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A compartmental model for the dynamic simulation of pandemics with a multi-phase vaccination and its application to Italian COVID-19 data

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  • Cerqueti, Roy
  • Ramponi, Alessandro
  • Scarlatti, Sergio

Abstract

We introduce a generalization of the 4 compartments SVIR epidemic model discussed in [1] for the first time. Our model has K+4 compartments. K-1 of these compartments represent additional subsequent vaccination stages not considered in the original SVIR model, while a further compartment accounts for dead people. We analyze the equilibrium points of the model. A time-varying parameters version of it, having K=3 vaccination compartments, is then calibrated to Italian COVID-19 dataset. This analysis is carried out for three specific sub-periods: the first one, ranging from February 24th, 2020, up to December 26th 2020, when no vaccines were available; the second one, from the December 27th, 2020 up to December 31st, 2021, during which the Delta variant of the virus prevailed and Delta-targeted vaccination doses were administered to the population for the first time; finally, the last considered period is ranging from January 10th, 2022 up to June 3rd, 2022, and it was characterized by the diffusion of the Omicron variant. To tackle the problem of undetected infected or undetected recovered people we adopt an approach relying on different scenarios. The calibration of the model uses the property that the discrete-time version of it turns out to be explicitly solvable with respect to the parameters, hence providing a daily estimate of the involved parameters. This produces meaningful evolution patterns of the COVID-19 epidemic which allow a better understanding of the diffusive behavior of the pandemic along time. Lastly a statistical analysis of the epidemiological parameters estimators supports the non stationarity of their time series.

Suggested Citation

  • Cerqueti, Roy & Ramponi, Alessandro & Scarlatti, Sergio, 2025. "A compartmental model for the dynamic simulation of pandemics with a multi-phase vaccination and its application to Italian COVID-19 data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 124-146.
  • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:124-146
    DOI: 10.1016/j.matcom.2024.08.011
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    References listed on IDEAS

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    1. Fanelli, Duccio & Piazza, Francesco, 2020. "Analysis and forecast of COVID-19 spreading in China, Italy and France," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Yaesoubi, Reza & Cohen, Ted, 2011. "Generalized Markov models of infectious disease spread: A novel framework for developing dynamic health policies," European Journal of Operational Research, Elsevier, vol. 215(3), pages 679-687, December.
    3. Taylor, James W. & Taylor, Kathryn S., 2023. "Combining probabilistic forecasts of COVID-19 mortality in the United States," European Journal of Operational Research, Elsevier, vol. 304(1), pages 25-41.
    4. Wang, Jinliang & Zhang, Ran & Kuniya, Toshikazu, 2021. "A reaction–diffusion Susceptible–Vaccinated–Infected–Recovered model in a spatially heterogeneous environment with Dirichlet boundary condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 848-865.
    5. Eleonora Agostini & Francesco Bloise & Massimiliano Tancioni, 2024. "Vaccination policy and mortality from COVID-19 in the European Union," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages 299-322.
    6. Seth Flaxman & Swapnil Mishra & Axel Gandy & H. Juliette T. Unwin & Thomas A. Mellan & Helen Coupland & Charles Whittaker & Harrison Zhu & Tresnia Berah & Jeffrey W. Eaton & Mélodie Monod & Azra C. Gh, 2020. "Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe," Nature, Nature, vol. 584(7820), pages 257-261, August.
    7. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    8. Yang, Xiaochen & Yang, Zhanwen & Zhang, Chiping, 2023. "Numerical analysis of the Linearly implicit Euler method with truncated Wiener process for the stochastic SIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 1-14.
    9. Chen, Ziren & Feng, Lin & Lay, Harold A. & Furati, Khaled & Khaliq, Abdul, 2022. "SEIR model with unreported infected population and dynamic parameters for the spread of COVID-19," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 31-46.
    10. Nikolopoulos, Konstantinos & Punia, Sushil & Schäfers, Andreas & Tsinopoulos, Christos & Vasilakis, Chrysovalantis, 2021. "Forecasting and planning during a pandemic: COVID-19 growth rates, supply chain disruptions, and governmental decisions," European Journal of Operational Research, Elsevier, vol. 290(1), pages 99-115.
    11. Das, Saikat & Bose, Indranil & Sarkar, Uttam Kumar, 2023. "Predicting the outbreak of epidemics using a network-based approach," European Journal of Operational Research, Elsevier, vol. 309(2), pages 819-831.
    12. Hosseini-Motlagh, Seyyed-Mahdi & Samani, Mohammad Reza Ghatreh & Homaei, Shamim, 2023. "Design of control strategies to help prevent the spread of COVID-19 pandemic," European Journal of Operational Research, Elsevier, vol. 304(1), pages 219-238.
    13. Vahdani, Behnam & Mohammadi, Mehrdad & Thevenin, Simon & Gendreau, Michel & Dolgui, Alexandre & Meyer, Patrick, 2023. "Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1249-1272.
    14. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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