Model structure and relevant variables are shown with respect to the antigenic type ax within a system with two alleles (a and b) at one locus and two alleles (x and y) at another (see model description in text for explanation).

Changes in the proportions of hosts that are infectious for the 12 different strains within a (3 × 4) system for various values of (γ, δ). (a) γ = 0.75, δ = 0.2. (b) γ = 0.6, δ = 0.0. (c) γ = 0.58, δ = 0.4. Model parameters used were μ = 0.02, b = 40, and s = 10. In each case, the black line tracks the fate of one particular (possibly hypervirulent) strain.

The intensity of single-strain dominance, ε, is shown for a variety of combinations of numbers of alleles (n × m) at two loci within the (γ, δ) parameter space. See model description in text for definitions of γ and δ. Other model parameters used were μ = 0.02, b = 40, and s = 10. The number of peaks, P, varied according to the convergence rate of ε.

Antigenic map of influenza. (a) Changes in the proportions of hosts that are infectious for the 32 different strains within a (2 × 2 × 2 × 2 × 2) system with δ = 0 and γ = 0.8. Other model parameters used were μ = 0.014, b = 400, and s = 100. The superimposed time series are not labeled by strain; however, this information is provided in SI. Twenty-five infected individuals were randomly sampled from the model population at 15 time points, corresponding to the peaks of 15 successive epidemics (dotted lines). Circles highlight the relative frequencies of the strains that were sampled at each time point. (b) The antigenic map of the sampled isolates, calculated by using multivariate analysis (see Methods for further details). Each circle represents one of the 375 sampled infected individuals, colored and labeled by time point. Each point was subjected to a small amount of random noise to simulate measurement error. (c) The antigenic map of human influenza A isolates sampled between 1968 and 2002 (adapted from ref. 18 with permission), calculated by using the same multivariate statistical analysis (see Methods).