Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators

Horst Thieme

doi:10.1016/j.jde.2011.01.007

Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators

Horst Thieme

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

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.

Original language	English (US)
Pages (from-to)	3772-3801
Number of pages	30
Journal	Journal of Differential Equations
Volume	250
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2011.01.007
State	Published - May 1 2011

Keywords

(Global) compact attractor
Extinction
Nonlinear incidence
Primary
Secondary
Threshold behavior
Uniform persistence
Volterra Lyapunov function

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2011.01.007

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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",

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doi = "10.1016/j.jde.2011.01.007",

language = "English (US)",

volume = "250",

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journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Global stability of the endemic equilibrium in infinite dimension

T2 - Lyapunov functions and positive operators

AU - Thieme, Horst

N1 - Funding Information: I thank Gauthier Sallet for useful remarks and for pointing me to the occurrence of the Volterra Lyapunov function in Volterra’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.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - 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.

AB - 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.

KW - (Global) compact attractor

KW - Extinction

KW - Nonlinear incidence

KW - Primary

KW - Secondary

KW - Threshold behavior

KW - Uniform persistence

KW - Volterra Lyapunov function

UR - https://www.scopus.com/pages/publications/79952039681

UR - https://www.scopus.com/pages/publications/79952039681#tab=citedBy

U2 - 10.1016/j.jde.2011.01.007

DO - 10.1016/j.jde.2011.01.007

M3 - Article

SN - 0022-0396

VL - 250

SP - 3772

EP - 3801

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators

Abstract

Keywords

ASJC Scopus subject areas

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