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Many viruses evolve rapidly. For example, hemagglutinin of the H3N2 influenzaA virus evolves to escape antibody binding. This evolution of the H3N2 virusmeans that people who have previously been exposed to an influenza strain maybe infected by a newly emerged virus. In this paper, we use Shannon entropy andrelative entropy to measure the diversity and selection pressure by antibody ineach amino acid site of H3 hemagglutinin between the 1992-1993 season and the2009-2010 season. Shannon entropy and relative entropy are two independentstate variables that we use to characterize H3N2 evolution. The entropy methodestimates future H3N2 evolution and migration using currently available H3hemagglutinin sequences. First, we show that the rate of evolution increaseswith the virus diversity in the current season. The Shannon entropy of thesequence in the current season predicts relative entropy between sequences inthe current season and those in the next season. Second, a global migrationpattern of H3N2 is assembled by comparing the relative entropy flows ofsequences sampled in China, Japan, the USA, and Europe. We verify this entropymethod by describing two aspects of historical H3N2 evolution. First, weidentify 54 amino acid sites in hemagglutinin that have evolved in the past toevade the immune system. Second, the entropy method shows that epitopes A and Bin the top of hemagglutinin evolve most vigorously to escape antibody binding.Our work provides a novel entropy-based method to predict and quantify futureH3N2 evolution and to describe the evolutionary history of H3N2.

Quantifying Selection and Diversity in Viruses by Entropy Methods, with Application to the Hemagglutinin of H3N2 Influenza