Network and Algebraic Topology of Influenza Evolution
With respect to human infection, there are two types of influenza—seasonal and pandemic influenza—that each present a unique set of problems.
Although vaccines pose the best means of preventing seasonal influenza infection, strain selection and optimal implementation remain difficult due to antigenic drift and a lack of understanding global spread. Detecting viral movement by sequence analysis is complicated by skewed geographic and seasonal distributions in viral isolates. We propose a probabilistic method that accounts for this sampling bias and represents the global spread of seasonal influenza as a network of transmission events between different climates, continents, and even countries. Network analysis suggests China and Hong Kong as the origins of new seasonal H3N2 strains and USA as a region where increased vaccination would maximally disrupt global spread of the virus.
Pandemic strains of influenza often arise through a combination of mutational drift and reassortment. The classic representation of this evolutionary process is through phylogenetic construction; however, a single phylogeny cannot faithfully represent the evolutionary history of all genes in a virus that has reasserted. Drawing from algebraic topology, we present a novel evolutionary analysis of influenza independent of phylogeny. We show that while clonal evolution can be summarized as a tree, reassortment exhibits non-trivial topology of dimension greater than zero. Our method effectively characterizes influenza undergoing both clonal evolution and reassortment. Beyond simple detection of reassortments, we succinctly recapitulate the history of complex genetic exchanges involving more than two parental strains, such as the triple reassortment of H7N9 avian influenza. In addition, we identify global patterns of reticulate evolution, including frequent PB2-PB1-PA-NP co-segregation during avian influenza reassortment. Finally, we bound the rate of reticulate events (i.e., 20 reassortments per year in avian influenza). Our method not only captures reticulate events precluding phylogeny, but also indicates the evolutionary scales where phylogenetic inference could be accurate.