Infectious disease modeling has become one of the hottest topics in mathematical biology but as I will show many of the models are suspect as certain basic mathematical techniques are overlooked. I will focus
on models
for HIV dynamics and show the ways that we can improve upon our
modeling of
diseases. For instance, numerous models have been used to predict
parameters from patient
data in HIV but applying a simple technique from algebra, called model
identifiability, I have
been able to show that the models we have been using are not
identifiable to the parameters.
Hence, we have begun to explore ways of putting modeling of ID on solid
ground using
techniques such as identifiability, sensitivity, and selection; also
techniques from
statistical methods such as bootstrapping and monte carlo.
I will comment on the progress that we have been making in these areas
and also comment on
improvements that we have found in modeling using delay differential
equations.
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