Global dynamics of an SEIR epidemic model with saturating contact rate.

Abstract:

:Heesterbeek and Metz [J. Math. Biol. 31 (1993) 529] derived an expression for the saturating contact rate of individual contacts in an epidemiological model. In this paper, the SEIR model with this saturating contact rate is studied. The basic reproduction number R0 is proved to be a sharp threshold which completely determines the global dynamics and the outcome of the disease. If R0 < or =1, the disease-free equilibrium is globally stable and the disease always dies out. If R0 > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists at an endemic equilibrium state if it initially exists. The contribution of the saturating contact rate to the basic reproduction number and the level of the endemic equilibrium is also analyzed.

journal_name

Math Biosci

journal_title

Mathematical biosciences

authors

Zhang J,Ma Z

doi

10.1016/s0025-5564(03)00087-7

subject

Has Abstract

pub_date

2003-09-01 00:00:00

pages

15-32

issue

1

eissn

0025-5564

issn

1879-3134

pii

S0025556403000877

journal_volume

185

pub_type

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