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

Author

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  • 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
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    References listed on IDEAS

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    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.
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