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Mathematical Modelling of Immune Response in Infectious Diseases

  • Book
  • © 1997

Overview

Authors:
  1. Guri I. Marchuk

    1. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 395)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    1. Introduction

      • Guri I. Marchuk
      Pages 1-3

  3. Fundamental Problems in Mathematical Modeling of Infectious Diseases

    1. Front Matter

      Pages 5-5
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    2. General Knowledge, Hypotheses, and Problems

      • Guri I. Marchuk
      Pages 7-47

    3. Survey of Mathematical Models in Immunology

      • Guri I. Marchuk
      Pages 48-74

    4. Simple Mathematical Model of Infectious Disease

      • Guri I. Marchuk
      Pages 75-115

    5. Mathematical Modeling of Antiviral and Antibacterial Immune Responses

      • Guri I. Marchuk
      Pages 116-149

    6. Identification of Parameters of Models

      • Guri I. Marchuk
      Pages 150-198

    7. Numerical Realization Algorithms for Mathematical Models

      • Guri I. Marchuk
      Pages 199-220

  4. Models of Viral and Bacterial Infections

    1. Front Matter

      Pages 221-221
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    2. Viral Hepatitis B

      • Guri I. Marchuk
      Pages 223-268

    3. Viral And Bacterial Infections of Respiratory Organs

      • Guri I. Marchuk
      Pages 269-289

    4. Model of Experimental Influenza Infection

      • Guri I. Marchuk
      Pages 290-302

    5. Adjoint Equations and Sensitivity Study for Mathematical Models of Infectious Diseases

      • Guri I. Marchuk
      Pages 303-323

  5. Back Matter

    Pages 325-350
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

    Guri I. Marchuk

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