scholarly journals Flip bifurcations of an SIR epidemic model with birth pulse and pulse vaccination

2017 ◽  
Vol 43 ◽  
pp. 579-591 ◽  
Author(s):  
Xiangsen Liu ◽  
Binxiang Dai
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Birth Pulse ◽  
Sir Epidemic

scholarly journals Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Wencai Zhao ◽  
Juan Li ◽  
Xinzhu Meng
Keyword(s):  
Periodic Solution ◽  
Epidemic Model ◽  
Fixed Point Theory ◽  
Positive Periodic Solution ◽  
Point Theory ◽  
Dynamical Analysis ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Disease Free

SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. Lastly, some simulations are given to validate the theoretical results.

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.

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