Abstract. 

The COVID-19 pandemic has moved into the stage of a dynamic confrontation between the pathogen mutating in the regions and accumulating (natural and vaccine) population immunity. Pandemic influenza strains in a similar collision faded after three waves. SARS-COV-2 has an amazing rate of renewal of several of its structural proteins at once, which leads to new oscillations in the number of infections and competition between the evolutionary branches of virus strains. The variety of strains and variability of virus antigens periodically increases, but then some strains go out of distribution, but the rest give rise to new branches. Dynamically, this is reflected in waves of the number of recorded infections, the frequency and amplitude of peaks of which vary significantly in the regions. This is how regional epidemic scenarios are formed, some of which are quite unusual. Classical damped oscillations have been observed in South Africa. In spring of 2023, the next 7th local COVID wave begins in Australia. For a phenomenological model description of the observed dynamics, we propose to use equations with delay is flexible tool for describing complex forms of oscillatory dynamics, where we proposed to include special threshold damping functions. It was possible to obtain solutions for both collapsing and damped scillations with the possibility of new outbreak, which made it possible to describe the effect of single extreme wave that arose in early 2022 in New York and earlier in Brazil after an increase in the length of active infection chains, a sharp Λ-shaped peak with vibrational damping. The scenario differs significantly from both the primary outbreak and Japanese epidemic scenario – a series of successive short-term waves with increasing amplitude. Only slowing down the evolution of the virus can stop the pandemic, and heterogeneity of population immunity become an important factor, if antibodies are developed for the same epitopes, then changes in these protein regions trigger another wave. In august, earlier than the forecast, COVID-wave of the strain EG.5 "Eris" began.

Keywords: 

system analysis of epidemic factors, differentiation of regional epidemics, infection chains, oscillatory modes of infection cases, equations with delay, birth bifurcations and destruction of cyclic trajectories

PP. 114-126.

DOI: 10.14357/20790279230312

 

References

1. Magnitskiy N.A. 2020. O perekhode k khaosu v odnoy modeli dinamiki populyatsiy [On the transition to chaos in one model of population dynamics]. Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk [Proceedings of the Institute of System Analysis of the Russian Academy of Sciences] 70 (2): 71-74.

2. Perevaryukha A.Yu. 2021. Model stsenariya istoshcheniya bioresursov pri ekspertnom upravlenii strategiyey ekspluatatsii [Bioresource Depletion Scenario Model under Expert Management of Exploitation Strategy] Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk [Proceedings of the Institute of System Analysis of the Russian Academy of Sciences] 71 (3): 36-46.

3. Belotelov N.V. 2018. Problems of modeling in ecology [Problems of modeling in ecology] Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk [Proceedings of the Institute of System Analysis of the Russian Academy of Sciences] 68 (2): 16-21.

4. Kamenev G.K. 2018. Investigation of Bifurcation Properties of a Population Using Metric Networks [Investigation of Bifurcation Properties of a Population Using Metric Networks] Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk [Proceedings of the Institute of System Analysis of the Russian Academy of Sciences] 68 (2): 26-29.

5. Sokolov A.V. 2014. Modelirovaniye evolyutsii populyatsiy s vozrastnoy strukturoy: svyaz’ rozhdayemosti so skorost’yu izmeneniya sredy [Modeling the evolution of populations with age structure: the relationship between fertility and the rate of environmental change]. Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk [Proceedings of the Institute for System Analysis of the Russian Academy of Sciences] 64 (3): 53-59.

6. Perevaryukha A.Yu. 2015. Gibridnaya model’ razvitiya lokal’no vzryvoobraznogo populyatsionnogo protsessa nasekomogo [A hybrid model of the development of a locally explosive population process of an insect]. Trudy Instituta sistemnogo analiza Rossiyskoy akademii nauk  [Proceedings of the Institute for System Analysis of the Russian Academy of Sciences] 65 (2): 94-104.

7. Delorey T.M., Ziegler C.G.K., Heimberg G. 2021. COVID-19 tissue atlases reveal SARS-CoV-2 pathology and cellular targets. Nature 595: 107– 113. https://doi.org/10.1038/s41586-021-03570-8

8. Lamb K.D., Luka M.M., Saathoff M., Orton R. 2023. SARS-CoV-2’s evolutionary capacity is mostly driven by host antiviral molecules. bioRxiv 2023.04.07.536037. https://doi.org/10.1101/2023.04.07.536037

9. Cilia R. 2022. SARS-CoV-2-specific CD4+ and CD8+ T cell responses can originate from crossreactive CMV-specific T cells. eLife. 11. art. no: e82050.

10. Ioannidis J.P.A., Cripps S. 2022. Tanner M. Forecasting for COVID-19 has failed // International Journal of Forecasting. 2: 423–438. doi.org/10.7554/eLife.82050

11. Сhin V., Samia N.I., Marchant R. 2020. A case study in model failure? COVID-19 daily deaths and ICU bed utilisation predictions in New York state. European Journal of Epidemiology. 35: 733–742. https://doi.org/10.1007/s10654-020-00669-6

12. Moein S., Nickaeen N., Roointan A. 2021. Inefficiency of SIR models in forecasting COVID-19 epidemic: a case study of Isfahan. Scientific Reports. 11 аrt no. 4725. https://doi.org/10.1038/s41598-021-84055-6

13. Nikitina A.V. 2020. Study of the spread of viral diseases based on modifications of the SIR model. Computational Mathematics and Information Technologies. 1: 19–30.

