The Croonian Lecture, 1994. Populations, infectious disease and immunity: a very nonlinear world.

The interaction between the variables that determine the typical course of infection in an individual patient and those that determine transmission in communities of people is often complex and very nonlinear in form. Mathematical models of infection and immunity are used to study the interaction in a wide variety of problems including the role of antigenic variation in pathogen persistence in the host, the design of vaccination policies for the control of childhood viral infections, the role of heterogeneity in sexual behaviour as a determinant of the epidemiology of sexually transmitted diseases and the demographic impact of infectious disease on human population growth. The themes of dynamical complexity in outcome deriving from simple biological assumptions, the evolution of the parasite under selection by the immune system, heterogeneities in the interacting systems, and the necessity of comparing prediction with observation reoccur in each problem. It is argued that much is to be gained from the use of mathematics in biology, concomitant with experiment and observation, in providing precision in interpretation and in facilitating the formulation and testing of hypotheses to explain observed pattern. Special emphasis is placed on the need for interdisciplinary research on the epidemiology of infectious diseases that combines molecular, immunological, field study and theoretical approaches.