Abstract
The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level.
Highlights
Two subtypes of influenza type A virus (H3N2 and H1N1) cocirculate in human populations along with the influenza type B virus
Invasion condition of the mutant cluster We start our analysis by examining the dynamical impact of the four modelling assumptions (SBRS, Status based model with reduced infectivity (SBRI), history based model with reduced susceptibility (HBRS) and history based model with reduced infectivity (HBRI)) corresponding respectively to equations (1), (2) and (3)) thorough calculation of invasion conditions of the mutant cluster within the environment corresponding to the equilibrium of the resident cluster
In this paper we have focused on exploring to what extent the complex processes shaping influenza dynamics can be approximated by a minimal serial SIR system, emphasising rare mutations with strong antigenic effects
Summary
Two subtypes of influenza type A virus (H3N2 and H1N1) cocirculate in human populations along with the influenza type B virus. In temperate zones and during inter-pandemic periods, their dynamics lead to annual epidemics of variable amplitude caused by alternating types and subtypes [1]. Worldwide, these annual epidemics result in about three to five million cases of severe illness, and about 250 000 to 500 000 deaths [2]. The recurrence of influenza A epidemics is still not thoroughly understood despite a large amount of empirical and theoretical investigations It has originally been explained by the evolution of the main surface glycoproteins of the virus (mainly haemagglutinin, HA, and Neuraminidase, NA) inducing possible ‘‘reinfection’’ of previously infected hosts. This ‘‘continuous antigenic drift’’ scenario [3] where viruses continuously escape immunity as mutations accumulate has recently been challenged by new sequences data and theoretical developments
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