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Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Author

Listed:
  • Yanshu Wang

    (School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, China)

  • Hailiang Zhang

    (School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, China)

Abstract

Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R ρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19.

Suggested Citation

  • Yanshu Wang & Hailiang Zhang, 2023. "Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine," Mathematics, MDPI, vol. 11(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3526-:d:1217780
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    References listed on IDEAS

    as
    1. Huaixing Li & Jiaoyan Wang, 2021. "Global Dynamics of an SEIR Model with the Age of Infection and Vaccination," Mathematics, MDPI, vol. 9(18), pages 1-23, September.
    2. Griffiths, Jeff & Lowrie, Dawn & Williams, Janet, 2000. "An age-structured model for the AIDS epidemic," European Journal of Operational Research, Elsevier, vol. 124(1), pages 1-14, July.
    3. Cyrille Kenne & Gisèle Mophou & René Dorville & Pascal Zongo, 2022. "A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    4. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Yang, Peng & Wang, Yuanshi, 2019. "Dynamics for an SEIRS epidemic model with time delay on a scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
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