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Global stability of an epidemic model with age-dependent vaccination, latent and relapse

Author

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  • Li, Yingke
  • Teng, Zhidong
  • Hu, Cheng
  • Ge, Qing

Abstract

The vaccination, latent and relapse period are three important factors affecting the whole disease development. In this paper, we propose an SVEIR epidemic model with continuous age-dependent vaccination, latency and relapse, at the same time, the nonlinear incidence rate is also considered. Uniform persistence of the model is proved by reformulating it as the so called Volterra integral equations. The basic reproduction number R0, which completely determines the global dynamics of the model, is derived. By using Lyapunov functionals, the global stability of the equilibria is obtained. Namely, the disease-free equilibrium is globally asymptotically stable if R0<1, while if R0>1 the endemic equilibrium is globally asymptotically stable. Finally, two numerical examples support our main analytical results.

Suggested Citation

  • Li, Yingke & Teng, Zhidong & Hu, Cheng & Ge, Qing, 2017. "Global stability of an epidemic model with age-dependent vaccination, latent and relapse," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 195-207.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:195-207
    DOI: 10.1016/j.chaos.2017.10.027
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    Citations

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    Cited by:

    1. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    2. Matthias Klumpp & Dominic Loske & Silvio Bicciato, 2022. "COVID-19 health policy evaluation: integrating health and economic perspectives with a data envelopment analysis approach," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 23(8), pages 1263-1285, November.
    3. Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    4. Sun, Dandan & Teng, Zhidong & Wang, Kai & Zhang, Tailei, 2023. "Stability and Hopf bifurcation in delayed age-structured SVIR epidemic model with vaccination and incubation," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Chen, Yi & Wang, Lianwen & Zhang, Jinhui, 2024. "Global asymptotic stability of an age-structured tuberculosis model: An analytical method to determine kernel coefficients in Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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