Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1165.34421
Röst, Gergely; Wu, Jianhong
SEIR epidemiological model with varying infectivity and infinite delay. (English)
[J] Math. Biosci. Eng. 5, No. 2, 389-402 (2008). ISSN 1547-1063; ISSN 1551-0018/e

Summary: A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number $\cal R_0 $, which is a threshold quantity for the stability of equilibria, is calculated. If $\cal R_0 < 1$, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if $\cal R_0 > 1$, 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 $\cal R_0 > 1$.

MSC 2000:: *34K60 Applications of functional-differential equations
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Keywords: mathematical epidemiology; infinite delay; SEIR model; stability; permanence

Cited in: Zbl 1190.34108

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]