Competitive evolution of H1N1 and H3N2 influenza viruses in the United States: A mathematical modeling study

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 antigenic change rate of the viruses from the changes in amino acid sequences. By incorporating the time-varying antigenic change rate into the transmission models, we found that the models could capture the evolutionary transmission dynamics of influenza viruses in the United States. Our modeling results also showed that the antigenic change of the virus plays an essential role in seasonal influenza dynamics.


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The spread of the influenza virus is a major public health threat that leads to mortality, 39 hospitalization, and an economic impact. Each year, there are one billion influenza cases globally, 40 including 3 to 5 million cases of severe illness 1,2 and at least 200,000 to 600,000 recorded deaths 3-41 6 . In the US, seasonal influenza accounts for more than tens of thousands of deaths during annual 42 epidemics 7 . Moreover, the economic burden of seasonal influenza in the US has been estimated at 43 more than ten billion dollars in healthcare and social costs 7 . The influenza epidemics recur   These evolutionary processes are believed to be a major driver of seasonal influenza 67 transmission 20 . 68 In the US, influenza subtype A(H3N2) emerges and spreads more frequently than 69 A(H1N1). Nevertheless, the two subtypes seem to be competitive for the susceptible hosts. Each 70 year, the subtype virus that gets the highest fitness from mutation may spread predominantly in 71 the population. In general, individuals infected with a single influenza strain will acquire immunity 72 against that specific strain 16,22 . Partial or cross-immunity to other subtypes is also observed 15,25-29 .

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However, the level of cross-immunity is weakening with an increasing antigenic change of the 74 influenza virus 2 . Therefore, co-circulation of the two influenza subtypes may result in cross-75 immunity.

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Mathematical models, specifically the compartmental frameworks, have been widely used 77 to investigate the transmission dynamics of influenza viruses. Most of the previous studies focused 78 on the impact of seasonality on influenza transmission dynamics 12,13,30-33 . Subsequently, the 79 evolution of these viruses has increasingly been studied as an important source of disease burden 6 .

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In this study, we investigated the impact of antigenic change on transmission dynamics of 92 seasonal influenza. We, therefore, proposed epidemiological models for seasonal influenza 93 A(H3N2) and A(H1N1) viruses that incorporate the antigenic changes of the viruses. The models 94 integrated the data on the changes of amino acid sequences of HA proteins in epitope sites into the 95 transmission models. To do so, we first estimated the time-varying antigenic change rate of each 96 influenza subtype using the sequence data. We then incorporated this antigenic change rate into 97 the transmission models to investigate the transmission dynamics of seasonal influenza in the US. 98 We utilized long-term influenza surveillance data 35 from October 2002 to April 2019 in the US to 99 fit the models. Finally, we demonstrated that antigenic changes of the virus could play an important 100 role in changing seasonal influenza transmission dynamics at the population level.  replaced by gaps. Aligned sequences were then edited using ClustalW, and the incomplete 125 sequences were manually removed 43,44 . Since the major target of immunity against influenza is 126 located in the epitope sites of the HA proteins 6,7,20 , we used only the amino acid sequences 127 encoding the epitope sites of these proteins to analyze the antigenic change of the virus. represented by an antigenic change rate ( ! ( )) as described in eq. (13). We assumed that recovered 142 individuals ( ) could become susceptible again at rate ! ( ) . The evolutionary and transmission 143 dynamics of influenza are described by the following ordinary differential equations (ODEs):  Table   152 1.

Evolution and transmission model with selective competition
182 "' !" 185  Table S1 and Table S2 in the Supplementary Information.

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To estimate the antigenic change among influenza viruses, we considered aligned amino    (Figure 3(B)). This result suggested that .//012!$3214 might be a potential   (Figure S4 and Figure S5 in the supplementary results). 331 We then further investigated the effects of cross-immunity between the two subtypes. The 332 strength of cross-immunity between the two influenza subtypes is represented by the parameter Ψ.  These results highlight the importance of incorporating the antigenic change rate into the model.