title: Epidemiological models with age structure, proportionate mixing, and cross-immunity.
abstract: Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains, cross-immunity, age structure, and infectious disease dynamics. Simulation and analysis of models with cross-immunity indicate that sustained oscillations cannot be maintained by age-specific infection activity level rates when the mortality rate is constant; but are possible if mortalities are age-specific, even if activity levels are independent of age. Sustained oscillations do not seem possible for a single-strain model, even in the presence of age-specific mortalities; and thus it is suggested that the interplay between cross-immunity and age-specific mortalities may underlie observed oscillations.
authors.affiliation: Ecology and Systematics, Cornell University, Ithaca, NY 14853.
authors.forename: C
authors.initials: C
authors.lastname: Castillo-Chavez
authors.forename: H W
authors.initials: HW
authors.lastname: Hethcote
authors.forename: V
authors.initials: V
authors.lastname: Andreasen
authors.forename: S A
authors.initials: SA
authors.lastname: Levin
authors.forename: W M
authors.initials: WM
authors.lastname: Liu
mesh_terms: D000375:Aging; D004812:Epidemiologic Methods; D006801:Humans; D007109:Immunity; D007251:Influenza, Human / Q000453:epidemiology*; D008962:Models, Theoretical