Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0991.92029
Li, Michael Y.; Smith, Hal L.; Wang, Liancheng
Global dynamics of an SEIR epidemic model with vertical transmission. (English)
[J] SIAM J. Appl. Math. 62, No.1, 58-69 (2001). ISSN 0036-1399; ISSN 1095-712X/e

Summary: We study a population model for an infectious disease that spreads in the host population through both horizontal and vertical transmission. The total host population is assumed to have constant density and the incidence term is of the bilinear mass-action form. We prove that the global dynamics are completely determined by the basic reproduction number $R_{0}(p,q)$, where $p$ and $q$ are fractions of infected newborns from the exposed and infectious classes, respectively. If $R_0(p,q)\le 1,$ the disease-free equilibrium is globally stable and the disease always dies out. If $R_{0}(p,q)>1$, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at an endemic equilibrium state if it initially exists. The contribution of the vertical transmission to the basic reproduction number is also analyzed.

MSC 2000:: *92D30 Epidemiology
34D23 Global stability
34D20 Lyapunov stability of ODE

Keywords: epidemic models; vertical transmission; endemic equilibrium; latent period; compound matrices

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

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

Advanced Search

Zentralblatt MATH Berlin [Germany]