Mathematical biology. Modeling and analysis

Description

The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for rese.  Read more... Abstract: Considers models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.  Read more... Content: Cover Title page Contents Preface Chapter 1. Introductory biology Chapter 2. Introduction to modeling Chapter 3. Models of population dynamics 3.1. Chemostat 3.2. Infectious diseases 3.3. A cancer model Chapter 4. Cancer and the immune system Chapter 5. Parameters estimation Chapter 6. Mathematical analysis inspired by cancer models Chapter 7. Mathematical model of atherosclerosis: Risk of high cholesterol Chapter 8. Mathematical analysis inspired by the atherosclerosis model Chapter 9. Mathematical models of chronic wounds. Chapter 10. Mathematical analysis inspired by the chronic wound modelAppendix: Introduction to PDEs A.1. Elliptic equations A.2. Parabolic equations A.3. Nonlinear equations and systems A.4. Free boundary problems Bibliography Index Back Cover.