An analysis is presented of universal stages in the development of the COVID-19 virus infection epidemic. It is assumed that during a pandemic the growth rate in the number of infections in a country occurs similarly to the process of virion replication in an infected organism. The exponent of the growth rate of the number of infection cases reflects not only biomedical parameters of a virus infection but also distinctive features of the social behavior of the population of a country. The dynamics of the change in the growth rate exponents is simulated by a system of relaxation-type ordinary differential equations. In applied mathematics, based on the imbedding method, limit values are forecast for exponents of the growth rate of the number of cases using the currently available experimental data. These values “forecast ahead” are subsequently approached by the actual exponents of growth in the number of infectees. The search for unknown parameters is carried out by minimizing a specially constructed quadratic functional accounting for all confirmed cases of COVID-19 infection. The functional minimum is found via iterations by solving a system of ordinary differential equations.
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X. Fu, Q. Ying, T. Zeng, T. Long, and Y. Wang, Simulating and forecasting the cumulative confirmed cases of SARSCoV-2 in China by Boltzmann function-based regression analyses, J. Infection, Lett. Ed., 80, Issue 5, 602–605 (2020).
W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. A: Math., Phys. Eng. Sci., 115, No. 772, 700–721 (1927).
Z. Wanga, C. T. Bauch, S. Bhattacharyya, еt al., Statistical physics of vaccination, Phys. Rep., 664, 1–113 (2016).
S. Flaxman, S. Mishra, A. Gandy, et al., Estimating the number of infections and the impact of nonpharmaceutical interventions on COVID-19 in 11 European countries, Imperial College London (30-03-2020); https://doi.org/10.25561/77731.
N. M. Ferguson, D. Laydon, G. Nedjati-Gilani, et al., Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, Imperial College London (16-03-2020); https://doi.org/10.25561/77482.
S. Eubank, I. Eckstrand, B. Lewis, еt al., Commentary on Ferguson et al. impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, Bull. Math. Biol., 82, No. 52 (2020); https://doi.org/10.1007/s11538-020-00726-x.
L. Lü, D. Chen, X.-L. Ren, Q.-M. Zhang, Y.-C. Zhang, and T. Zhou, Vital nodes identification in complex networks, Phys. Rep., 650, 1–63 (2016).
J. Enrighta and R. R. Kao, Epidemics on dynamic networks, Epidemics, 24, 88–97 (2018).
T. I. Vasylyeva, S. R. Friedman , D. Paraskevis, and G. Magiorkinis, Integrating molecular epidemiology and social network analysis to study infectious diseases: Towards a socio-molecular era for public health, Infect., Genet. Evol., 46, 248–255 (2016).
K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J. M. Hyman, P. Yan, and G. Chowell, Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020, Infect. Dis. Model., 5, 256–263 (2020).
X.-S. Wang, J. Wu, and Y. Yang, Richards model revisited: Validation by and application to infection dynamics, J. Theor. Biol., 313, 12–19 (2012).
G. Chowell, L. Sattenspiel, S. Bansal, and C. Viboud, Mathematical models to characterize early epidemic growth: A review, Phys. Life Rev., 18, 66–97 (2016).
J. Casti and R. Kalaba, Imbedding Methods in Applied Mathematics [Russian translation], Mir, Moscow (1976).
L. Yu. Levin, M. A. Semin, and A. V. Zaitsev, Solution of an inverse Stefan problem in analyzing the freezing of groundwater in a rock mass, J. Eng. Phys. Thermophys., 91, No. 3, 611−618 (2018).
A. G. Vikulov and A. V. Nenarokomov, Identification of mathematical models of the heat excange in space vehicles, J. Eng. Phys. Thermophys., 92, No. 1, 29−42 (2019).
I. V. Derevich and A. A. Panova, Calculati on of thermodynamic equilibrium of a multicomponent two-phase system based on minimization of the Gibbs potential, J. Eng. Phys. Thermophys., 93, No. 2, 247−260 (2020).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 1, pp. 22–34, January–February, 2021.
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Derevich, I.V., Panova, A.A. Estimation of Covid-19 Infection Growth Rate Based on the Imbedding Method. J Eng Phys Thermophy 94, 18–29 (2021). https://doi.org/10.1007/s10891-021-02269-x
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DOI: https://doi.org/10.1007/s10891-021-02269-x