This is the abstract of a talk prepared for the Oeiras Mathematical and Computational Biology Workshop. June 20, 2003, Instituto Gulbenkian de Ciência
Abstract: The development of mathematical models to describe epidemic behaviour was initiated by Daniel Bernoulli (1766). His static model, specifically developed for smallpox, predicts the gain in life expectancy resulting from immunization. Smallpox is now eradicated, but the model applies to many other viruses capable of inducing lifelong immunity (such as measles, mumps, rubella). Dynamical models, consisting of systems of ODEs, were introduced in the early 1990s. Simple models are quickly constructed and analysed, constituting useful first line exploratory tools. Models are crucial to determine thresholds in transmission, providing important guidelines to control planning. Tuberculosis will be used for illustration.
Pathogens mutate and often recombine, generating a rich pool of antigenic types. The pressures of transmission and host immunity restrict diversity. Selection occurs and pathogen population structure emerges. Pathogen population structure and evolution must be related to the epidemic dynamics of the disease. But how? What can we say about control? How do interventions affect pathogen population structure, and what are the consequences for epidemic dynamics? Computational models are beginning to address these challenges. There is a desperate need for new ideas and talents. Flu will be used for illustration.
Mathematical and computational models arise out of assumed biological mechanisms. These are executed to produce outcomes comparable with observations. As the models increase in sophistication, so do the requirements for data collection and processing. And with this we leave my area of expertise, and enter my interest in this platform.