK
ISBN 13 : 0191588512
Total Pages : 253 pages
Book Rating : 4.18/5 ( download)

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Download or read book Virus Dynamics : Mathematical Principles of Immunology and Virology written by Martin Nowak and published by Oxford University Press, UK. This book was released on 2000-11-23 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking book describes the emerging field of theoretical immunology, in particular the use of mathematical models to describe the spread of infectious diseases within patients. It reveals fascinating insights into the dynamics of viral and other infections, and the interactions between infectious agents and immune responses. Structured around the examples of HIV/AIDS and hepatitis B, Nowak and May show how mathematical models can help researchers to understand the detailed dynamics of infection and the effects of antiviral therapy. Models are developed to describe the dynamics of drug resistance, immune responses, viral evolution and mutation, and to optimise the design of therapy and vaccines. - ;We know, down to the tiniest details, the molecular structure of the human immunodeficiency virus (HIV). Yet despite this tremendous accomplishment, and despite other remarkable advances in our understanding of individual viruses and cells of the immune system, we still have no agreed understanding of the ultimate course and variability of the pathogenesis of AIDS. Gaps in our understanding like these impede our efforts towards developing effective therapies and preventive vaccines. Martin Nowak and Robert M May describe the emerging field of theoretical immunology in this accessible and well- written text. Using mathematical modelling techniques, the authors set out their ideas about how populations of viruses and populations of immune system cells may interact in various circumstances, and how infectious diseases spread within patients. They explain how this approach to understanding infectious diseases can reveal insights into the dynamics of viral and other infections, and the interactions between infectious agents and immune responses. The book is structured around the examples of HIV/AIDS and Hepatitis B virus, although the approaches described will be more widely applicable. The authors use mathematical tools to uncover the detailed dynamics of the infection and the effects of antiviral therapy. Models are developed to describe the emergence of drug resistance, and the dynamics of immune responses, viral evolution, and mutation. The practical implications of this work for optimisation of the design of therapy and vaccines are discussed. The book concludes with a glance towards the future of this fascinating, and potentially highly useful, field of study. - ;... an excellent introduction to a field that has the potential to advance substantially our understanding of the complex interplay between virus and host - Nature

Author : Guri I. Marchuk
Publisher : Springer Science & Business Media
ISBN 13 : 9401587981
Total Pages : 356 pages
Book Rating : 4.83/5 ( download)

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Download or read book Mathematical Modelling of Immune Response in Infectious Diseases written by Guri I. Marchuk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Khalid Hattaf
Publisher : Springer Nature
ISBN 13 : 3030498964
Total Pages : 348 pages
Book Rating : 4.62/5 ( download)

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Download or read book Mathematical Modelling and Analysis of Infectious Diseases written by Khalid Hattaf and published by Springer Nature. This book was released on 2020-07-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Fred Brauer
Publisher : Springer Nature
ISBN 13 : 1493998285
Total Pages : 628 pages
Book Rating : 4.89/5 ( download)

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Download or read book Mathematical Models in Epidemiology written by Fred Brauer and published by Springer Nature. This book was released on 2019-10-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Matt J. Keeling
Publisher : Princeton University Press
ISBN 13 : 1400841038
Total Pages : 385 pages
Book Rating : 4.35/5 ( download)

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Download or read book Modeling Infectious Diseases in Humans and Animals written by Matt J. Keeling and published by Princeton University Press. This book was released on 2011-09-19 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kasia Anna Pawelek
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.53/5 ( download)

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Download or read book Mathematical Modeling of Virus Infections and Immune Responses written by Kasia Anna Pawelek and published by . This book was released on 2012 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the dissertation studies mathematical models for the HIV infection. such mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models brings challenges to both the mathematical analysis of the models and comparison of their predictions with patient data. We study recent models for HIV dynamics and incorporate two time delays, one represents the time needed for infected cells to produce virions after viral entry, and other other one is the time needed for the adaptive immune response to emerge to control viral replication. We begin the analysis of the model with a proof of the positivity and boundedness of the solutions, the local stability of the infection-free and infected steady states, and the uniform persistence of the system. By developing different Lyapunov functionals, we obtain conditions that ensure the global stability of the steady states. We also compare the model with two delays to viral load data from 10 patients during primary HIV-1 infection, and this allows us to estithe parameter values. The second part of the dissertation deals with mathematical models for the Influenza infection. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. We developed a mathematical model including both innate and adaptive immune responses, to study the within-host dynamics of equine influenza virus infection in horses. By comparing the predictions of the model with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection. These two topics form a contribution to our expanding knowledge of the HIV-1 and Influenza infections and immune responses.

Author : Martin A. Nowak
Publisher : Oxford University Press
ISBN 13 : 0198504179
Total Pages : 253 pages
Book Rating : 4.77/5 ( download)

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Download or read book Virus Dynamics written by Martin A. Nowak and published by Oxford University Press. This book was released on 2000-11-23 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the emerging field of theoretical immunology, in particular the use of mathematical models to describe the spread of infectious diseases within patients. It reveals insights into the dynamics of viral & other infections.