Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

2011 ◽  
Vol 218 (5) ◽  
pp. 1682-1693 ◽  
Author(s):  
Chun-Hsien Li ◽  
Chiung-Chiou Tsai ◽  
Suh-Yuh Yang
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Birth Rate ◽  
Sir Epidemic Model ◽  
Density Dependent ◽  
Sir Epidemic ◽  
Distributed Time Delay

scholarly journals Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Shujing Gao ◽  
Zhidong Teng ◽  
Juan J. Nieto ◽  
Angela Torres
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Epidemic Model ◽  
Discrete Dynamical System ◽  
Vaccination Rate ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Distributed Time Delay ◽  
Large Pulse

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

Global asymptotic stability of an SIR epidemic model with distributed time delay

2001 ◽  
Vol 47 (6) ◽  
pp. 4107-4115 ◽  
Author(s):  
Edoardo Beretta ◽  
Tadayuki Hara ◽  
Wanbiao Ma ◽  
Yasuhiro Takeuchi
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Distributed Time Delay

scholarly journals Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Li Yingke ◽  
Chen Liang ◽  
Wang Kai
Keyword(s):  
Differential Equations ◽  
Epidemic Model ◽  
Birth Rate ◽  
Distributed Delay ◽  
Threshold Value ◽  
Sir Epidemic Model ◽  
Classical Analysis ◽  
Density Dependent ◽  
Analysis Techniques ◽  
Sir Epidemic

Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.

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