Mathematics for Life Science and Medicine is one of two collections of papers arising from a 2004 symposium called “Dynamical Systems Theory and Its Applications to Biology and Environmental Sciences”. The companion volume, Mathematics for Ecology and Environmental Science, is reviewed separately.
This volume, with an introduction and nine papers, focuses on infectious disease dynamics and the evolution of pathogens. For the most part, the papers are accessible to non-experts. Each paper provides the basic background material in biology necessary to understand the mathematical models that are developed. Epidemiology — especially with the models treated here — demands less in the way of biological background than many other areas in the broad field of mathematical biology.
To give some sense of the book’s contents, I’ll briefly summarize three representative papers. The first paper in this volume offers an introductory treatment of the modeling of epidemics and identifies some trends of current research. It includes an example that develops a model for the Severe Acute Respiratory Syndrome (SARS) outbreak in China and considers the effectiveness of a variety of control measures. Another paper investigates competition and coexistence of populations of micro-parasites. In particular, the author tries to understand how to devise control strategies for infectious disease derived from parasites without creating resistant parasites or driving them to increased virulence. An intriguing paper on the evolution of viruses within a single human host is relevant to treatment of hepatitis B and C viruses as well as the human immunodeficiency virus. The authors develop models that show how human immune system selection influences the direction of viral evolution and suggest a potential direction of treatment.
The papers in this volume provide a taste of the subject matter and a means of entry into this field of mathematical biology. Most of the material is accessible to non-specialists and the applications are of real value. The mathematical prerequisites are modest and include basic knowledge of systems of differential equations. The book is rather pricey for its size, and might be most appropriate for departmental or library collections.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.