Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate

Wanbiao Ma; Yasuhiro Takeuchi

doi:10.3934/dcdsb.2004.4.671

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2004, Volume 4, Issue 3: 671-678. Doi: 10.3934/dcdsb.2004.4.671

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Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate

Wanbiao Ma^1, and
Yasuhiro Takeuchi^2,

1.
Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083
2.
Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561

Received: October 31, 2002

Revised: December 31, 2003

Published: July 2005

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Abstract

In this paper, we consider a delayed $SIR$ epidemic model with density dependent birth process. For the model with larger birth rate, we discuss the asymptotic property of its solutions. Furthermore, we also study the existence of Hopf bifurcation from the endemic equilibrium of the model and local asymptotic stability of the endemic equilibrium.

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Mathematics Subject Classification: Primary: 34K20, 34KD05, 45J05, 92D30.

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