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Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

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  • Khan, Muhammad Altaf
  • Atangana, Abdon

Abstract

We construct a new mathematical model to better understand the novel coronavirus (omicron variant). We briefly present the modeling of COVID-19 with the omicron variant and present their mathematical results. We study that the Omicron model is locally asymptotically stable if the basic reproduction number R0<1, while for R0≤1, the model at the disease-free equilibrium is globally asymptotically stable. We extend the model to the second-order differential equations to study the possible occurrence of the layers(waves). We then extend the model to a fractional stochastic version and studied its numerical results. The real data for the period ranging from November 1, 2021, to January 23, 2022, from South Africa are considered to obtain the realistic values of the model parameters. The basic reproduction number for the suggested data is found to be approximate R0≈2.1107 which is very close to the actual basic reproduction in South Africa. We perform the global sensitivity analysis using the PRCC method to investigate the most influential parameters that increase or decrease R0. We use the new numerical scheme recently reported for the solution of piecewise fractional differential equations to present the numerical simulation of the model. Some graphical results for the model with sensitive parameters are given which indicate that the infection in the population can be minimized by following the recommendations of the world health organizations (WHO), such as social distances, using facemasks, washing hands, avoiding gathering, etc.

Suggested Citation

  • Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003326
    DOI: 10.1016/j.physa.2022.127452
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    References listed on IDEAS

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    1. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
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    3. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Zhang, Zizhen, 2020. "A novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Aldila, Dipo, 2020. "Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Nabi, Khondoker Nazmoon & Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Projections and fractional dynamics of COVID-19 with optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    9. Zhang, Zizhen, 2020. "Corrigendum to a novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels [Chaos Solitons & Fractals 139 (2020) 110060]," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Ayinde, Kayode & Lukman, Adewale F. & Rauf, Rauf I. & Alabi, Olusegun O. & Okon, Charles E. & Ayinde, Opeyemi E., 2020. "Modeling Nigerian Covid-19 cases: A comparative analysis of models and estimators," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Samiran Ghosh & Vitaly Volpert & Malay Banerjee, 2022. "An Epidemic Model with Time Delay Determined by the Disease Duration," Mathematics, MDPI, vol. 10(15), pages 1-19, July.

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