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Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19

Author

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  • Vasileios E. Papageorgiou

    (Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece)

  • Georgios Vasiliadis

    (Department of Mathematics, University of Western Macedonia, 52100 Kastoria, Greece)

  • George Tsaklidis

    (Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece)

Abstract

Several research papers have attempted to describe the dynamics of COVID-19 based on systems of differential equations. These systems have taken into account quarantined or isolated cases, vaccinations, control measures, and demographic parameters, presenting propositions regarding theoretical results that often investigate the asymptotic behavior of the system. In this paper, we discuss issues that concern the theoretical results proposed in the paper “An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter”. We propose detailed explanations regarding the resolution of these issues. Additionally, this paper focuses on extending the local stability analysis of the disease-free equilibrium, as presented in the aforementioned paper, while emphasizing the derivation of theorems that validate the global stability of both epidemic equilibria. Emphasis is placed on the basic reproduction number R 0 , which determines the asymptotic behavior of the system. This index represents the expected number of secondary infections that are generated from an already infected case in a population where almost all individuals are susceptible. The derived propositions can inform health authorities about the long-term behavior of the phenomenon, potentially leading to more precise and efficient public measures. Finally, it is worth noting that the examined paper still presents an interesting epidemiological scheme, and the utilization of the Kalman filtering approach remains one of the state-of-the-art methods for modeling epidemic phenomena.

Suggested Citation

  • Vasileios E. Papageorgiou & Georgios Vasiliadis & George Tsaklidis, 2023. "Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19," Mathematics, MDPI, vol. 12(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:55-:d:1306374
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    References listed on IDEAS

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    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    2. Korolev, Ivan, 2021. "Identification and estimation of the SEIRD epidemic model for COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 63-85.
    3. 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.
    4. Papageorgiou, Vasileios E. & Tsaklidis, George, 2023. "An improved epidemiological-unscented Kalman filter (hybrid SEIHCRDV-UKF) model for the prediction of COVID-19. Application on real-time data," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    Full references (including those not matched with items on IDEAS)

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