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# Mathematical Models of the Cell and Cell Associated Objects,206

**Viktor Ivanov, Natalya Ivanova**

ISBN **0444527141**

Pages **354**

Description

The book contains five main parts: Introduction: Evolutionary System and Development Modelling; Part I: A Survey of MM of CAO (cell associated objects); Part II: MM (mathematical models) of Development; Part III: Introduction to Applications; Appendix: Mathematics of Development.

The part I gives the reader a survey of hundreds results in the field of the cell and cell associated objects modelling, which are not easy accessible. The original four parts of the book have no analogy in the literature, except the previous book of the first author 'Model Development and Optimization', KAP, 1999, and the book 'Mathematical Modeling in Economics, Ecology and the Environment', KAP, 1999, by N. Hritonenko, Yu. Yatsenko (Yu. Yatsenko is a pupil of the first author of the cell book).

The present book is different from the previous mainly by much more profound investigation of such a complicated object as the cell and by much more detailed description of applications to modelling AIDS, cancers, and life longevity.

Key features:

- Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development .

- Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions.

- Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network .

- Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc.

- Detailed analysis of applications to modelling AIDS, cancers, and life longevity.

- Introducing and grounding the respective numerical algorithms and software.

- Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects.

Contents

Preface List of abbreviations List of notations Introduction: Evolutionary Systems and Development Modeling Part 1: SURVEY OF MM OF CAO Chapter 1: General Methods of Inlet and Analysis of MM Chapter 2: MM of Enzyme Reactions Chapter 3: MM of Kinetic Cellular Theory Chapter 4: Some Other MM Part 2: MM OF DEVELOPMENT Chapter 5: Base MM Chapter 6: Examples of CAO and Their MM Chapter 7: MM of the Cell Chapter 8: MM of the Immune Network Chapter 9: MM of Some Other CAO Part 3: INTRODUCTION TO APPLICATIONS Chapter 10: AIDS Chapter 11: Cancers Chapter 12: On Life Longevity Problems Chapter 13: On MM of a Disease Appendix: MATHEMATICS OF DEVELOPMENT Chapter 14: Investigation of Equations Chapter 15: Investigation of Optimization Problems Chapter 16: Numerical Methods and Software Summary Bibliography Index About the Authors