14. Barnard R.C. 2022. Modelling the medium-term dynamics of sars-cov-2 transmission in England in the omicron era. Nature Communication. 13: Art.no 4879. https://doi.org/10.1038/s41467-022-32404-y

15. Ghosh S.K., Ghosh S. 2023. A mathematical model for COVID-19 considering waning immunity, vaccination and control measures. Scientific

Reports. 13: art. no. 3610. https://doi.org/10.1038/s41598-023-30800-y

16. Kevin W. et al. 2020. Preexisting and de novo humoral immunity to SARS-CoV-2 in humans. Science. 370:1339-1343. https://doi.org/10.1126/ science.abe1107

17. Perevaryukha A.Y. 2021. A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors. Biophysics. 66: 327–348. https://doi.org/10.1134/ S0006350921020160

18. Hutchinson G.E. 1948. Circular causal systems in ecology. Ann. N. Y. Acad. Sci. 50(4): 221–246.

19. Kolesov A.Yu., Kolesov Yu.S. 1993. Relaksatsionnyye kolebaniya v matematicheskikh modelyakh ekologii [Relaxation oscillations in mathematical models of ecology]. Trudy MIAN [Proceedings of MIAN] 199: 3–124.

20. Trofimova I.V., Perevaryukha A.Y., Manvelova A.B. 2022. Adequacy of Interpretation of Monitoring Data on Biophysical Processes in Terms of the Theory of Bifurcations and Chaotic Dynamics. Technical Physics Letters. 48 (12): 305–310.

https://doi.org/10.1134/S1063785022110025

21. Fabiano N., Radenovic S.N. 2021. The second COVID-19 wave of 2020 in Italy: a brief analysis. Military Technical Courier. 69 (1): 1–7.

22. Shabunin A.V. 2022. Gibridnaya SIRSmodel’ rasprostraneniya infektsiy. Prikladnaya nelineynaya dinamika [Hybrid SIRS-model of the spread of infections]. [Applied nonlinear dynamics] 30 (6): 717–731.

23. Abotaleb M.S., Makarovskikh T.A. 2021. Development of algorithms for choosing the best time series models and neural networks to predict COVID-19 cases. Bulletin of the South Ural State University. 21 (3): 26–35.

24. Zaikovskaya A.V., Gladysheva A.V., Kartashov M.Yu. 2022. Izucheniye v usloviyakh in vitro biologicheskikh svoystv shtammov koronavirusa SARS-COV-2, otnosyashchikhsya k razlichnym geneticheskim variantam [In vitro study of the biological properties of SARS-COV-2 coronavirus strains belonging to different genetic variants]. Problemy osobo opasnykh infektsiy [Problems of especially dangerous infections] 1: 94–100.

25. Vechorko V.I., Averkov O.V., Zimin A.A. 2022. Izucheniye v usloviyakh in vitro biologicheskikh svoystv shtammov koronavirusa SARS-COV-2, otnosyashchikhsya k razlichnym geneticheskim variantam [New strain SARS-COV-2 Omikron – clinic, treatment, prevention (literature review)]. Problemy osobo opasnykh infektsiy [Cardiovascular therapy and prevention] 21(6): 89–98.

26. Silva S.J., Pardee K., Pena L., Kohl A. 2022. Recent insights into SARS-COV-2 omicron variant. Reviews in Medical Virology 33: Art no: e2373. doi: 10.1002/rmv.2373.

27. Juul F.E., Jodal H.C., Barua I. 2022. Mortality in Norway and Sweden during the COVID-19 pandemic. Scandinavian Journal of Public Health 50: 38-45. doi:10.1177/14034948211047137

28. Brusselaers N., Steadson D., Bjorklund K. 2022. Evaluation of science advice during the COVID-19 pandemic in Sweden. Humanities and Social Sciences Communications. 9 Art no: 91.

https://doi.org/10.1057/s41599-022-01097-5

29. Phetsouphanh C., Darley D.R., Wilson D.B. 2022. Immunological dysfunction persists for 8 monthsfollowing initial mild-to-moderate SARS-CoV-2 infection. Nature Immunology. 210–216. https:// doi.org/10.1038/s41590-021-01113-x

30. Oshitani H. 2022. COVID lessons from Japan: the right messaging empowers citizens. Nature 605 

Art no: 589. https://doi.org/10.1038/d41586-022-01385-9

31. Corey L, Beyrer C, Cohen M., Michael N., Bedford T, Rolland M. 2021. SARS-CoV-2 variants in patients with immunosuppression. The New England Journal of Medicine. 385: 562–566. doi:10.1056/NEJMsb2104756. pmid:34347959

32. Shrock E.L., Timms R.T. 2023. Germline-encoded amino acid–binding motifs drive immunodominant public antibody responses. Science 380 (6640):

798-816. https://doi.org/10.1126/science.adc9498

33. Markov P.V., Ghafari M., Beer M. 2023. The evolution of SARS-CoV-2 // Nature Reviews Microbiology 21: 195–210. https://doi.

org/10.1038/s41579-023-00878-2

34. Perevaryukha A.Y. 2016. An iterative continuousevent model of the population outbreak of a phytophagous hemipteran. Biophysics 61(2): 334-341.

35. Lloyd-Smith J.O., Schreiber S.J., Kopp P.E., Getz W.M. 2005. Superspreading and the effect of individual variation on disease emergence. Nature. 438: 355–359.

36. Mikhailov V.V., Perevaryukha A.Y., Trofimova, I.V. 2022. Computational Modeling of the Nonlinear Metabolism Rate as a Trigger Mechanism of Extreme Dynamics of Invasion Processes. Technical Physics Letters. 48: 301–304. https:// doi.org/10.1134/S1063785022110013.