The use of antiviral drugs has been recognized as the primary public
health strategy for mitigating the severity of a new influenza pandemic
strain. However, the success of this strategy requires the prompt onset of
therapy within 48 hours of the appearance of clinical symptoms. The
evolution of drug resistance in the virus can also pose a problem for
antiviral treatment strategies. I'll present a compartmental model that
monitors the density of infected individuals in terms of the time elapsed
since the onset of symptoms. Such a model can be expressed by a system of
delay differential equations with both discrete and distributed delays,
and is based on the interaction between viral dynamics at the host level
and the spread of the disease in the population. It shows that treatment
alone is unlikely to control an outbreak unless other control measures to
reduce the spread of disease are also in place. Furthermore, we show that
levels of treatment that have a chance of controlling the disease will
also drive the emergence of drug resistant outbreaks. While an antiviral
treatment is helpful for containing a pandemic, its effectiveness depends
critically on timely and strategic use of drugs.

I will give a survey of what is known at present concerning the way solutions to the Porous medium equation "fill holes" in their support. There turn out to be some surprising similarities with Euclidean and Affine Curve Shortening.

Abstract
Oncogene signaling is known to deregulate cell proliferation re-
sulting in uncontrolled growth and cellular transformation. Gene
amplification and/or somatic mutations of the HER2/Neu (ErbB2)
protooncogene occur in approximately 20% of breast cancers. A
therapeutic strategy that has been used to block HER2 function is
the small molecule tyrosine kinase inhibitor lapatinib. Using human
mammary epithelial cells that overexpress HER2, we determined the
antiproliferative effect of lapatinib through measuring the total cell
number and analyzing the cell cycle distribution. A mathematical
model was used to interpret the experimental data. The model sug-
gests that lapatinib acts as expected by slowing the transition through
G1 phase. However, the experimental data indicated a previously un-
reported late cytotoxic effect, which was incorporated into the model.
Both effects depend on the dosage of the drug in a linearsaturating
fashion. The model separates quantitatively the cytostatic and cy-
totoxic effects of lapatinib and may have implications for preclinical
studies with other antioncogene therapies.
This is joint work with Dr. Shizhen Emily Wang (Department
of Cancer Biology, Vanderbilt University), Dr. Carlos Arteaga (De-
partment of Cancer Biology and Department of Medicine, Vanderbilt
University), and Dr. Glenn F. Webb, (Department of Mathematics,
Vanderbilt University).