IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp222-230.html
   My bibliography  Save this article

Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data

Author

Listed:
  • Abdel-Gawad, Hamdy I.
  • Abdel-Gawad, Ahmed H.

Abstract

Very recently, various mathematical models, for the dynamics of COVID-19 with main contribution of suspected–exposed–infected–recovered people have been proposed. Some models that account for the deceased, quarantined or social distancing functions were also presented. However, in any local space the real data reveals that the effects of lock-down and traveling are significant in decreasing and increasing the impact of this virus respectively. Here, discrete and continuum models for the dynamics of this virus are suggested. The continuum dynamical model is studied in detail. The present model deals with exposed, infected, recovered and deceased individuals (EIRD), which accounts for the health isolation and travelers (HIT) effects. Up to now no exact solutions of the parametric-dependent, nonlinear dynamical system NLDS were found. In this work, our objective is to find the exact solutions of a NLDS. To this issue, a novel approach is presented where a NLDS is recast to a linear dynamical system LDS. This is done by implementing the unified method (UM), with auxiliary equations, which are taken coupled linear ODE’s (LDS). Numerical results of the exact solutions are evaluated, which can be applied to data in a local space (or anywhere) when the initial data for the IRD are known. Here, as an example, initial conditions for the components in the model equation of COVID-19, are taken from the real data in Egypt. The results of susceptible, infected, recovered and deceased people are computed. The comparison between the computed results and the real data shows an agreement up to a relative error 10−3. On the other hand it is remarked that locking-down plays a dominant role in decreasing the number of infected people. The equilibrium states are determined and it is found that they are stable. This reveals a relevant result that the COVID-19 can be endemic in the case of a disturbance in the number of the exposed people. A disturbance in the form of an increase in the exposed number, leads to an increase in the number of infected people. This result is, globally, valid. Furthermore, initial states control is analyzed, where region of initial conditions for infected and exposed is determined. We developed a software tool to interact with the model and facilitate applying various data of different local spaces.

Suggested Citation

  • Abdel-Gawad, Hamdy I. & Abdel-Gawad, Ahmed H., 2021. "Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 222-230.
  • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:222-230
    DOI: 10.1016/j.matcom.2021.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421001889
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2021.05.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Kevin Linka & Mathias Peirlinck & Francisco Sahli Costabal & Ellen Kuhl, 2020. "Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 23(11), pages 710-717, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Chenciner Bifurcation Presenting a Further Degree of Degeneration," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    2. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.

    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. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    2. Sheng Zhang & Jiao Gao & Bo Xu, 2022. "An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
    3. Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
    4. Marcos Deuñas & Mercedes Campi & Luis Olmos, 2020. "Changes in mobility and socioeconomic conditions in Bogotá city during the COVID-19 outbreak," Working Papers 30, Red Nacional de Investigadores en Economía (RedNIE).
    5. Nguyen, Lu Trong Khiem, 2015. "Modified homogeneous balance method: Applications and new solutions," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 148-155.
    6. M. Ali Akbar & Md. Nur Alam & Md. Golam Hafez, 2016. "Application of the novel (G′/G)-expansion method to construct traveling wave solutions to the positive Gardner-KP equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 85-96, March.
    7. Bao-Linh Tran & Chi-Chung Chen & Wei-Chun Tseng & Shu-Yi Liao, 2020. "Tourism under the Early Phase of COVID-19 in Four APEC Economies: An Estimation with Special Focus on SARS Experiences," IJERPH, MDPI, vol. 17(20), pages 1-13, October.
    8. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
    9. Bekir, Ahmet & Cevikel, Adem C., 2009. "New exact travelling wave solutions of nonlinear physical models," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1733-1739.
    10. Md. Mokhlesur Rahman & Jean-Claude Thill & Kamal Chandra Paul, 2020. "COVID-19 Pandemic Severity, Lockdown Regimes, and People’s Mobility: Early Evidence from 88 Countries," Sustainability, MDPI, vol. 12(21), pages 1-17, November.
    11. Marta Borowska-Stefańska & Michał Kowalski & Paulina Kurzyk & Alireza Sahebgharani & Szymon Wiśniewski, 2022. "Spatiotemporal Changeability of the Load of the Urban Road Transport System under Permanent and Short-Term Legal and Administrative Retail Restrictions," Sustainability, MDPI, vol. 14(9), pages 1-30, April.
    12. Liu, Yi & Zhang, Hengyuan & Chen, Daniel Q., 2024. "On the economic implications of international travel restrictions: Evidence from Chinese MNEs’ firm value," Journal of Business Research, Elsevier, vol. 170(C).
    13. Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Ruguo Fan & Yibo Wang & Jinchai Lin, 2021. "Study on Multi-Agent Evolutionary Game of Emergency Management of Public Health Emergencies Based on Dynamic Rewards and Punishments," IJERPH, MDPI, vol. 18(16), pages 1-22, August.
    15. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    16. Alfonso Orro & Margarita Novales & Ángel Monteagudo & José-Benito Pérez-López & Miguel R. Bugarín, 2020. "Impact on City Bus Transit Services of the COVID–19 Lockdown and Return to the New Normal: The Case of A Coruña (Spain)," Sustainability, MDPI, vol. 12(17), pages 1-30, September.
    17. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
    18. Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    19. Perjan Taha & Arazoo Tahir & Fatima Ahmed & Runak Radha & Ari Taha & Shameran Slewa-Younan, 2023. "Depression and Generalized Anxiety as Long-Term Mental Health Consequences of COVID-19 in Iraqi Kurdistan," IJERPH, MDPI, vol. 20(13), pages 1-13, July.
    20. Liu, Shasha & Yamamoto, Toshiyuki, 2022. "Role of stay-at-home requests and travel restrictions in preventing the spread of COVID-19 in Japan," Transportation Research Part A: Policy and Practice, Elsevier, vol. 159(C), pages 1-16.

    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:eee:matcom:v:190:y:2021:i:c:p:222-230. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.