Mathematics and epidemiology: an uneasy friendship David Ozonoff, MD, MPH Boston University School of Public Health

Role of mathematics Applied mathematician –Conceptual economy –Strip extraneous details –Mathematical form is essence theories and science itself –Demonstration of what is logically possible Biologist –Ignoring details is weakness, not strength –Science need not be mathematical –Mathematical form is not necessarily science –Interested in what does explain, not what can explain

“Models” for biologist Usually means a model organism –E.g., fruitfly, E. coli, mouse or rat Stable target for explanation (Keller) Not a simplification but particular biological system with all its complexity

Epidemiologists on “modeling” Modelers don’t like to get their hands dirty with real data Uneasy with many non-data based elements (e.g., parameters or unrealistic assumptions) Real problems not well characterized May be used for non-scientific purposes (e.g., political “cover”)

“I spend my time trying to advance a science of infection transmission system analysis. An infection transmission system is that set of elements and processes that circulate infection through populations. Models that can interact with data are the basis of this science. Just plain deterministic compartmental (DC) models constructed from differential equations are a start for such a science but are inadequate on their own.” [epidemio-L] listserv, June 5, 2002

Important elements Recognize that observation is what makes something scientific and that the data are at the center of attention Recognize that explanatory power is connected to what is really happening, not to what could possibly be happening Recognize the powerful role of metaphor and image

Likely areas of collaboration Infectious disease models that respect important facts about disease transmission –Individuals are different in important ways –Interactions are not random –Biological processes are not instantaneous –Genetic effects are important All of these are now recognized in the most sophisticated research and responsible for success of this research area

Other areas Methods to detect unknown patterns in large, machine-readable datasets where there is lack of precision and accuracy Methods to extract specified kinds of data in large, machine-readable datasets where there is lack of precision and accuracy Order-theoretic methods as way to formalize practice (NB Special Focus Workshop) Combinations, e.g., SIRS models on scale-free networks