IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v637y2024ics0378437124001158.html
   My bibliography  Save this article

On the repeated epidemic waves

Author

Listed:
  • Shnip, A.I.
  • Trigger, S.A.

Abstract

Based on the discrete model of infection spread in a closed population, appearance of epidemic waves associated with strengthening and weakening quarantine measures in the present paper is shown. The effect of quarantine measures is considered in the model under consideration via time dependence in the infection transmission rate. It was shown that the epidemic development is controlled by four key parameters: the number of infected persons, the average virus carriage time (as applied to COVID-19-type epidemics caused by the virus SARS-CoV-2 spread), the average number of dangerous contacts (which can cause virus transfer from an infected person to healthy men) of one infectious person (virus carrier) per day and the probability of infection due to a hazardous contact. The two latter parameters enter the model only as a product called the indicator of infection growth (IG) in population. The found solutions depend also on the population size and on the initial number of infected persons. The IG in the model under consideration is similar in meaning to the reproductive number in continuous SIR and SEIR models. At the same time, due to the prolonged virus carriage characteristic of COVID-19, the solutions proposed here are based on the equations with delay, and even without temporal variations of the IG, differ significantly from the SIR and SEIR models. The effect of the feedback between the epidemic spread rate and variations in the IG, caused by strengthening or weakening quarantine measures is studied. It results in a principal change in the epidemic behavior, which not reaching the saturation mode, transforms to its wavy flow mode. The dependence of the onset of epidemic waves on characteristic times of quarantine restriction weakening was revealed. In the model under consideration, the possibility of complete epidemic end in the case of long-term restricted quarantine measures was shown. The possible existence of the quasi-steady mode of low-intensity epidemic was detected. In this mode, the number of virus carriers remains unchanged for a long time due to the balance of the number of infections and recoveries per day.

