Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment

This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.

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Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.479-481.1495 ◽

2012 ◽

Vol 479-481 ◽

pp. 1495-1498 ◽

Cited By ~ 1

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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Positive Recurrence and Extinction of Hybrid Stochastic SIRS Model with Nonlinear Incidence Rate

Journal of Mathematics ◽

10.1155/2021/6699024 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Liang Chen ◽

Shan Wang

Keyword(s):

Incidence Rate ◽

Dynamic Behavior ◽

Nonlinear Incidence Rate ◽

Positive Recurrence ◽

Nonlinear Incidence ◽

Sirs Model

In this paper, the dynamic behavior of a class of hybrid SIRS model with nonlinear incidence is studied. Firstly, we provide the condition under which the positive recurrence exists and then give the threshold R 0 S for disease extinction, that is, when R 0 S < 1 , the disease will die out. Finally, some examples are constructed to verify the conclusion.

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Extinction and persistence of a stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible

Journal of Physics Conference Series ◽

10.1088/1742-6596/1324/1/012016 ◽

2019 ◽

Vol 1324 ◽

pp. 012016

Author(s):

Qiuhua Zhang ◽

Kai Zhou

Keyword(s):

Incidence Rate ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Sirs Model

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Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2962 ◽

2013 ◽

Vol 37 (14) ◽

pp. 2150-2163

Author(s):

Rui Xu ◽

Xiaohong Tian

Keyword(s):

Hopf Bifurcation ◽

Incidence Rate ◽

Epidemic Model ◽

Stage Structure ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence

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Stability and Hopf bifurcation analysis of an SEIR model with nonlinear incidence rate and relapse

Journal of Statistics and Management Systems ◽

10.1080/09720510.2016.1228321 ◽

2017 ◽

Vol 20 (3) ◽

pp. 483-497

Author(s):

B. G. Sampath Aruna Pradeep ◽

Wanbiao Ma ◽

Wei Wang

Keyword(s):

Hopf Bifurcation ◽

Incidence Rate ◽

Bifurcation Analysis ◽

Nonlinear Incidence Rate ◽

Seir Model ◽

Nonlinear Incidence

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Stability and Hopf bifurcation analysis of an SIS epidemic model with latency and nonlinear incidence rate

10.1063/1.5136445 ◽

2019 ◽

Author(s):

Anthony M. Pasion ◽

Juancho A. Collera

Keyword(s):

Hopf Bifurcation ◽

Incidence Rate ◽

Bifurcation Analysis ◽

Epidemic Model ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Sis Epidemic Model ◽

Sis Epidemic

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Dynamics Analysis of an SEIQS Model with a Nonlinear Incidence Rate

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.157-158.1220 ◽

2012 ◽

Vol 157-158 ◽

pp. 1220-1223

Author(s):

Ning Cui ◽

Jun Hong Li ◽

Jiao Qu ◽

Hong Dan Xue

Keyword(s):

Lyapunov Function ◽

Incidence Rate ◽

Matrix Theory ◽

Invariant Set ◽

Dynamics Analysis ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Asymptotical Stable ◽

Compound Matrix ◽

Disease Free

This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.

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Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.155-156.23 ◽

2012 ◽

Vol 155-156 ◽

pp. 23-26

Author(s):

Jun Hong Li ◽

Ning Cui ◽

Liang Cui ◽

Cai Juan Li

Keyword(s):

Hopf Bifurcation ◽

Dynamic Analysis ◽

Numerical Simulations ◽

Epidemic Model ◽

Global Dynamics ◽

Nonlinear Incidence Rate ◽

Dulac Function ◽

Sirs Epidemic Model ◽

Sirs Model ◽

Disease Free

In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical 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 an- alytical results.

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