title: Seir epidemiological model with varying infectivity and infinite delay.
abstract: A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when R0 > 1.
authors.affiliation: Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, Hungary, H-6720 Szeged, Aradi vértanúk tere 1. rost@math.u-szeged.hu
authors.forename: Gergely
authors.initials: G
authors.lastname: Röst
authors.forename: Jianhong
authors.initials: J
authors.lastname: Wu
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004196:Disease Outbreaks; D018572:Disease-Free Survival; D004813:Epidemiology; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D011157:Population Dynamics