Antigenic distance and cross-immunity, invasibility and coexistence of pathogen strains in an epidemiological model with discrete antigenic space

In models of pathogen interaction and evolution discrete genotypes in the form of bit strings may be mapped to points in a discrete phenotype space based on similarity in antigenic structure. Cross-immunity between strains. that is the reduction in Susceptibility to strain A conferred to a host by infection with strain B, call then be defined for pairs of points in the antigenic space by a specified function Analysis of an SIR type model shows that, if two strains are at equilibrium, the shape of the cross-immunity function has a strong influence on the invasion and coexistence of a third strain and, consequently, the expected evolutionary pathway. A function that is constant except for discontinuities at the end points is expected to result in the accumulation of diversity until a pair of discordant strains occurs that call, depending on parameter values, exclude all other strains. For a function of the form f (h) = h(q), where h is the antigenic distance between two strains, invasion and coexistence is always possible if q