IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v145y2021ics0960077921001247.html
   My bibliography  Save this article

COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission

Author

Listed:
  • Batabyal, Saikat

Abstract

The outbreak of coronavirus is spreading at an unprecedented rate to the human populations and taking several thousands of life all over the globe. In this paper, an extension of the well-known susceptible-exposed-infected-recovered (SEIR) family of compartmental model has been introduced with seasonality transmission of SARS-CoV-2. The stability analysis of the coronavirus depends on changing of its basic reproductive ratio. The progress rate of the virus in critical infected cases and the recovery rate have major roles to control this epidemic. Selecting the appropriate critical parameter from the Turing domain, the stability properties of existing patterns is obtained. The outcomes of theoretical studies, which are illustrated via Hopf bifurcation and Turing instabilities, yield the result of numerical simulations around the critical parameter to forecast on controlling this fatal disease. Globally existing solutions of the model has been studied by introducing Tikhonov regularization. The impact of social distancing, lockdown of the country, self-isolation, home quarantine and the wariness of global public health system have significant influence on the parameters of the model system that can alter the effect of recovery rates, mortality rates and active contaminated cases with the progression of time in the real world.

Suggested Citation

  • Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001247
    DOI: 10.1016/j.chaos.2021.110772
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921001247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110772?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. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    3. S. Gonçalves & G. Abramson & M. Gomes, 2011. "Oscillations in SIRS model with distributed delays," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 81(3), pages 363-371, June.
    4. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Changjin Xu & Yusen Wu, 2013. "Dynamics in a Lotka-Volterra Predator-Prey Model with Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    7. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
    8. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
    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. Yangcheng Zheng & Yunpeng Wang, 2022. "How Seasonality and Control Measures Jointly Determine the Multistage Waves of the COVID-19 Epidemic: A Modelling Study and Implications," IJERPH, MDPI, vol. 19(11), pages 1-11, May.

    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. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Amouch, Mohamed & Karim, Noureddine, 2021. "Modeling the dynamic of COVID-19 with different types of transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Otunuga, Olusegun Michael, 2021. "Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Ichino, Andrea & Favero, Carlo A. & Rustichini, Aldo, 2020. "Restarting the economy while saving lives under Covid-19," CEPR Discussion Papers 14664, C.E.P.R. Discussion Papers.
    8. M. Hashem Pesaran & Cynthia Fan Yang, 2022. "Matching theory and evidence on Covid‐19 using a stochastic network SIR model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1204-1229, September.
    9. Wei Zhong, 2017. "Simulating influenza pandemic dynamics with public risk communication and individual responsive behavior," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 475-495, December.
    10. S. M. Niaz Arifin & Christoph Zimmer & Caroline Trotter & Anaïs Colombini & Fati Sidikou & F. Marc LaForce & Ted Cohen & Reza Yaesoubi, 2019. "Cost-Effectiveness of Alternative Uses of Polyvalent Meningococcal Vaccines in Niger: An Agent-Based Transmission Modeling Study," Medical Decision Making, , vol. 39(5), pages 553-567, July.
    11. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Bisin, Alberto & Moro, Andrea, 2022. "Spatial‐SIR with network structure and behavior: Lockdown rules and the Lucas critique," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 370-388.
    13. Mirjam Kretzschmar & Rafael T Mikolajczyk, 2009. "Contact Profiles in Eight European Countries and Implications for Modelling the Spread of Airborne Infectious Diseases," PLOS ONE, Public Library of Science, vol. 4(6), pages 1-8, June.
    14. Gillis, Melissa & Urban, Ryley & Saif, Ahmed & Kamal, Noreen & Murphy, Matthew, 2021. "A simulation–optimization framework for optimizing response strategies to epidemics," Operations Research Perspectives, Elsevier, vol. 8(C).
    15. Valentina Marziano & Giorgio Guzzetta & Alessia Mammone & Flavia Riccardo & Piero Poletti & Filippo Trentini & Mattia Manica & Andrea Siddu & Antonino Bella & Paola Stefanelli & Patrizio Pezzotti & Ma, 2021. "The effect of COVID-19 vaccination in Italy and perspectives for living with the virus," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
    16. Nikolaos P. Rachaniotis & Thomas K. Dasaklis & Filippos Fotopoulos & Platon Tinios, 2021. "A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination," IJERPH, MDPI, vol. 18(5), pages 1-21, March.
    17. Thomas Ash & Antonio M. Bento & Daniel Kaffine & Akhil Rao & Ana I. Bento, 2022. "Disease-economy trade-offs under alternative epidemic control strategies," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    18. Lewandowski, Piotr, 2020. "Occupational Exposure to Contagion and the Spread of COVID-19 in Europe," IZA Discussion Papers 13227, Institute of Labor Economics (IZA).
    19. Yifeng Liu & Yuan Lai, 2024. "Analyzing jogging activity patterns and adaptation to public health regulation," Environment and Planning B, , vol. 51(3), pages 670-688, March.
    20. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

    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:chsofr:v:145:y:2021:i:c:s0960077921001247. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.