Each virion is placed at a point x in a 3D 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 vaccine/last-infection strain sits at the origin, and a translucent sphere 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the origin creeps outward — the same positive selection for immune-escape variants that drives seasonal flu vaccines out of date.
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).