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Applications of calculus to biology and medicine. Case studies from Lake Victoria. (English) Zbl 1380.92001

Hackensack, NJ: World Scientific (ISBN 978-981-3222-77-9/hbk). xv, 255 p. (2018).
This book is designed as an introductory textbook aiming to bridge the knowledge requirements of both biologists and mathematicians. Written with novices in mind, the book seamlessly integrates elements of calculus, biological description of well-known and frequently used examples (such as population modelling, drug modelling, predator-prey interactions) and elements of programming in Sage, an open-source computer algebra system written in Python.
The book is structured in five parts and one of its unique features is the presence of numerous exercises, questions for thought, problems and the review of techniques for approaching a real-world problem and seeing it through to a research paper format. The “modelling interludes” aimed at dissecting the modelling process and critically analysing the proposed models (using, e.g., sensitivity analyses or examples of misapplied or poorly calibrated models) coupled with the “research interludes” on how to read and extract information from research papers, on how to write a manuscript and how to present figures and tables in an informative manner, underline the ultimate purpose of the textbook.
Particular topics discussed in detail include the logistic growth used in population modelling and the mathematical description and use of Euler’s method, the description of models used in pharmacokinetics (e.g., the half-life model, methods for drug administration, with an example for halofantrine), the damped and undamped Lotka-Volterra equations for modelling the predator-prey interaction and the modelling of infectious diseases (the case studies focus on malaria and HIV/AIDS).
The book is written in an accessible style suitable for a wide range of researchers with various backgrounds. However, the authors have structured the text with young students/researchers in mind and therefore the book follows a formative approach in the description of the calculus-related topics.

MSC:

92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology
92B05 General biology and biomathematics
92Dxx Genetics and population dynamics

Software:

SageMath; Python
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