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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

 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.
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 and 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), 931-952. doi: 10.3934/mbe.2011.8.931. [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), 1-14. doi: 10.1016/j.jmaa.2010.10.010. [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), 1897-1910. doi: 10.1016/j.nonrwa.2010.12.002. [4] R. Xu and Y. Du, A delayed SIR epidemic model with saturation incidence and constant infectious period, J. Appl. Math. Comput., 35 (2010), 229-250. doi: 10.1007/s12190-009-0353-3. [5] R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos, Solitons & Fractals, 41 (2009), 2319-2325. doi: 10.1016/j.chaos.2008.09.007. [6] R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence, Nonlinear Dynam., 61 (2010), 229-239. doi: 10.1007/s11071-009-9644-3.

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##### References:
 [1] E. Beretta and D. Breda, An SEIR epidemic model with constant latency time and infectious period, Math. Biosci. Eng., 8 (2011), 931-952. doi: 10.3934/mbe.2011.8.931. [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), 1-14. doi: 10.1016/j.jmaa.2010.10.010. [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), 1897-1910. doi: 10.1016/j.nonrwa.2010.12.002. [4] R. Xu and Y. Du, A delayed SIR epidemic model with saturation incidence and constant infectious period, J. Appl. Math. Comput., 35 (2010), 229-250. doi: 10.1007/s12190-009-0353-3. [5] R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos, Solitons & Fractals, 41 (2009), 2319-2325. doi: 10.1016/j.chaos.2008.09.007. [6] R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence, Nonlinear Dynam., 61 (2010), 229-239. doi: 10.1007/s11071-009-9644-3.
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