Suggested Citation

  • Shnip, A.I. & Trigger, S.A., 2024. "On the repeated epidemic waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    • Handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124001158
    DOI: 10.1016/j.physa.2024.129607
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124001158
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129607?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. Juliet Bedford & Jeremy Farrar & Chikwe Ihekweazu & Gagandeep Kang & Marion Koopmans & John Nkengasong, 2019. "A new twenty-first century science for effective epidemic response," Nature, Nature, vol. 575(7781), pages 130-136, November.
    2. Simón A. Rella & Yuliya A. Kulikova & Emmanouil T. Dermitzakis & Fyodor A. Kondrashov, 2021. "Rates of SARS-COV-2 transmission and vaccination impact the fate of vaccine-resistant strains," Working Papers 2129, Banco de España.
    3. S. A. Trigger & A. M. Ignatov, 2022. "Strain-stream model of epidemic spread in application to COVID-19," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-8, November.
    4. Iván Area & Henrique Lorenzo & Pedro J. Marcos & Juan J. Nieto, 2021. "One Year of the COVID-19 Pandemic in Galicia: A Global View of Age-Group Statistics during Three Waves," IJERPH, MDPI, vol. 18(10), pages 1-14, May.
    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. S. A. Trigger & A. M. Ignatov, 2022. "Strain-stream model of epidemic spread in application to COVID-19," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-8, November.
    2. Saba Wajeeh & Abhishek Lal & Naseer Ahmed & Md. Ibrahim Khalil & Afsheen Maqsood & Akram Mojidea M Alshammari & Abdulelah Zaid Alshammari & Meshari Musallam Mohammed Alsharari & Abdulelah Hamdan Alrus, 2021. "Operational Implications and Risk Assessment of COVID-19 in Dental Practices," IJERPH, MDPI, vol. 18(22), pages 1-13, November.
    3. Jorge Varanda & Luzia Gonçalves & Isabel Craveiro, 2020. "The Unlikely Saviour: Portugal’s National Health System and the Initial Impact of the COVID-19 Pandemic?," Development, Palgrave Macmillan;Society for International Deveopment, vol. 63(2), pages 291-297, December.
    4. Imdad, Kashif & Sahana, Mehebub & Rana, Md Juel & Haque, Ismail & Patel, Priyank Pravin & Pramanik, Malay, 2020. "The COVID-19 pandemic's footprint in India: An assessment on the district-level susceptibility and vulnerability," MPRA Paper 100727, University Library of Munich, Germany.
    5. Xiyun Zhang & Zhongyuan Ruan & Muhua Zheng & Jie Zhou & Stefano Boccaletti & Baruch Barzel, 2022. "Epidemic spreading under mutually independent intra- and inter-host pathogen evolution," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    6. Patrick Mellacher, 2022. "Endogenous viral mutations, evolutionary selection, and containment policy design," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(3), pages 801-825, July.
    7. Gabriela Lobinska & Ady Pauzner & Arne Traulsen & Yitzhak Pilpel & Martin A. Nowak, 2022. "Evolution of resistance to COVID-19 vaccination with dynamic social distancing," Nature Human Behaviour, Nature, vol. 6(2), pages 193-206, February.
    8. Gopal Krishna Roy, 2022. "An Economic Case for Waiving Intellectual Property Rights on Covid Vaccines," India Quarterly: A Journal of International Affairs, , vol. 78(1), pages 143-147, March.
    9. Xiaoli Wang & Lin Fan & Ziqiang Dai & Li Li & Xianliang Wang, 2022. "Predictive Model for National Minimal CFR during Spontaneous Initial Outbreak of Emerging Infectious Disease: Lessons from COVID-19 Pandemic in 214 Nations and Regions," IJERPH, MDPI, vol. 20(1), pages 1-16, December.
    10. Jamie Bedson & Laura A. Skrip & Danielle Pedi & Sharon Abramowitz & Simone Carter & Mohamed F. Jalloh & Sebastian Funk & Nina Gobat & Tamara Giles-Vernick & Gerardo Chowell & João Rangel Almeida & Ran, 2021. "A review and agenda for integrated disease models including social and behavioural factors," Nature Human Behaviour, Nature, vol. 5(7), pages 834-846, July.
    11. Qin Huang & Chuanhao Fan & Jigan Wang & Shiying Zheng & Guilu Sun, 2022. "An Empirical Study on the Incentive Mechanism for Public Active Involvement in Grass-Roots Social Governance Based on Stimulus-Organism-Response Theory," Sustainability, MDPI, vol. 14(21), pages 1-28, October.
    12. Amina Chebli & Foued Ben Said, 2020. "The Impact of Covid-19 on Tourist Consumption Behaviour : A Perspective Article," Journal of Tourism Management Research, Conscientia Beam, vol. 7(2), pages 196-207.
    13. Yen-Chang Chang & Ching-Ti Liu, 2022. "A Stochastic Multi-Strain SIR Model with Two-Dose Vaccination Rate," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
    14. Grass, D. & Wrzaczek, S. & Caulkins, J.P. & Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Kuhn, M. & Prskawetz, A. & Sanchez-Romero, M. & Seidl, A., 2024. "Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses," Theoretical Population Biology, Elsevier, vol. 156(C), pages 46-65.
    15. Abolfazl Mollalo & Alireza Mohammadi & Sara Mavaddati & Behzad Kiani, 2021. "Spatial Analysis of COVID-19 Vaccination: A Scoping Review," IJERPH, MDPI, vol. 18(22), pages 1-14, November.
    16. Marcelo Castro & Enlinson Mattos & Fernanda Patriota, 2021. "The effects of health spending on the propagation of infectious diseases," Health Economics, John Wiley & Sons, Ltd., vol. 30(10), pages 2323-2344, September.
    17. Lívia Madeira Triaca & Felipe Garcia Ribeiro & César Augusto Oviedo Tejada, 2021. "Mosquitoes, birth rates and regional spillovers: Evidence from the Zika epidemic in Brazil," Papers in Regional Science, Wiley Blackwell, vol. 100(3), pages 795-813, June.
    18. Yonggeng Xiong & Min Xu & Yan Zhao, 2024. "Resident Preferences for Urban Green Spaces in Response to Pandemic Public Health Emergency: A Case Study of Shanghai," Sustainability, MDPI, vol. 16(9), pages 1-25, April.
    19. Vinyas Harish & Felipe J. Colón-González & Filipe R. R. Moreira & Rory Gibb & Moritz U. G. Kraemer & Megan Davis & Robert C. Reiner & David M. Pigott & T. Alex Perkins & Daniel J. Weiss & Isaac I. Bog, 2024. "Human movement and environmental barriers shape the emergence of dengue," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    20. Emily J. Tetzlaff & Nicholas Goulet & Melissa Gorman & Gregory R. A. Richardson & Glen P. Kenny, 2023. "The Intersection of the COVID-19 Pandemic and the 2021 Heat Dome in Canadian Digital News Media: A Content Analysis," IJERPH, MDPI, vol. 20(17), pages 1-16, August.

    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:phsmap:v:637:y:2024:i:c:s0378437124001158. 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/physica-a-statistical-mechpplications/ .

    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.