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January  2013, 18(1): 173-183. doi: 10.3934/dcdsb.2013.18.173

A note on the global stability of an SEIR epidemic model with constant latency time and infectious period

Yoshiaki Muroya 1, , Yoichi Enatsu 2, and  Huaixing Li 3,

1. 

Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555
2. 

Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555
3. 

College of Sciences, Tianjin University of Technology, Binshui West Road, Xiqing District, 300384, China

Received  February 2012 Revised  August 2012 Published  September 2012

In this note, under the condition for the permanence used by [Beretta and Breda, An SEIR epidemic model with constant latency time and infectious period, Math. Biosci. Eng. 8 (2011) 931-952], applying modified monotone sequences, we establish the global asymptotic stability of the endemic equilibrium of this SEIR epidemic model, without any other additional conditions on the global stability.
Keywords: monotone iterative technique., global asymptotic stability, nonlinear incidence rate, SEIR epidemic model.
Mathematics Subject Classification: Primary: 34K19, 34K20, 92D3.
Citation: Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li. A note on the global stability of an SEIR epidemic model with constant latency time and infectious period. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 173-183. doi: 10.3934/dcdsb.2013.18.173
References:
[1]

E. Beretta and D. Breda, An SEIR epidemic model with constant latency time and infectious period,, Math. Biosci. Eng., 8 (2011), 931.  doi: 10.3934/mbe.2011.8.931.  Google Scholar

[2]

Y. Muroya, Y. Enatsu and Y. Nakata, Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate,, J. Math. Anal. Appl., 377 (2011), 1.  doi: 10.1016/j.jmaa.2010.10.010.  Google Scholar

[3]

Y. Muroya, Y. Enatsu and Y. Nakata, Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays,, Nonlinear Analysis RWA, 12 (2011), 1897.  doi: 10.1016/j.nonrwa.2010.12.002.  Google Scholar

[4]

R. Xu and Y. Du, A delayed SIR epidemic model with saturation incidence and constant infectious period,, J. Appl. Math. Comput., 35 (2010), 229.  doi: 10.1007/s12190-009-0353-3.  Google Scholar

[5]

R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate,, Chaos, 41 (2009), 2319.  doi: 10.1016/j.chaos.2008.09.007.  Google Scholar

[6]

R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence,, Nonlinear Dynam., 61 (2010), 229.  doi: 10.1007/s11071-009-9644-3.  Google Scholar

show all references

References:
[1]

E. Beretta and D. Breda, An SEIR epidemic model with constant latency time and infectious period,, Math. Biosci. Eng., 8 (2011), 931.  doi: 10.3934/mbe.2011.8.931.  Google Scholar

[2]

Y. Muroya, Y. Enatsu and Y. Nakata, Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate,, J. Math. Anal. Appl., 377 (2011), 1.  doi: 10.1016/j.jmaa.2010.10.010.  Google Scholar

[3]

Y. Muroya, Y. Enatsu and Y. Nakata, Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays,, Nonlinear Analysis RWA, 12 (2011), 1897.  doi: 10.1016/j.nonrwa.2010.12.002.  Google Scholar

[4]

R. Xu and Y. Du, A delayed SIR epidemic model with saturation incidence and constant infectious period,, J. Appl. Math. Comput., 35 (2010), 229.  doi: 10.1007/s12190-009-0353-3.  Google Scholar

[5]

R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate,, Chaos, 41 (2009), 2319.  doi: 10.1016/j.chaos.2008.09.007.  Google Scholar

[6]

R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence,, Nonlinear Dynam., 61 (2010), 229.  doi: 10.1007/s11071-009-9644-3.  Google Scholar

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