@article{9c2b93d39cf945a7b279e46e0d0bd318,
title = "Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators",
abstract = "The global stability of the endemic equilibrium is shown for an endemic model with infinite-dimensional population structure using a Volterra like Lyapunov function and the Krein-Rutman theorem.",
keywords = "(Global) compact attractor, Extinction, Nonlinear incidence, Primary, Secondary, Threshold behavior, Uniform persistence, Volterra Lyapunov function",
author = "Horst Thieme",
note = "Funding Information: I thank Gauthier Sallet for useful remarks and for pointing me to the occurrence of the Volterra Lyapunov function in Volterra{\textquoteright}s book [64]. I am grateful to Pierre Magal for helpful remarks concerning persistence attractors. I thank Tanya Kostova for pointing me to the paper [60] and Andrei Korobeinikov, Michael Li, and Connell McCluskey for sending me their preprints. This work was supported in part by NSF Grant DMS-0715451.",
year = "2011",
month = may,
day = "1",
doi = "10.1016/j.jde.2011.01.007",
language = "English (US)",
volume = "250",
pages = "3772--3801",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "9",
}