scholarly journals Qualitative analysis of a SIR epidemic model with saturated treatment rate

2009 ◽  
Vol 34 (1-2) ◽  
pp. 177-194 ◽  
Author(s):  
Zhang Zhonghua ◽  
Suo Yaohong
Keyword(s):  
Qualitative Analysis ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Sir Epidemic ◽  
Saturated Treatment

scholarly journals Bifurcation analysis of an SIR epidemic model with saturated treatment function

2021 ◽  
Author(s):  
Phuc Ngo
Keyword(s):  
Epidemic Models ◽  
Stable Node ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Sir Epidemic Models ◽  
Saturated Treatment ◽  
Disease Free

In this thesis we investigate the dynamics and bifurcation of SIR epidemic models with horizontal and vertical transmissions and saturated treatment rate. It is proved that such SIR epidemic models always have positive disease free equilibria and also have three positive epidemic equilibria. The ranges of the parameters related in the model were found under which the equilibria of the models are positive. By applying the qualitative theory of planar systems, it is shown the disease free equilibria is a saddle, stable node and globally asymptotically stable. Furthermore, it is also shown that the interior equilibria are saddle, saddle node or saddle point.

scholarly journals Qualitative and Bifurcation Analysis of an SIR Epidemic Model with Saturated Treatment Function and Nonlinear Pulse Vaccination

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Xiangsen Liu ◽  
Binxiang Dai
Keyword(s):  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Existence And Stability ◽  
The Stability ◽  
Saturated Treatment ◽  
Disease Free

An SIR epidemic model with saturated treatment function and nonlinear pulse vaccination is studied. The existence and stability of the disease-free periodic solution are investigated. The sufficient conditions for the persistence of the disease are obtained. The existence of the transcritical and flip bifurcations is considered by means of the bifurcation theory. The stability of epidemic periodic solutions is discussed. Furthermore, some numerical simulations are given to illustrate our results.

scholarly journals Optimal Vaccination Strategies of an SIR Epidemic Model with a Saturated Treatment

2013 ◽  
Vol 1 (3) ◽  
pp. 185-191
Author(s):  
Hassan Laarabi ◽  
Mostafa Rachik ◽  
Ouafa El Kahlaoui ◽  
El Houssine Labriji
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Vaccination Strategies ◽  
Sir Epidemic ◽  
Saturated Treatment
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