Hybrid Models of Transformations of Epidemic Waves

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Abstract

We analyze specific options for the development of the current epidemic situation due to regularly updated SAR-CoV-2 strains and compare methods for modeling the spread of infection. The relevance of the development of scenario modeling methodology is due to the renewed waves of growth in COVID cases in a number of regions in 2024 as an unusual variant of a pulsating epidemic process. The next surges of infections are determined by the activity of the evolutionary branch of the BA.2.86 Pirola strains, which have managed to split, which are better in affinity and antibody avoidance than the previously dominant Omicron EG.5 or XBB.1.5 lines. Strains in 2023 retained sufficient transmissibility with reduced affinity for the ACE2 receptor and a lower replication rate compared to Delta, but the persistence time of the virus increased. In the situation of immunization of the population, the trend of virus evolution has changed with an emphasis on the complication of the phylogenetic tree and with the selection of Spike protein variants that provide balanced characteristics for replication and evasion of antibodies. The potential for variability of coronavirus proteins is clearly not exhausted, and methods for predicting their promising mutations are under development. Methods for computational research of epidemic scenarios based on those modified by expanding the set of statuses of individuals in office “SIR” models are discussed. Variants of systems of equations based on SIR do not describe the resumption of COVID waves, which was already observed in 2020. Status transition schemes based on fundamental aspects are poorly suited for describing nonlinear oscillatory regimes of the epidemic, even when second-order oscillatory equations are included in the linear SIR scheme. The models developed by the author for decaying COVID waves based on equations with delay and with threshold effects were modified to take into account that the new Omicron lines change fluctuation regimes. The changes in oscillation modes that we have identified with an increase in repeated cases are not described only by restructuring the parameters of the equations with damping functions. According to the observed epidemic graphs of COVID waves, the models require a restructuring of regulatory functions. We propose to model aspects of the transition phases of the modern epidemic using special computational tools and based on the nature of nonlinear oscillations. An original method for forming a structure for a hybrid model is substantiated based on a set of right-hand sides of differential equations with heterogeneous delayed regulation parameters that generate relaxation oscillations and are redefined when the criteria for the truth of predicates are violated. It has been shown that changes in the binding affinity of S-protein variants with ACE2 are a key indicator for modeling periods of attenuation and activation of waves associated with the evolution of the virus, as in 2024 for the JN.1 strain. The new hybrid model with evet time describes event-based transformations in the shape of epidemic waves associated with disturbances in the mutational landscape of the coronavirus, which can now be established by monitoring mutations and the frequency of occurrence of strains.

