Following antigenic shift the new influenza variant is in competition with an incumbent strain that is already at equilibrium in the population which suggests that the growth rate r is small, so Wv0. From the perspective of directionality theory (Table S1 ) the favourable condition for establishment of the new type is higher entropy relative to the existing circulating sub-types (DSw0), i.e. a longer duration of infection. In the antigenic shift case we are addressing infection in the entire global population so, in effect the population of infectives, N is very large. Therefore the role of the demographic index term c (though again it will be small and ,0, for influenza) is minimal.