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Seasonal influenza causes vast public health and economic impact globally. The prevention and control of the annual epidemics remain a challenge due to the antigenic evolution of the viruses. Here, we presented a novel modeling framework based on changes in amino acid sequences and relevant epidemiological data to retrospectively investigate the competitive evolution and transmission of H1N1 and H3N2 influenza viruses in the United States during October 2002 and April 2019. To do so, we estimated the time-varying disease transmission rate from the reported influenza cases and the time-varying evolutionary rate of the viruses from the changes in amino acid sequences. By incorporating these time-varying rates into the transmission models, we found that the models could accurately capture the evolutionary transmission dynamics of influenza viruses in the United States. Our modeling results also showed that models incorporating evolutionary change of the virus could provide better modeling performance suggesting the critical role of the evolutionary change of virus on the disease transmission.

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