Shaping the phylogenetic tree of influenza by cross-immunity

Coexistence conditions for strains of influenza with immune cross-reaction

“…We consider an extension of the model proposed by Andreasen and Sasaki (2006), hereafter denoted the AS-model. This framework focuses on the seasonal dynamics of influenza to separate the epidemiological and evolutionary timescales.…”

“…The proportional reduction in infectivity due to partial cross-immunity of hosts who are currently infected with strain A, have recovered from an infection with strain B in the current season, but have never been infected prior to the current season ( IR 0 ) is τ 2 . Following Andreasen and Sasaki (2006), we assume that the host population has experienced annual outbreaks of a single constantly evolving virus line (A) for a long time, and hence the fractions s k of hosts last infected k seasons ago are at steady state. The equilibrium values of s k at the onset of season are thus given by…”

“…A key feature of influenza A evolution is that, despite the appearance and spread of new strains each year, the vast majority become rapidly extinct and the number of persistent branches in the phylogenetic tree remains small (Bush et al 1999;Smith et al 2004;Holmes et al, 2005). One of the most important factors responsible for maintaining this slim phylogenetic tree is likely to be cross-immunity (Andreasen et al, 1997;Ferguson et al 2003; Koelle et al 2006, Andreasen andSasaki, 2006), whereby infection with one strain suppresses subsequent infections with antigenically similar strains. Cross-immunity is a major determinant of phylogenetic branching because it can make it difficult for a mutant strain to coexist with the parental or sibling strains.…”

“…To understand the ecology and evolution of influenza, it is vital to understand the way in which host immunity mediates the epidemiological and antigenic interaction of viral strains in the context of seasonal epidemics. An earlier study (Andreasen and Sasaki, 2006) considered a simple model in which discrete annual epidemics of influenza were assumed to be caused by antigenic variants derived from a common ancestor in the previous year. The variants occupied a low-dimensional antigenic space and emerged serially to cause sequential, non-overlapping epidemics.…”

“…The variants occupied a low-dimensional antigenic space and emerged serially to cause sequential, non-overlapping epidemics. This analysis indicated that strong temporary broad cross-immunity between all viral strains, a high basic reproductive rate and rapid decay in long term strain specific cross-immunity are required to prevent evolutionary branching and maintain the slim antigenic phylogeny of influenza (Andreasen and Sasaki, 2006). Empirical studies, however, show that antigenic variants do not appear in strict sequence each season and there may be extensive co-circulation.…”