scholarly journals Threshold dynamics of an SIRS model with nonlinear incidence rate and transfer from infectious to susceptible

2017 ◽  
Vol 70 ◽  
pp. 52-57 ◽  
Author(s):  
Ting Li ◽  
Fengqin Zhang ◽  
Hanwu Liu ◽  
Yuming Chen
Keyword(s):  
Incidence Rate ◽  
Threshold Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Model

An SIRS model with a nonlinear incidence rate

2007 ◽  
Vol 34 (5) ◽  
pp. 1482-1497 ◽  
Author(s):  
Yu Jin ◽  
Wendi Wang ◽  
Shiwu Xiao
Keyword(s):  
Incidence Rate ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Model

scholarly journals Coexistence of Limit Cycles and Homoclinic Loops in a SIRS Model with a Nonlinear Incidence Rate

2008 ◽  
Vol 69 (2) ◽  
pp. 621-639 ◽  
Author(s):  
Yilei Tang ◽  
Deqing Huang ◽  
Shigui Ruan ◽  
Weinian Zhang
Keyword(s):  
Incidence Rate ◽  
Limit Cycles ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sirs Model

scholarly journals Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Junyuan Yang ◽  
Xiaoyan Wang
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Age Dependent ◽  
The Basic Reproduction Number

We propose an SIR epidemic model with different susceptibilities and nonlinear incidence rate. First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next-generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number ℛ0 and some assumptions for the incidence rate.

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 479-481 ◽  
pp. 1495-1498 ◽  
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Hong Kai Sun
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Asymptotical Stable ◽  
Disease Free

An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

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