  Until now, design of the annual influenza vaccine has relied on phylogenetic
or whole-sequence comparisons of the viral coat proteins hemagglutinin and
neuraminidase, with vaccine effectiveness assumed to correlate monotonically to
the vaccine-influenza sequence difference. We use a theory from statistical
mechanics to quantify the non-monotonic immune response that results from
antigenic drift in the epitopes of the hemagglutinin and neuraminidase
proteins. The results explain the ineffectiveness of the 2003--2004 influenza
vaccine in the United States and provide an accurate measure by which to
optimize the effectiveness of future annual influenza vaccines.
