American Institute of Mathematical Sciences

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January  2007, 7(1): 77-86. doi: 10.3934/dcdsb.2007.7.77

Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission

Shujing Gao 1, , Dehui Xie 2, and  Lansun Chen 3,

1. 

College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
2. 

College of Business Administration, Gannan Normal University, Ganzhou 341000, China
3. 

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China

Received  October 2005 Revised  June 2006 Published  October 2006

Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. In this paper, a delayed SIR epidemic model with pulse vaccination and vertical transmission is proposed. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic infection-free solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if $R^$*$<1$. Moreover, we obtain that the disease is uniformly persistent if . Our results indicate that a large pulse vaccination rate is sufficient condition for the extinction of the disease.
Keywords: Permanence., Vertical transmission, Pulse vaccination, Global attractivity, SIR epidemic model, Delay.
Mathematics Subject Classification: Primary: 34A37, 34C25; Secondary: 92B0.
Citation: Shujing Gao, Dehui Xie, Lansun Chen. Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 77-86. doi: 10.3934/dcdsb.2007.7.77
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