Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

Jun Hong Li; Ning Cui; Liang Cui; Cai Juan Li

doi:10.4028/www.scientific.net/AMM.155-156.23

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 155-156Dynamic Analysis of an SIRS Model with Nonlinear...

Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

Abstract:

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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Periodical:

Applied Mechanics and Materials (Volumes 155-156)

Pages:

23-26

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.155-156.23

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Online since:

February 2012

Authors:

Jun Hong Li, Ning Cui, Liang Cui, Cai Juan Li

Keywords:

Global Stability, Hopf Bifurcation, Limit Cycle, Simulation, SIRS Model

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References

[1] Zhixing Hu, Ping Bi, et al. Bifurcations of an SIRS epidemic model with nonlinear incidence rate. Discrete and Continuous Dynamical Systems Series B, 2011, 15(1) 93-112.

Google Scholar

[2] Wendi Wang, Shigui Ruan. Bifurcations in an epidemic model with constant removal rate of the infectives. J. Math. Appl. 291(2004) 775-793.

DOI: 10.1016/j.jmaa.2003.11.043

Google Scholar

[3] G. Li, W. Wang. Bifurcation analysis of an epidemic model with nonlinear incidence rate. Appl. Math. Comput., 214(2009) 411-423.

Google Scholar

[4] Yu Jin, Wendi Wang, Shiwu Xiao. An SIRS model with a nonlinear incidence rate. Chaos, Solit- ons and Fractals, 34(2007) 1482-1497.

DOI: 10.1016/j.chaos.2006.04.022

Google Scholar

[5] W. M. Liu, S. A. Levin, Y. Iwasa. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol., 23(1986) 187-204.

DOI: 10.1007/bf00276956

Google Scholar

[6] Ruan S, Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. Journal of Differential Equations, 188(2003) 135-163.

DOI: 10.1016/s0022-0396(02)00089-x

Google Scholar

[7] Dongmei Xiao, Shigui Ruan. Global analysis of an epidemic model with nonmonotone incidence rate. Mathematical Biosciences, 208(2007) 419-429.

DOI: 10.1016/j.mbs.2006.09.025

Google Scholar

[8] T.K. Kar et al. Modeling and analysis of an epidemic model with non-monotonic incidence rate under treatment. Journal of Mathematics Research, 2010, 2(1) 103-115.

Google Scholar