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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.
Forward
Introduction
What is a Model?
Projectile Motion
Problems
Mathematical Background
Mathematical Preliminaries
Linearization
Qualitative Analysis
Problems
Appendix: Planar Example
Introduction to the Numerical Methods
Introduction
Best Practices in Coding
Getting the Programs Running
Initial Programs
Problems
Ecology
Historical Background
Single Species Models
Competitive Exclusion
State of the Art and Caveats
Problems
Within-host Disease Models
Historical Background
Pathological: Tumor
Viral: Acute Infection
Chronic: Tuberculosis
Problems
Appendix
Between-Host Disease Models
Historical Background
Two Compartment Models
Classical SIR
Waning Antigens
Caveats and State of the Art
Problems
Microbiology
Historical Background
Bacterial Growth: Chemostat
Multiple State Model: Free/Attached
Cooperators, Cheaters, and Competitions
Problems
Circulation and Cardiac Physiology
Historical Background
Blood Circulation Models
Cardiac Physiology
Problems
Neuroscience
Historical Background
Action Potential
Fitzhugh-Nagumo
Problems
Genetics
Historical Background
Heredity
Problems