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Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Author

Listed:
  • Zhe Yin

    (Department of mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Yongguang Yu

    (Department of mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Zhenzhen Lu

    (Department of mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

Suggested Citation

  • Zhe Yin & Yongguang Yu & Zhenzhen Lu, 2020. "Stability Analysis of an Age-Structured SEIRS Model with Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:455-:d:335795
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    References listed on IDEAS

    as
    1. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    2. Akimenko, Vitalii V., 2017. "Asymptotically stable states of non-linear age-structured monocyclic population model II. Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 24-38.
    3. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A., 2015. "On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 953-976.
    4. Akimenko, Vitalii V., 2017. "Nonlinear age-structured models of polycyclic population dynamics with death rates as power functions with exponent n," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 175-205.
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