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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
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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