Mathematics and epidemiology: an uneasy friendship

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Mathematics and epidemiology an uneasy
friendship

• David Ozonoff, MD, MPH
• Boston University School of Public Health

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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

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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

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Epidemiologists on modeling

• Modelers dont 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)

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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
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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

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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

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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