American Institute of Mathematical Sciences

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August  2004, 4(3): 671-678. doi: 10.3934/dcdsb.2004.4.671

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, China
2. 

Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan

Received  November 2002 Revised  January 2004 Published  May 2004

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.
Keywords: time delay, Epidemic model, asymptotic stability..
Mathematics Subject Classification: Primary: 34K20, 34KD05, 45J05, 92D3.
Citation: Wanbiao Ma, Yasuhiro Takeuchi. Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 671-678. doi: 10.3934/dcdsb.2004.4.671
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