Introduction to Mathematical Biology: Modeling, Analysis, and Simulations

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Springer, Apr 27, 2016 - Mathematics - 172 pages

This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience.


The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research.


Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.

 

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Contents

1 Introduction
1
2 Bacterial Growth in Chemostat
3
3 System of Two Linear Differential Equations
28
4 Systems of Two Differential Equations
43
5 PredatorPrey Models
51
6 Two Competing Populations
65
7 General Systems of Differential Equations
75
8 The Chemostat Model Revisited
86
10 Enzyme Dynamics
105
11 Bifurcation Theory
116
The Risk of High Cholesterol
129
13 CancerImmune Interaction
137
14 Cancer Therapy
147
15 Tuberculosis
157
Solutions
165
Index
170

9 Spread of Disease
97

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About the author (2016)

Ching-Shan Chou is an Associate Professor in the Department of Mathematics at Ohio State University. She received her Ph.D. in the area of applied mathematics from Brown University. She is currently working in the area of computational and mathematical biology.
Avner Friedman is a Distinguished University Professor at Ohio State University. He received his Ph.D. in 1956 from the Hebrew University. His research interests include partial differential equations, both general mathematical theory as well as applications to models that arise in the physical and life sciences, in engineering, and in industry.

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