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Global stability of an age-structure epidemic model with imperfect vaccination and relapse

Author

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  • Cao, Bin
  • Huo, Hai-Feng
  • Xiang, Hong

Abstract

A new age-structured epidemic model with imperfect vaccination and relapse is proposed. The total population of our model is partitioned into five subclasses: susceptible class S, vaccinated class V, exposed class E, infectious class I and removed class R. Age-structures are equipped with in exposed and recovered classes. Furthermore, imperfect vaccination is also introduced in our model. The basic reproduction number R0 is defined and proved as a threshold parameter of the model. Asymptotic smoothness of solutions and uniform persistence of the system are showed via reformulating the system as a system of Volterra integral equation. Furthermore, by constructing proper Volterra-type Lyapunov functional we get when R0<1, the disease-free equilibrium is globally asymptotically stable. When R0>1, the endemic equilibrium is globally stable. Our results show that to increase the efficiency of vaccination and reduce influence of relapse are vital essential for controlling epidemic.

Suggested Citation

  • Cao, Bin & Huo, Hai-Feng & Xiang, Hong, 2017. "Global stability of an age-structure epidemic model with imperfect vaccination and relapse," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 638-655.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:638-655
    DOI: 10.1016/j.physa.2017.05.056
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    Citations

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    Cited by:

    1. 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.
    2. Li, Yan & Ye, Ming & Zhang, Qimin, 2019. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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