Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 103–118. ISSN 2079-6641
MSC 65L05
Research Article
Numerical implementation of a mathematical model (SEIRD) based on data from the spread of the fifth wave of COVID-19 in Russia and regions
A. F. Tsakhoeva, D. D. Shigin
North Ossetian State University named after K. L. Khetagurov, 362025, Vladikavkaz, Vatutin str., 44-46, Russia
E-mail: shigin.d1@yandex.ru
In the present paper, a fractional-order epidemic model with operator called the Caputo operator for the transmission of COVID-19 epidemic is analyzed. This model takes into account the following groups of people: susceptible (S), exposed (E), infected (I), recovered (R) and deceased (D). The model is called SEIRD, from the first letters of the names of the described groups. Calculations are based on public data on incidence in Russia and the following subjects: Moscow, St. Petersburg and Kamchatka Krai.
Key words: Fractional-order derivative, COVID-19, SEIRD model.
DOI: 10.26117/2079-6641-2022-39-2-103–118
Original article submitted: 10.06.2022
Revision submitted: 23.08.2022
For citation. Tsakhoeva A. F., Shigin D. D. Numerical implementation of a mathematical model (SEIRD) based on data from the spread of the fifth wave of COVID-19 in Russia and regions. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 103–118. DOI: 10.26117/2079-6641-2022-39-2-103–118
Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.
The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)
© Tsakhoeva A. F., Shigin D. D., 2022
References
- Wilhelm A., et al. Reduced Neutralization of SARS- CoV-2 Omicron Variant by Vaccine Sera and Monoclonal Antibodies, medRxiv, 2021 DOI: 10.1101/2021.12.07.21267432.
- Liu L., et al. Striking antibody evasion manifested by the Omicron variant of SARS-CoV-2, Nature, 2022. vol. 602, no. 7896, pp. 676—681 DOI: 10.1038/s41586-021-04388-0
- Rossler A., Riepler L., Bante D., Dorothee von Laer, Kimpel J. SARS-CoV-2 B.1.1.529 variant (Omicron) evades neutralization by sera from vaccinated and convalescent individuals, New England Journal of Medicine, 2022. vol. 386, no. 7, pp. 698–700 DOI:10.1056/NEJMc21192362
- Balcilar M., Bouri E., Gupta R., Roubaud D. Can volume predict Bitcoin returns and volatility? A quantiles-based approach, Economic Modelling, 2017. vol. 64, pp. 74–81 DOI: 10.1016/j.econmod.2017.03.019
- Hirata Y., Aihara K. Improving time series prediction of solar irradiance after sunrise: Comparison among three methods for time series prediction, Solar Energy, 2017, pp. 294–301 DOI: 10.1016/j.solener.2017.04.020
- Chiyaka C., Garira W., Dube S. Transmission model of endemic human malaria in a partially immune population, Mathematical and Computer Modelling, 2007. vol. 46, no. 5, pp. 806–822 DOI: 10.1016/j.mcm.2006.12.010
- Danca M. F., Kuznetsov N. Matlab code for Lyapunov exponents of fractional-order systems, Int. J. Bifurcation Chaos Appl. Sci. Eng, 2018. vol. 28, no. 5, pp. 14 DOI: 10.1142/S0218127418500670
- Ogren P., Martin C. F. Vaccination strategies for epidemics in highly mobile populations, Applied Mathematics and Computation, 2002. vol. 127, no. 2, pp. 261–276 DOI: 10.1016/S0096-3003(01)00004-2
- Kucharski A. J., et al. Early dynamics of transmission and control of covid-19: a mathematical modelling study, Lancet Infectious Diseases, 2020. vol. 20, no. 5, pp. 553–558 DOI: 10.1016/S1473-3099(20)30144-4
- Rajagopal K., et al. A fractional-order model for the novel coronavirus (COVID-19) outbreak, Nonlinear Dynamics, 2020. vol. 101, no. 1, pp. 711–718 DOI: 10.1007/s11071-020-05757-6
- Anastassopoulou C., Russo L., Tsakris A., Siettos C. Data-based analysis, modelling and forecasting of the COVID-19 outbreak, PLOS ONE, 2020. vol. 15, no. 3, pp. 1–21 DOI: 10.1371/journal.pone.0230405
- Casella F. Can the COVID-19 epidemic be controlled on the basis of daily test reports? IEEE Control Syst. Lett. 2020, vol. 5(3), pp. 1079–1084 DOI: 10.1109/LCSYS.2020.3009912
- Wu J. T., et al. Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China, Nature Medicine, 2020. vol. 26, no. 4, pp. 506–510 DOI: 10.1038/s41591-020-0822-7
- Joel H., et al. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts, The Lancet Global Health, 2020. vol. 8, no. 4, pp. 488–496 DOI: 10.1016/S2214-109X(20)30074-7
- Pskhu A. V. Fractional diffusion equation with a discretely distributed differentiation operator, Sib. Elektron. Math. Rep. 2016, vol. 13, pp. 1078–1098. DOI: 10.17377/semi.2016.13.086 (In Russian).
- Pskhu A. V. Initial-value problem for a linear ordinary differential equation of noninteger order Sb. Math. 2011. vol. 202, no. 4, pp. 571–582 DOI: 10.1070/SM2011v202n04ABEH004156
- Wang W., Khan M. A. Analysis and numerical simulation of fractional model of bank data with fractal-fractional Atangana-Baleanu derivative, Journal of Computational and Applied Mathematics, 2020. vol. 369, pp. 15 DOI: 10.1016/j.cam.2019.112646
- Diethelm K., Ford N. J. Analysis of fractional differential equations,Journal of Mathematical Analysis and Applications, 2002. vol. 265, no. 2, pp. 229–248.
- Yu F. Integrable coupling system of fractional soliton equation hierarchy, Physics Letters. A, 2009. vol. 373, no. 41, pp. 3730–3733 DOI: 10.1016/j.physleta.2009.08.017
- Demirci E., Unal A., Ozalp N. A fractional order SEIR model with density dependent death rate, Hacettepe journal of mathematics and statistics, 2011. vol. 40, pp. 287–295.
- Lin W. Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl. 332(1), 709–726 (2007). DOI: 10.1016/j.jmaa.2006.12.036
- Nakhushev A. M., Fractional calculus and its applications, Fizmatlit, Moscow, 2003. DOI: 10.1016/j.jmaa.2006.12.036 (In Russian).
- Chicchi L., Patti F.D., Fanelli D., Piazza F., Ginelli F. First results with a SEIRD model. Quantifying the population of asymptomatic individuals in Italy, Part of the project “Analysis and forecast of COVID-19 spreading 2020.
- Taukenova F. I., Shkhanukov-Lafishev M. Kh. Difference methods for solving boundary value problems for differential equations of fractional order, Comput. Math. Math. Phys., 2006. V. 46, No. 10, pp. 1785–1795 DOI: 10.1134/S0965542506100149. DOI: 10.1134/S0965542506100149 (In Russian).
Tsakhoeva Albina Feliksovna – Candidate of Pedagogical Sciences, Associate Professor, Department of Applied Mathematics and Informatics, North Ossetian State University named after K. L. Khetagurov, Vladikavkaz, Russia, ORCID 0000-0002-4179-9598.
Shigin Dmitry Dmitrievich – master student of the Faculty of Mathematics and Computer Science, specialty “Applied Mathematics and Informatics North Ossetian State University named after K. L. Khetagurov, Vladikavkaz, Russia, ORCID 0000-0002-5156-8048.