Antigenic evolution of viruses in host populations

To escape immune recognition in previously infected hosts, viruses evolve genetically in immunologically important regions. The host’s immune system responds by generating new memory cells recognizing the mutated viral strains. Despite recent advances in data collection and analysis, it remains conceptually unclear how epidemiology, immune response, and evolutionary factors interact to produce the observed speed of evolution and the incidence of infection. Here we establish a general and simple relationship between long-term cross-immunity, genetic diversity, speed of evolution, and incidence. We develop an analytic method fusing the standard epidemiological susceptible-infected-recovered approach and the modern virus evolution theory. The model includes the factors of selection due to immune memory cells, random genetic drift, and clonal interference effects. We predict that the distribution of recovered individuals in memory serotype creates fitness landscape for the circulating strains which drives antigenic escape. Analysis predicts that the rate of evolution is proportional to the reproductive number in the absence of immunity R₀ and inversely proportional to the cross-immunity distance a, defined as the genetic distance of a virus strain from a previously infecting strain conferring 50% decrease in infection probability. Evolution rate increases logarithmically with genomic mutation rate and host population size. Fitting our analytic model to genomic data obtained for influenza A H3N2, we obtain annual infection incidence within a previously estimated range (7%), estimate the antigenic mutation rate of U_b = 3 ⋅ 10⁻⁵ per transmission event, and predict the cross-immunity distance of a = 14.7 nucleotide substitutions confirmed by independent data.