Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

2019 ◽  
Vol 29 (3) ◽  
pp. 033129 ◽  
Author(s):  
Chun-Hsien Li ◽  
A. M. Yousef
Keyword(s):  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Saturated Treatment

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.

Discrete-Time Fractional Order SIR Epidemic Model with Saturated Treatment Function

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mahmoud A. M. Abdelaziz ◽  
Ahmad Izani Ismail ◽  
Farah A. Abdullah ◽  
Mohd Hafiz Mohd
Keyword(s):  
Numerical Simulations ◽  
Discrete Time ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sir Epidemic Model ◽  
Delayed Treatment ◽  
Sir Epidemic ◽  
Treatment Function ◽  
Saturated Treatment

AbstractIn this paper, a discrete-time fractional-order SIR epidemic model with saturated treatment function is investigated. The local asymptotic stability of the equilibrium points is analyzed and the threshold condition basic reproduction number is derived. Backward bifurcation is shown when the model possesses a stable disease-free equilibrium point and a stable endemic point coexisting together when the basic reproduction number is less than unity. It is also shown that when the treatment is partially effective, a transcritical bifurcation occurs at $\Re_{0}=1$ and reappears again when the effect of delayed treatment is getting stronger at $\Re_{0}<1$. The analysis of backward and forward bifurcations associated with the transcritical, saddle-node, period-doubling and Neimark–Sacker bifurcations are discussed. Numerical simulations are carried out to illustrate the complex dynamical behaviors of the model. By carrying out bifurcation analysis, it is shown that the delayed treatment parameter ε should be less than two critical values ε1 and ε2 so as to avoid $\Re_{0}$ belonging to the dangerous range $\left[ \Re_{0},1\right]$. The results of the numerical simulations support the theoretical analysis.

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.

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