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Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period

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  • Li, Guihua
  • Jin, Zhen

Abstract

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0⩽1, the disease-free equilibrium is globally stable and the disease always dies out. If R0>1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when α1=α2=0 and the disease persists at an endemic equilibrium state if it initially exists.

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  • Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1177-1184
    DOI: 10.1016/j.chaos.2004.11.062
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    1. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
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    2. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
    3. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
    4. Zhang, Tailei & Teng, Zhidong, 2009. "Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2411-2425.
    5. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    6. Wen, Luosheng & Yang, Xiaofan, 2008. "Global stability of a delayed SIRS model with temporary immunity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 221-226.
    7. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    8. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    9. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    10. Weibin Wang & Zeyu Xia, 2023. "Study of COVID-19 Epidemic Control Capability and Emergency Management Strategy Based on Optimized SEIR Model," Mathematics, MDPI, vol. 11(2), pages 1-31, January.
    11. Zhou, Yugui & Xiao, Dongmei & Li, Yilong, 2007. "Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1903-1915.
    12. Zhao, Zhong & Chen, Lansun & Song, Xinyu, 2008. "Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 500-510.
    13. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    14. Ndanguza, Denis & Mbalawata, Isambi S. & Haario, Heikki & Tchuenche, Jean M., 2017. "Analysis of bias in an Ebola epidemic model by extended Kalman filter approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 113-129.
    15. Mugnaine, Michele & Gabrick, Enrique C. & Protachevicz, Paulo R. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Batista, Antonio M. & Caldas, Iberê L. & Szezech Jr, José D. & V, 2022. "Control attenuation and temporary immunity in a cellular automata SEIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    16. Wang, Yi & Cao, Jinde, 2014. "Global dynamics of multi-group SEI animal disease models with indirect transmission," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 81-89.
    17. Wei, Fengying & Xue, Rui, 2020. "Stability and extinction of SEIR epidemic models with generalized nonlinear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 1-15.
    18. Meng, Xinzhu & Jiao, Jianjun & Chen, Lansun, 2009. "Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2114-2125.
    19. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.

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