Epidemic influenza is responsible for between 250,000 and 500,000 global deaths annually, with influenza A (and in particular, A/H3N2) having caused the bulk of human mortality and morbidity [1
]. Influenza A (H3N2) has continually circulated within the human population since its introduction in 1968, exhibiting recurrent seasonal epidemics in temperate regions and less periodic transmission in the tropics. During this time, H3N2 influenza has continually evolved both genetically and antigenically. Most antigenic drift is thought to be driven by changes to epitopes in the hemagglutinin (HA) protein [2
]. Phylogenetic analysis of the relationships among HA sequences has revealed a distinctive genealogical tree showing a single predominant trunk lineage and side branches that persist for only 1 to 5 years before going extinct [3
]. This tree shape is indicative of serial replacement of strains over time; H3N2 influenza shows rapid evolution, but low standing genetic diversity.
This observation has remained puzzling from an epidemiological standpoint. Antigenic evolution occurs rapidly, and strong diversifying selection exists to escape from human immunity; why then do we see serial replacement of strains rather than continual genetic and antigenic diversification? Indeed, simple epidemiological models show explosive diversity of genotype and phenotype over time [4
]. Previous work has sought model-based explanations of the limited diversity of influenza, relying on short-lived strain-transcending immunity [4
], complex genotype-to-phenotype maps [6
], or a limited repertoire of antigenic phenotypes [7
Experimental characterization of antigenic phenotype is possible through the hemagglutination inhibition (HI) assay, which measures the cross-reactivity of HA from one virus strain to serum raised against another strain [8
]. The results of many HI assays can be combined to yield a two-dimensional map, representing antigenic similarity and distance between strains as an easily visualized and quantified measure [9
]. The path traced across this map by influenza A (H3N2) from 1968 until present is largely linear, showing serial replacement of one strain by another; there are no major bifurcations of antigenic phenotype [9
Herein, we seek to simultaneously model the genetic and antigenic evolution of the influenza virus. We represent antigenic phenotypes as points in a N
-dimensional Euclidean space. Based on the finding that a two-dimensional map adequately explains observed antigenic distance between strains [9
], we begin with antigenic phenotypes as points on a plane, but relax this assumption later on in the analysis. After exposure to a virus, a host's risk of infection is proportional to the Euclidean distance between the infecting phenotype and the closest phenotype in the host's immune history. Mutations perturb antigenic phenotype, moving phenotype in a random radial direction and for a randomly distributed distance. We implemented this geometrical model in a large-scale individual-based simulation intended to directly model the antigenic map and genealogical tree of the global influenza population. The simulation includes multiple host populations with different seasonal forcing, hosts with complete immune histories of infection, and viruses with antigenic phenotypes. As the simulation proceeds, infections are tracked and a complete genealogy connecting virus samples is constructed. Results shown here are for simulations of 40 years of virus evolution in a population of 90 million hosts.