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Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate

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  • Li, Xue-Zhi
  • Zhou, Lin-Lin

Abstract

In this paper, the SEIR epidemic model with vertical transmission and the saturating contact rate is studied. It is proved that the global dynamics are completely determined by the basic reproduction number R0(p,q), where p and q are fractions of infected newborns from the exposed and infectious classes, respectively. If R0(p,q)⩽1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If R0(p,q)>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists.

Suggested Citation

  • Li, Xue-Zhi & Zhou, Lin-Lin, 2009. "Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 874-884.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:874-884
    DOI: 10.1016/j.chaos.2007.08.035
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    References listed on IDEAS

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    1. Jin, Yu & Wang, Wendi & Xiao, Shiwu, 2007. "An SIRS model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1482-1497.
    2. 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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    Cited by:

    1. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.
    2. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    3. Yin, Qian & Wang, Zhishuang & Xia, Chengyi & Dehmer, Matthias & Emmert-Streib, Frank & Jin, Zhen, 2020. "A novel epidemic model considering demographics and intercity commuting on complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Lan, Guijie & Song, Baojun & Yuan, Sanling, 2023. "Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. 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.

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