Bifurcation Analysis of Discrete SIS Model with Saturated Incidence and Saturated Treatment Function

2019 ◽  
Vol 08 (04) ◽  
pp. 242-247
Author(s):  
雨青 陈
Keyword(s):  
Bifurcation Analysis ◽  
Sis Model ◽  
Treatment Function ◽  
Saturated Incidence ◽  
Saturated Treatment

scholarly journals Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Yanju Xiao ◽  
Weipeng Zhang ◽  
Guifeng Deng ◽  
Zhehua Liu
Keyword(s):  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sis Model ◽  
Delayed Treatment ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Lyapunov Coefficient ◽  
Saturated Treatment ◽  
Theoretical Results ◽  
Disease Free

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

scholarly journals Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jinhong Zhang ◽  
Jianwen Jia ◽  
Xinyu Song
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Treatment Function ◽  
Threshold Conditions ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Saturated Treatment

The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.

scholarly journals Qualitative and bifurcation analysis using an SIR model with a saturated treatment function

2012 ◽  
Vol 55 (3-4) ◽  
pp. 710-722 ◽  
Author(s):  
Jinliang Wang ◽  
Shengqiang Liu ◽  
Baowen Zheng ◽  
Yasuhiro Takeuchi
Keyword(s):  
Bifurcation Analysis ◽  
Sir Model ◽  
Treatment Function ◽  
Saturated Treatment
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