-the seasonal peak value of R 0 , here termed R p , and its relative amplitude d (R p (1 -d) being the seasonal minimum value of R 0 ). Strictly, these parameters control overall transmissibility and the magnitude of seasonal forcing of transmission; -the timescale for the generation of antigenically new strains, represented by mean duration of immunity to the current influenza strain, D, and the crossimmunity between strains, f ( §2); -the degree of assortativity in the contact patterns between children and adults, u; -external force of infection, e, representing effect of contact between members of the modelled population and infected individuals outside the modelled population.