IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i13p1564-d587883.html
   My bibliography  Save this article

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Author

Listed:
  • Gilberto Gonzalez-Parra

    (Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA)

  • Abraham J. Arenas

    (Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, Colombia)

Abstract

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R 0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

Suggested Citation

  • Gilberto Gonzalez-Parra & Abraham J. Arenas, 2021. "Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness," Mathematics, MDPI, vol. 9(13), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1564-:d:587883
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/13/1564/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/13/1564/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zindoga Mukandavire & Farai Nyabadza & Noble J Malunguza & Diego F Cuadros & Tinevimbo Shiri & Godfrey Musuka, 2020. "Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-11, July.
    2. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Taneco-Hernández, Marco Antonio & Vargas-De-León, Cruz, 2020. "Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative: An HIV/AIDS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Meskaf, Adil & Khyar, Omar & Danane, Jaouad & Allali, Karam, 2020. "Global stability analysis of a two-strain epidemic model with non-monotone incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Yunhwan Kim & Ana Vivas Barber & Sunmi Lee, 2020. "Modeling influenza transmission dynamics with media coverage data of the 2009 H1N1 outbreak in Korea," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-21, June.
    6. Triambak, S. & Mahapatra, D.P., 2021. "A random walk Monte Carlo simulation study of COVID-19-like infection spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    7. Kimberly M. Thompson & Radboud J. Duintjer Tebbens & Mark A. Pallansch, 2006. "Evaluation of Response Scenarios to Potential Polio Outbreaks Using Mathematical Models," Risk Analysis, John Wiley & Sons, vol. 26(6), pages 1541-1556, December.
    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. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. 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.
    3. Naudé, Wim & Cameron, Martin, 2020. "Failing to Pull Together: South Africa's Troubled Response to COVID-19," IZA Discussion Papers 13649, Institute of Labor Economics (IZA).
    4. Hannah Al Ali & Alireza Daneshkhah & Abdesslam Boutayeb & Zindoga Mukandavire, 2022. "Examining Type 1 Diabetes Mathematical Models Using Experimental Data," IJERPH, MDPI, vol. 19(2), pages 1-20, January.
    5. Kimberly M. Thompson & Radboud J. Duintjer Tebbens & Mark A. Pallansch & Olen M. Kew & Roland W. Sutter & R. Bruce Aylward & Margaret Watkins & Howard Gary & James P. Alexander & Linda Venczel & Denis, 2006. "Development and Consideration of Global Policies for Managing the Future Risks of Poliovirus Outbreaks: Insights and Lessons Learned Through Modeling," Risk Analysis, John Wiley & Sons, vol. 26(6), pages 1571-1580, December.
    6. Radboud J. Duintjer Tebbens & Mark A. Pallansch & Konstantin M. Chumakov & Neal A. Halsey & Tapani Hovi & Philip D. Minor & John F. Modlin & Peter A. Patriarca & Roland W. Sutter & Peter F. Wright & S, 2013. "Review and Assessment of Poliovirus Immunity and Transmission: Synthesis of Knowledge Gaps and Identification of Research Needs," Risk Analysis, John Wiley & Sons, vol. 33(4), pages 606-646, April.
    7. Abidemi, Afeez & Ackora-Prah, Joseph & Fatoyinbo, Hammed Olawale & Asamoah, Joshua Kiddy K., 2022. "Lyapunov stability analysis and optimization measures for a dengue disease transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    8. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    9. Li, Tingting & Guo, Youming, 2022. "Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    10. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    11. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    12. Negar Darabi & Niyousha Hosseinichimeh, 2020. "System dynamics modeling in health and medicine: a systematic literature review," System Dynamics Review, System Dynamics Society, vol. 36(1), pages 29-73, January.
    13. Abidemi, Afeez & Owolabi, Kolade M. & Pindza, Edson, 2022. "Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    14. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    15. Radboud J. Duintjer Tebbens & Mark A. Pallansch & Olen M. Kew & Roland W. Sutter & R. Bruce Aylward & Margaret Watkins & Howard Gary & James Alexander & Hamid Jafari & Stephen L. Cochi & Kimberly M. T, 2008. "Uncertainty and Sensitivity Analyses of a Decision Analytic Model for Posteradication Polio Risk Management," Risk Analysis, John Wiley & Sons, vol. 28(4), pages 855-876, August.
    16. Kimberly M. Thompson, 2006. "Poliomyelitis and the Role of Risk Analysis in Global Infectious Disease Policy and Management," Risk Analysis, John Wiley & Sons, vol. 26(6), pages 1419-1421, December.
    17. Esther De Gourville & Radboud J. Duintjer Tebbens & Nalinee Sangrujee & Mark A. Pallansch & Kimberly M. Thompson, 2006. "Global Surveillance and the Value of Information: The Case of the Global Polio Laboratory Network," Risk Analysis, John Wiley & Sons, vol. 26(6), pages 1557-1569, December.
    18. Whenayon Simeon Ajisegiri & Abrar Ahmad Chughtai & C. Raina MacIntyre, 2018. "A Risk Analysis Approach to Prioritizing Epidemics: Ebola Virus Disease in West Africa as a Case Study," Risk Analysis, John Wiley & Sons, vol. 38(3), pages 429-441, March.
    19. Wang, Chaoqian, 2020. "Dynamics of conflicting opinions considering rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    20. Wen-Jing Zhu & Shou-Feng Shen & Wen-Xiu Ma, 2022. "A (2+1)-Dimensional Fractional-Order Epidemic Model with Pulse Jumps for Omicron COVID-19 Transmission and Its Numerical Simulation," Mathematics, MDPI, vol. 10(14), pages 1-14, July.

    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:9:y:2021:i:13:p:1564-:d:587883. 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.