Mathematical Biology: Modeling and Analysis
About this Title
Avner Friedman, Ohio State University, Columbus, OH
Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 2018; Volume 127
ISBNs: 978-1-4704-4715-1 (print); 978-1-4704-4803-5 (online)
MathSciNet review: MR3793187
MSC: Primary 92D25; Secondary 35Q92, 35R35, 49J10, 92C42, 92C50
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 research at the interface of mathematics and biology.
This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs.
Graduate students and researchers interested in applications of PDEs to math biology.
Table of Contents
- Introductory biology
- Introduction to modeling
- Models of population dynamics
- Cancer and the immune system
- Parameters estimation
- Mathematical analysis inspired by cancer models
- Mathematical model of artherosclerosis: Risk of high cholesterol
- Mathematical analysis inspired by the atherosclerosis model
- Mathematical models of chronic wounds
- Mathematical analysis inspired by the chronic wound model
- Introduction to PDEs