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.