This book provides a systematic treatment of the mathematical
underpinnings of work in the theory of outbreak dynamics and their
control, covering balanced perspectives between theory and practice
including new material on contemporary topics in the field of infectious
disease modelling. Specifically, it presents a unified mathematical
framework linked to the distribution theory of non-negative random
variables; the many examples used in the text, are introduced and
discussed in light of theoretical perspectives.
The book is organized into 9 chapters: The first motivates the
presentation of the material on subsequent chapters; Chapter 2-3
provides a review of basic concepts of probability and statistical
models for the distributions of continuous lifetime data and the
distributions of random counts and counting processes, which are linked
to phenomenological models. Chapters 4 focuses on dynamic behaviors of a
disease outbreak during the initial phase while Chapters 5-6 broadly
cover compartment models to investigate the consequences of epidemics as
the outbreak moves beyond the initial phase. Chapter 7 provides a
transition between mostly theoretical topics in earlier chapters and
Chapters 8 and 9 where the focus is on the data generating processes and
statistical issues of fitting models to data as well as specific
mathematical epidemic modeling applications, respectively.
This book is aimed at a wide audience ranging from graduate students to
established scientists from quantitatively-oriented fields of
epidemiology, mathematics and statistics. The numerous examples and
illustrations make understanding of the mathematics of disease
transmission and control accessible. Furthermore, the examples and
exercises, make the book suitable for motivated students in applied
mathematics, either through a lecture course, or through self-study.
This text could be used in graduate schools or special summer schools
covering research problems in mathematical biology.
