IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2022i1p142-d1017179.html
   My bibliography  Save this article

A New Mathematical Model of COVID-19 with Quarantine and Vaccination

Author

Listed:
  • Ihtisham Ul Haq

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Numan Ullah

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Nigar Ali

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, Collage of Arts and Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia)

Abstract

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R 0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R 0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.

Suggested Citation

  • Ihtisham Ul Haq & Numan Ullah & Nigar Ali & Kottakkaran Sooppy Nisar, 2022. "A New Mathematical Model of COVID-19 with Quarantine and Vaccination," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:142-:d:1017179
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/1/142/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/1/142/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    3. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    4. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    5. Chen, Yuyang & Bi, Kaiming & Zhao, Songnian & Ben-Arieh, David & Wu, Chih-Hang John, 2017. "Modeling individual fear factor with optimal control in a disease-dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 531-545.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    2. Ahsan, Muhammad & Bohner, Martin & Ullah, Aizaz & Khan, Amir Ali & Ahmad, Sheraz, 2023. "A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 166-180.
    3. Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    4. Ahmad, Shabir & Ullah, Aman & Al-Mdallal, Qasem M. & Khan, Hasib & Shah, Kamal & Khan, Aziz, 2020. "Fractional order mathematical modeling of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Yi-Fang Luo & Shu-Ching Yang & Shih-Chieh Hung & Kun-Yi Chou, 2022. "Exploring the Impacts of Preventative Health Behaviors with Respect to COVID-19: An Altruistic Perspective," IJERPH, MDPI, vol. 19(13), pages 1-14, June.
    6. Lee, Chaeyoung & Li, Yibao & Kim, Junseok, 2020. "The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Rahman, Mati ur & Ahmad, Saeed & Matoog, R.T. & Alshehri, Nawal A. & Khan, Tahir, 2021. "Study on the mathematical modelling of COVID-19 with Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    9. Shao, Quan & Wang, Hong & Zhu, Pei & Dong, Min, 2021. "Group emotional contagion and simulation in large-scale flight delays based on the two-layer network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    10. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    12. Wen Dong & Peng Zhang & Quan-Li Xu & Zhong-Da Ren & Jie Wang, 2022. "A Study on a Neural Network Risk Simulation Model Construction for Avian Influenza A (H7N9) Outbreaks in Humans in China during 2013–2017," IJERPH, MDPI, vol. 19(17), pages 1-16, August.
    13. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    14. Postavaru, O. & Anton, S.R. & Toma, A., 2021. "COVID-19 pandemic and chaos theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 138-149.
    15. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    16. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    17. Igor Sinitsyn & Vladimir Sinitsyn & Eduard Korepanov & Tatyana Konashenkova, 2022. "Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    18. Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.
    19. Jahangiri, Ali & Mohammadi, Samira & Akbari, Mohammad, 2019. "Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 13-26.
    20. Awati, Vishwanath B. & Goravar, Akash & N., Mahesh Kumar, 2024. "Spectral and Haar wavelet collocation method for the solution of heat generation and viscous dissipation in micro-polar nanofluid for MHD stagnation point flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 158-183.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:142-:d:1017179. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.