Mathematical Modelling of Immune Response in Infectious Diseases

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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(s): Guri I. Marchuk (auth.)
Series: Mathematics and Its Applications 395
Edition: 1
Publisher: Springer Netherlands
Year: 1997

Language: English
Pages: 350
Tags: Mathematical and Computational Biology; Immunology; Infectious Diseases; Computational Mathematics and Numerical Analysis; Systems Theory, Control

Front Matter....Pages i-x
Introduction....Pages 1-3
Front Matter....Pages 5-5
General Knowledge, Hypotheses, and Problems....Pages 7-47
Survey of Mathematical Models in Immunology....Pages 48-74
Simple Mathematical Model of Infectious Disease....Pages 75-115
Mathematical Modeling of Antiviral and Antibacterial Immune Responses....Pages 116-149
Identification of Parameters of Models....Pages 150-198
Numerical Realization Algorithms for Mathematical Models....Pages 199-220
Front Matter....Pages 221-221
Viral Hepatitis B....Pages 223-268
Viral And Bacterial Infections of Respiratory Organs....Pages 269-289
Model of Experimental Influenza Infection....Pages 290-302
Adjoint Equations and Sensitivity Study for Mathematical Models of Infectious Diseases....Pages 303-323
Back Matter....Pages 325-350