Each virion is placed at a point x in a 2D antigenic map — an abstraction (after Smith et al., "Mapping the Antigenic and Genetic Evolution of Influenza Virus", Science 2004) where distance stands in for how differently antibodies react to two strains. The map's dimensionality is a modelling choice, not part of the theory itself — the original antigenic-cartography method plots strains on a 2D plane by multidimensional scaling of pairwise assay data, so this projection uses exactly the same distance-based equations as a 3D antigenic space. The vaccine/last-infection strain sits at the origin, and a dashed circle of radius R marks the reach of existing neutralizing antibodies.
d(x) = |x| antigenic distance from origin
P_neutralize(d) = 1 / (1 + exp(k·(d − R))) soft boundary, k = steepness
P_clear = selection · P_neutralize(d) chance a virion is cleared this generation
Antigenic drift: every generation, each surviving virion mutates with probability = mutation rate, taking a random step in antigenic space (point substitutions in the hemagglutinin/neuraminidase epitopes). Virions that drift outside R are no longer recognized and are cleared far less often, so on average the population's mean distance from the origin creeps outward — the same positive selection for immune-escape variants that drives seasonal flu vaccines out of date. The chart below the map tracks that outward creep generation by generation.
Antigenic shift: the "reassortment" button instantly relocates a subset of the population to a distant random point — modeling two influenza strains (e.g. human + avian) swapping whole gene segments in a co-infected host and producing a novel HA subtype in one step, instead of many small mutations. This is the mechanism behind pandemic strains such as 2009 H1N1.
- Mutation rate — probability per generation that a given virion takes a drift step.
- Immune selection pressure — how aggressively the antibody repertoire clears virions still inside R; survivors replicate toward a fixed carrying capacity, so escaped variants make up a growing share of the population.
- Colour runs green (neutralized, inside R) → red (escaped, outside R).
- Drag the map to pan, scroll or pinch to zoom — the view follows the outbreak, it never resets it.