American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Direct exponential ordering for neutral compartmental systems with non-autonomous $\mathbf{D}$-operator
  • DCDS-B Home
  • This Issue
  • Next Article
    Exact travelling wave solutions and their dynamical behavior for a class coupled nonlinear wave equations
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

[1]

Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016
[2]

C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837-850. doi: 10.3934/mbe.2010.7.837
[3]

Zhixing Hu, Ping Bi, Wanbiao Ma, Shigui Ruan. Bifurcations of an SIRS epidemic model with nonlinear incidence rate. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 93-112. doi: 10.3934/dcdsb.2011.15.93
[4]

Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 133-149. doi: 10.3934/dcdsb.2016.21.133
[5]

Yoshiaki Muroya, Toshikazu Kuniya, Yoichi Enatsu. Global stability of a delayed multi-group SIRS epidemic model with nonlinear incidence rates and relapse of infection. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3057-3091. doi: 10.3934/dcdsb.2015.20.3057
[6]

Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences & Engineering, 2004, 1 (1) : 57-60. doi: 10.3934/mbe.2004.1.57
[7]

Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 61-74. doi: 10.3934/dcdsb.2011.15.61
[8]

Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma. Complex dynamics of a simple epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 161-173. doi: 10.3934/dcdsb.2007.8.161
[9]

Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525
[10]

Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4223-4242. doi: 10.3934/dcdsb.2018134
[11]

Yoichi Enatsu, Yukihiko Nakata. Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate. Mathematical Biosciences & Engineering, 2014, 11 (4) : 785-805. doi: 10.3934/mbe.2014.11.785
[12]

Julia Amador, Mariajesus Lopez-Herrero. Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3137-3151. doi: 10.3934/dcdsb.2017211
[13]

Hong Yang, Junjie Wei. Global behaviour of a delayed viral kinetic model with general incidence rate. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1573-1582. doi: 10.3934/dcdsb.2015.20.1573
[14]

Jinhu Xu, Yicang Zhou. Global stability of a multi-group model with generalized nonlinear incidence and vaccination age. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 977-996. doi: 10.3934/dcdsb.2016.21.977
[15]

Chengzhi Li, Jianquan Li, Zhien Ma. Codimension 3 B-T bifurcations in an epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1107-1116. doi: 10.3934/dcdsb.2015.20.1107
[16]

Chengxia Lei, Fujun Li, Jiang Liu. Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4499-4517. doi: 10.3934/dcdsb.2018173
[17]

C. Connell McCluskey. Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2009, 6 (3) : 603-610. doi: 10.3934/mbe.2009.6.603
[18]

Jinliang Wang, Xianning Liu, Toshikazu Kuniya, Jingmei Pang. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2795-2812. doi: 10.3934/dcdsb.2017151
[19]

Wanbiao Ma, Yasuhiro Takeuchi. Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 671-678. doi: 10.3934/dcdsb.2004.4.671
[20]

Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 1119-1128. doi: 10.3934/proc.2011.2011.1119

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences