title: The reinfection threshold regulates pathogen diversity: the case of influenza.
abstract: The awareness that pathogens can adapt and evolve over relatively short time-scales is changing our view of infectious disease epidemiology and control. Research on the transmission dynamics of antigenically diverse pathogens is progressing and there is increasing recognition for the need of new concepts and theories. Mathematical models have been developed considering the modelling unit in two extreme scales: either diversity is not explicitly represented or diversity is represented at the finest scale of single variants. Here, we use an intermediate approach and construct a model at the scale of clusters of variants. The model captures essential properties of more detailed systems and is much more amenable to mathematical treatment. Specificities of pathogen clusters and the overall potential for transmission determine the reinfection rates. These are, in turn, important regulators of cluster dynamics. Ultimately, we detect a reinfection threshold (RT) that separates different behaviours along the transmissibility axis: below RT, levels of infection are low and cluster substitutions are probable; while above RT, levels of infection are high and multiple cluster coexistence is the most probable outcome.
authors.affiliation: Instituto Gulbenkian de Ciência, Apartado 14, 2781-901 Oeiras, Portugal.
authors.forename: Dinis
authors.initials: D
authors.lastname: Gökaydin
authors.forename: José B
authors.initials: JB
authors.lastname: Oliveira-Martins
authors.forename: Isabel
authors.initials: I
authors.lastname: Gordo
authors.forename: M Gabriela M
authors.initials: MG
authors.lastname: Gomes
mesh_terms: D000818:Animals; D000940:Antigenic Variation / Q000235:genetics / Q000276:immunology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data*; D014644:Genetic Variation / Q000235:genetics; D006801:Humans; D009980:Influenza A virus / Q000235:genetics / Q000276:immunology*; D007251:Influenza, Human / Q000453:epidemiology* / Q000235:genetics / Q000276:immunology*; D018448:Models, Immunological; D011157:Population Dynamics