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Global dynamics of an SEIS epidemiological model with time delay describing a latent period

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  • Xu, Rui

Abstract

In this paper, an SEIS epidemiological model with a saturation incidence rate and a time delay representing the latent period of the disease is investigated. By means of Lyapunov functional, LaSalle's invariance principle and comparison arguments, it is shown that the global dynamics is completely determined by the basic reproduction number. It is proven that the basic reproduction number is a global threshold parameter in the sense that if it is less than unity, the disease-free equilibrium is globally asymptotically stable and therefore the disease dies out; whereas if it is greater than unity, there is a unique endemic equilibrium which is globally asymptotically stable and thus the disease becomes endemic in the population. Numerical simulations are carried out to illustrate the main results.

Suggested Citation

  • Xu, Rui, 2012. "Global dynamics of an SEIS epidemiological model with time delay describing a latent period," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 90-102.
    • Handle: RePEc:eee:matcom:v:85:y:2012:i:c:p:90-102
    DOI: 10.1016/j.matcom.2012.10.004
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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. Hou, Juan & Teng, Zhidong, 2009. "Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3038-3054.
    3. Jansen, H. & Twizell, E.H., 2002. "An unconditionally convergent discretization of the SEIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 147-158.
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    2. 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.
    3. Kerr, Gilbert & González-Parra, Gilberto & Sherman, Michele, 2022. "A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Nian, Fuzhong & Hu, Chasheng & Yao, Shuanglong & Wang, Longjing & Wang, Xingyuan, 2018. "An immunization based on node activity," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 228-233.
    5. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.
    6. Li, Hong-Li & Zhang, Long & Teng, Zhidong & Jiang, Yao-Lin & Muhammadhaji, Ahmadjan, 2018. "Global stability of an SI epidemic model with feedback controls in a patchy environment," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 372-384.

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