Mathematical modeling is one of the newest methods being used to understand how and why infectious diseases evolve and spread across the landscape. The development of this approach has been aided by dramatic improvements in computer power over the last quarter century. Mathematical modeling is a general approach that allows researchers to 'experiment' and test hypotheses about the mechanisms for disease evolution and transmission, without having to use the obviously unethical approaches of real human experimentation.
This chapter will begin by describing some of the major questions being addressed by anthropologists, mathematicians, and biologists interested in the evolution, transmission, and spread of infectious diseases. Following this, the principal modeling techniques used to answer these questions will be described. The chapter will conclude by illustrating the process of infectious disease modeling with a study of the impact of population travel patterns on the spread of a 1984 measles epidemic on the West Indian island of Dominica.
Population biologists traditionally study three fundamental ecological and evolutionary interactions: competition within and between species, predator-prey interactions, and the interaction between a pathogen and its host species. Mathematical modeling has been an important component in the study of these interactions for a century or more. Both mathematicians and ecologists have developed these models, resulting in a range of work from models focused on elegant but not necessarily practical formulations to those motivated by the need for answers to specific real-world problems. Underlying the best of these is a firm understanding of the essential biology of the ecological interaction considered. Consequently, before addressing the types of questions and models used in