Epidemic Modelling: An Introduction

This book tells what we knew about the mathematics of epidemics up until 1990. The differential equations (beginning with Bernoulli and moving forward) are presented well. That is, the variables are defined in the text and not too many steps are skipped in the derivations. The high point in this type of epidemiology came in 1927, when Kermack and McKendrick wrote the continuous-time epidemic equations. Diseases were characterized by the parameter rho, the relative removal rate. Up until the 1990s, we were just fitting our data to this model, and estimating rho.
Along came 'computational biology', or 'agent-based models' or 'numerical methods'. After 1990, these new techniques allowed us to escape from the perfect-mixing assumption that caused the Kermack and McKendrick model to depart from reality. With computation, we were able to see the impact of social networks, targeted innoculuations, and to test the value of different intervention strategies. See March 2005 Scientific American. None of those advances are discussed in this book. As a historical treatise, however, it is a superb addition to the library.