1st Edition
Mathematical Modeling the Life Sciences Numerical Recipes in Python and MATLAB®
The purpose of this unique textbook is to bridge the gap between the need for numerical solutions to modeling techniques through computer simulations to develop skill in employing sensitivity analysis to biological and life sciences applications.
The underpinning mathematics is minimalized. The focus is on the consequences, implementation, and application. Historical context motivates the models. An understanding of the earliest models provides insight into more complicated ones.
While the text avoids getting mired in the details of numerical analysis, it demonstrates how to use numerical methods and provides core codes that can be readily altered to fit a variety of situations.
Numerical scripts in both Python and MATLAB® are included. Python is compiled in Jupyter Notebook to aid classroom use. Additionally, codes are organized and available online.
One of the most important skills requiring the use of computer simulations is sensitivity analysis. Sensitivity analysis is increasingly used in biomathematics. There are numerous pitfalls to using sensitivity analysis and therefore a need for exposure to worked examples in order to successfully transfer their use from mathematicians to biologists.
The interconnections between mathematics and the life sciences have an extensive history. This book offers a new approach to using mathematics to model applications using computers, to employ numerical methods, and takes students a step further into the realm of sensitivity analysis. With some guidance and practice, the reader will have a new and incredibly powerful tool to use.
https://www.math.fsu.edu/~cogan/Book/Codes/Codes.html
Forward
1. Introduction
1.1 What is a Model?
1.2 Projectile Motion
1.3 Problems
2. Mathematical Background
2.1 Mathematical Preliminaries
2.2 Linearization
2.3 Qualitative Analysis
2.4 Problems
2.5 Appendix: Planar Example
3. Introduction to the Numerical Methods
3.1 Introduction
3.2 Best Practices in Coding
3.3 Getting the Programs Running
3.4 Initial Programs
3.5 Problems
4. Ecology
4.1 Historical Background
4.2 Single Species Models
4.3 Competitive Exclusion
4.4 State of the Art and Caveats
4.5 Problems
5. Within-host Disease Models
5.1 Historical Background
5.2 Pathological: Tumor
5.3 Viral: Acute Infection
5.4 Chronic: Tuberculosis
5.5 Problems
5.6 Appendix
6. Between-Host Disease Models
6.1 Historical Background
6.2 Two Compartment Models
6.3 Classical SIR
6.4 Waning Antigens
6.5 Caveats and State of the Art
6.6 Problems
7. Microbiology
7.1 Historical Background
7.2 Bacterial Growth: Chemostat
7.3 Multiple State Model: Free/Attached
7.4 Cooperators, Cheaters, and Competitions
7.5 Problems
8. Circulation and Cardiac Physiology
8.1 Historical Background
8.2 Blood Circulation Models
8.3 Cardiac Physiology
8.4 Problems
9. Neuroscience
9.1 Historical Background
9.2 Action Potential
9.3 Fitzhugh-Nagumo
9.4 Problems
10. Genetics
10.1 Historical Background
10.2 Heredity
10.3 Problems
Biography
Nicholas G. Cogan is Professor of Mathematics at Florida State University. He began studying mathematical biology in undergraduate school and received his Ph.D. from the University of Utah under James P. Keener. He routinely works with microbiologists, environmental engineers, clinicians, and other scientists outside of mathematics. He has taught for twenty years at the undergraduate level and his research focuses on mathematical modeling in the life sciences. He is the author of over fifty articles using mathematics with biology.
