Mathematical Models in Immunology, 1983, 378 pp., ISBN 0-911575-09-X, $98.00
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In this pioneering work Academician Gurij Ivanovich Marchuk
develops mathematical models for the immune response for the first time.
Beginning with a logical discussion devoid of mathematical formalism, the
author systematically constructs models, which are then verified by computer
simulation as well as by laboratory data. Indices are devised for use with
clinical data.
TABLE OF CONTENTS
List of Illustrations ..... ix
Foreword ..... xv
Preface ..... xxiii
CHAPTER 1. GENERAL CONCEPTS, HYPOTHESES AND PROBLEMS ..... 1
1.1. Basic Components of the Immune Response ..... 2
1.2. The Subclinical Form of a Disease ..... 8
1.3. The Acute Form of a Disease ..... 10
1.4. Immunological Interpretation ..... 12
1.5. A Canonical Diagram of a Disease ..... 15
1.6. Biostimulation of the Immune System ..... 18
1.7. Problems and Hypotheses ..... 22
1.8. Temperature Reaction of the Organism ..... 31
CHAPTER 2. THE SIMPLEST MATHEMATICAL MODEL
OF AN INFECTIOUS DISEASE ..... 35
2.1. Construction of the Simplest Model of an Infectious Disease ..... 40
2.2. Qualitative Analysis of the Simplest Model of a Disease (Analytical Investigation) ..... 48
2.3. Qualitative Analysis of the Simplest Model of a Disease (Numerical Experiments) ..... 84
2.4. Effect of Temperature Reactivity of the Organism on the Dynamics of a Disease ..... 102
2.5. Simulation of the Immune Response of the Organism to the Antigens of Two Types ..... 109
2.6. Level of Antibodies in a Chronic Disease ..... 134
2.7. "Chronization" of a Disease ..... 138
2.8. General Remarks ..... 144
CHAPTER 3. A MATHEMATICAL MODEL OF
ANTIVIRAL IMMUNE RESPONSE ..... 146
3.1. The Immuno-Genetical Description of Antiviral Immune Response ..... 146
3.2. Construction of Model Equations ..... 152
3.3. Main Theorems ..... 161
3.4. Cell-mediated Immune Response ..... 162
3.5. Humoral Immune Response ..... 164
CHAPTER 4. HEMOPOESIS AND THE IMMUNE RESPONSE MECHANISM ..... 168
4.1. A Theoretical Model of the Dynamics of Hemopoiesis ..... 171
4.2. Model of the Lymphoid Line of Hemopoiesis ..... 177
4.3. Model of the Erythroid Line of Hemopoiesis ..... 191
4.4. Model of the Macrophage-Granulocyte Line of Hemopoiesis ..... 235
4.5. Model of the Thrombocyte Line of Hemopoiesis .....
260
CHAPTER 5. MATHEMATICAL DATA PROCESSING
IN CLINICAL TREATMENT ..... 269
5.1. A Method for Constructing Generalized Clinical Indices of the Gravity of a Disease ..... 271
5.2. A Method for Constructing Generalized Laboratory Indices of the Gravity of a Disease ..... 280
5.3. General Problems of Methodology ..... 285
5.4. The Application of a Simple Mathematical Model of a Disease to the Analysis of Clinical and Laboratory Data ..... 288
5.5. The Correlation Analysis of a Pathological Process and the Expressivity of a Pathological Process ..... 299
5.6. Dynamics of Laboratory Indices ..... 306
Appendix ..... 320
Bibliography ..... 339
Index ..... 349