zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Global stability of an SIR epidemic model with constant infectious period. (English) Zbl 1136.92336
Summary: We derive and study an SIR epidemic model with constant infectious period which is incorporated as a time delay. Both trivial and endemic equilibria are found, and their stability is investigated. Using a Lyapunov functional approach, sufficient conditions for global stability of the endemic equilibrium are obtained.

MSC:
92D30Epidemiology
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] Takeuchi, Y.; Ma, W.; Beretta, E.: Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear anal. 42, 931-947 (2000) · Zbl 0967.34070
[2] Beretta, E.; Takeuchi, Y.: Global stability of an SIR epidemic mode1 with time delays. J. math. Biol. 83, 250-260 (1995) · Zbl 0811.92019
[3] Beretta, E.; Takeuchi, Y.: Convergence results in SIR epidemic mode1 with varying population sizes. Nonlinear anal. 28, 1909-1921 (1997) · Zbl 0879.34054
[4] Diekmann, O.; Heesterbeek, J. A. P.: Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. (2000) · Zbl 0997.92505
[5] Hethcote, Herbert W.; Tudor, David W.: Integral equation models for endemic infectious diseases. J. math. Biol. 9, 37-47 (1980) · Zbl 0433.92026
[6] Anderson, R. M.; May, R. M.: Infectious diseases of humans: dynamics and control. (1991)
[7] Grossman, H. W.: Osillatory phenomena in a model of infectious diseases. Theor. popul. Biol. 18, 204-243 (1980) · Zbl 0457.92020
[8] Kuang, Y.: Delay-differential equations with application in population biology. (1993) · Zbl 0777.34002
[9] Kyrychko, Yuliya N.; Blyuss, Konstantin B.: Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear anal., 495-507 (2005) · Zbl 1144.34374
[10] Keeling, M. J.; Grenfell, B. T.: Disease extinction and community size: modelling the persistence of measles. Science 275, 65-67 (1997)
[11] Hope-Simpson, R. E.: Infectiousness of communicable diseases in the household. Lancet 2, 549-554 (1952)