Bulletin of Mathematical Biology

, Volume 80, Issue 3, pp 657–669 | Cite as

Estimation of Cross-Immunity Between Drifted Strains of Influenza A/H3N2

  • Sarder Mohammed Asaduzzaman
  • Junling Ma
  • P. van den Driessche
Original Article


To determine the cross-immunity between influenza strains, we design a novel statistical method, which uses a theoretical model and clinical data on attack rates and vaccine efficacy among school children for two seasons after the 1968 A/H3N2 influenza pandemic. This model incorporates the distribution of susceptibility and the dependence of cross-immunity on the antigenic distance of drifted strains. We find that the cross-immunity between an influenza strain and the mutant that causes the next epidemic is 88%. Our method also gives estimates of the vaccine protection against the vaccinating strain, and the basic reproduction number of the 1968 pandemic influenza.


Cross-immunity Drift evolution Vaccine protection Seasonal influenza strains Basic reproduction number Evolutionary tree 



This research is partially supported by NSERC Discovery grants to JM and PvdD. We thank the anonymous reviewers for their constructive comments and suggestions.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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