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On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules

Author

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  • De la Sen, M.
  • Alonso-Quesada, S.
  • Ibeas, A.

Abstract

This paper discusses and formulates a continuous-time SEIR -type epidemic model of pseudo-mass action type with finitely distributed delays under a very general, potentially time-varying, vaccination control rule which eventually generates feedback actions on the susceptible, infectious and recovered subpopulations. A lot of particular vaccination laws can be got from the proposed general one. The disease-free and endemic equilibrium points are characterized and their local stability properties discussed depending on the limits of the vaccination control gains provided that they converge asymptotically. Then, the global asymptotic stability to the disease-free equilibrium point is studied under an infective transmission rate below a certain maximum threshold. Later on, an extended SEIR epidemic model is discussed through simulated examples with stochastic Wiener-type perturbations around the equilibrium points.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:953-976
    DOI: 10.1016/j.amc.2015.08.099
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    References listed on IDEAS

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    1. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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    Cited by:

    1. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    2. Raul Nistal & Manuel De la Sen & Santiago Alonso-Quesada & Asier Ibeas, 2018. "On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties," Mathematics, MDPI, vol. 7(1), pages 1-19, December.
    3. Santiago Alonso-Quesada & Manuel De la Sen & Raúl Nistal, 2021. "An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns," Mathematics, MDPI, vol. 10(1), pages 1-32, December.
    4. Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. 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.
    6. Manuel De la Sen & Asier Ibeas & Santiago Alonso-Quesada, 2022. "On the Supervision of a Saturated SIR Epidemic Model with Four Joint Control Actions for a Drastic Reduction in the Infection and the Susceptibility through Time," IJERPH, MDPI, vol. 19(3), pages 1-26, January.
    7. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    8. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    9. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    10. Liu, Songnan & Xu, Xiaojie & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of the DS-I-A model disease with periodic parameter function and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 66-84.

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