The coexistence or replacement of two subtypes of influenza

•A hybrid model is developed for the interaction of seasonal and pandemic inuenza A.•Pandemic subtype can replace seasonal one for intermediate levels of cross-immunity.•Pandemic and seasonal subtypes can coexist for high or low levels of cross-immunity.•Seasonal vaccination increases the chance of pandemic replacement.•Current seasonal vaccination rates only slightly increase this chance. A pandemic subtype of influenza A sometimes replaces but sometimes coexists with the previous seasonal subtype. For example, the 1957 pandemic subtype H2N2 replaced the seasonal subtype H1N1; whereas after 1977 subtypes H1N1 (from the pandemic) and H3N2 continue to coexist. In an attempt to understand these alternatives, a hybrid model for the dynamics of influenza A is formulated. During an epidemic season the model takes into account cross-immunity of strains depending on the most recent seasonal infection. This cross-immunity reduces susceptibility to related strains of the seasonal subtype, and wanes with time due to virus drift. The population is assumed to reach an equilibrium distribution in susceptibility after several seasons, and then a pandemic subtype appears. Individuals who have been infected by the seasonal subtype all have the same cross-immunity to the pandemic subtype. A combination of theoretical and numerical analyses shows that for very strong cross-immunity between the subtypes the pandemic cannot invade, whereas for strong and weak cross-immunity there is coexistence for the season following the pandemic, and for intermediate levels of cross-immunity the pandemic may replace the seasonal subtype. This replacement depends on the basic reproduction numbers of seasonal and pandemic influenza. Vaccination against the seasonal subtype is found to slightly increase this range for pandemic replacement, with the range increasing with increasing vaccine protection and with the length of time that vaccine-induced immunity lasts.