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Mathematical Modeling for Epidemiology and Ecology provides readers
with the mathematical tools needed to understand and use
mathematical models and read advanced mathematical biology books.
It presents mathematics in biological contexts, focusing on the
central mathematical ideas and the biological implications, with
detailed explanations. The author assumes no mathematics background
beyond elementary differential calculus. An introductory chapter on
basic principles of mathematical modeling is followed by chapters
on empirical modeling and mechanistic modeling. These chapters
contain a thorough treatment of key ideas and techniques that are
often neglected in mathematics books, such as the Akaike
Information Criterion. The second half of the book focuses on
analysis of dynamical systems, emphasizing tools to simplify
analysis, such as the Routh-Hurwitz conditions and asymptotic
analysis. Courses can be focused on either half of the book or
thematically chosen material from both halves, such as a course on
mathematical epidemiology. The biological content is self-contained
and includes many topics in epidemiology and ecology. Some of this
material appears in case studies that focus on a single detailed
example, and some is based on recent research by the author on
vaccination modeling and scenarios from the COVID-19 pandemic. The
problem sets feature linked problems where one biological setting
appears in multi-step problems that are sorted into the appropriate
section, allowing readers to gradually develop complete
investigations of topics such as HIV immunology and harvesting of
natural resources. Some problems use programs written by the author
for Matlab or Octave; these combine with more traditional
mathematical exercises to give students a full set of tools for
model analysis. Each chapter contains additional case studies in
the form of projects with detailed directions. New appendices
contain mathematical details on optimization, numerical solution of
differential equations, scaling, linearization, and sophisticated
use of elementary algebra to simplify problems.
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