About the authors

A. Yu Perevaryukha

St. Petersburg Federal Research Center, Russian Academy of Sciences

Email: temp_elf@mail.ru
St. Petersburg, Russia

References

  1. Переварюха А. Ю. Гибридная модель коллапса промысловой популяции краба Paralithodes camtschaticus (Decapoda, Lithodidae) Кадьякского архипелага. Биофизика , 67 (2), 386-408 (2022). doi: 10.31857/S0006302922020223
  2. Переварюха А. Ю. Непрерывная модель трех сценариев инфекционного процесса при факторах запаздывания иммунного ответа. Биофизика, 66 (2), 384407 (2021). doi: 10.31857/S0006302921020204
  3. Переварюха А. Ю. Моделирование сценариев глубокого популяционного кризиса быстро растущей популяции. Биофизика, 66 (6), 1144-1163 (2021). doi: 10.31857/S0006302921060107
  4. Соловьева Т. Н. Динамическая модель деградации запасов осетровых рыб со сложной внутрипопуляционной структурой. Информационно-управляющие системы , № 4 (83), 60-67 (2016). doi: 10.15217/issn1684-8853.2016.4.60
  5. Minkoff J. M. and Oever B. Innate immune evasion strategies of SARS-CoV-2. Nature Rev. Microbiol, 21, 178-190 (2023). doi: 10.1038/s41579-022-00839-1
  6. Duan T., Xing C., and Chu J. ACE2-dependent and -independent SARS-CcV-2 entries dictate viral replication and inflammatory response during infection. Nature, 26, 628-644 (2024). doi: 10.1038/s41556-024-01388-w
  7. Costa G., Lacerda S., and Figueiredo A. High SARS-CoV-2 tropism and activation of immune cells in the testes of non-vaccinated deceased COVID-19 patients. BMC Biol., 21, 36-48 (2023). doi: 10.1186/s12915-022-01497-8
  8. Flerlage T., Boyd D., and Meliopoulos V. Influenza virus and SARS-CoV-2: pathogenesis and host responses in the respiratory tract. Nature Rev. Microbiol., 19, 425-441 (2021). doi: 10.1038/s41579-021-00542-7
  9. Yang M., Meng Y., and Hao W. A prognostic model for SARS-CoV-2 breakthrough infection: Analyzing a prospective cellular immunity cohort. Int. Immuncpharmacol., 131 (20), 111829 (2024). doi: 10.1016/j.mtimp.2024.111829
  10. Нечипуренко Ю. Д., Анашкина А. А. и Матвеева О. В. Изменение антигенных детерминант S-белка вируса SARS-COV-2 как возможная причина антителозависимого усиления инфекции и цитокинового шторма. Биофизика, 65 (4), 824-832 (2020). doi: 10.31857/S0006302920040262
  11. Ванин А. Ф., Пекшев А. В. и Вагапов А. Б. Газообразный оксид азота и динитрозильные комплексы железа с тиолсодержащими лигандами как предполагаемые лекарственные средства, способные купировать СOVID-19. Биофизика, 66 (1), 183-194 (2021). doi: 10.31857/S0006302921010208
  12. Ванин А. Ф. Динитрозильные комплексы железа с тиолсодержащими лигандами могут как доноры катионов нитрозония подавлять вирусные инфекции (гипотеза). Биофизика, 65 (4), 818-823 (2020). doi: 10.31857/S0006302920040250
  13. Ершов П. В., Яблоков Е. О., Мезенцев Ю. В., Чуев Г. Н., Федотова М. В., Кручинин С. Е., Иванов А. С. Папаиноподобная протеаза PLPRO коронавируса SARS-COV-2 как противовирусная мишень для ингибиторов активного центра и белок-белковых взаимодействий. Биофизика, 67 (6), 1109-1121 (2022). doi: 10.31857/S0006302922060084
  14. Пал Д., Гхош Д., Сантра К. и Махапатра Г. Математический анализ модели эпидемии COVID-19 с использованием данных эпидемиологических параметров болезней, распространенных в Индии. Биофизика, 67 (2), 301-318 (2022). doi: 10.31857/S0006302922020132
  15. Louie J. and Agraz-Lara R. Tuberculosis-associated hospitalizations and deaths after COVID -19 shelter-in-place, San Francisco, California, USA. Emerg. Infect. Dis., 27 (8), 2227-2229 (2021). doi: 10.3201/eid2708.210670
  16. Planas D., Staropoli I., and Michel V. Distinct evolution of SARS-CoV-2 Omicron XBB and BA.2.86/JN.1 lineages combining increased fitness and antibody evasion. Nat. Commun., 15, 2254-2265 (2024). doi: 10.1038/s41467-024-46490-7
  17. Переварюха А. Ю. Анализ развития трендов современной эпидемической ситуации и факторов их локальной дифференциации. Биофизика, 68 (5), 10571073 (2023). doi: 10.31857/S0006302923050277
  18. Tamura T., Irie T., and Deguchi S. Virological characteristics of the SARS-CoV-2 Omicron XBB.1.5 variant. Nature Commun., 15, 1176-1188 (2024). doi: 10.1038/s41467-024-45274-3
  19. Kojimaa N. and Klausnerb J. Protective immunity after recovery from SARS-CoV-2 infection. Lancet Infect. Dis., 22 (1), 12-14 (2022). doi: 10.1016/S1473-3099(21)00676-9
  20. Swartz M. D. Antibody Duration After Infection From SARS-CoV-2 in the Texas coronavirus antibody response survey. J. Infect. Dis., 227 (2), 193-201 (2023). doi: 10.1093/infdis/jiac167
  21. Ioannidis J., Cripps S., and Tanner M. Forecasting for COVID-19 has failed. Int. J. Forecasting, 423, 423-438 (2022). doi: 10.1016/j.ijforecast.2020.08.004
  22. Wang Q., Guo Y., and Liu L. Antigenicity and receptor affinity ofSARS-CoV-2 BA.2.86 spike. Nature, 624, 639644 (2023). doi: 10.1038/s41586-023-06750-w
  23. Nussenblatt V Year-long COVID-19 infection reveals within-host evolution of SARS-CoV-2 in a patient with B cell depletion. J. Infect. Dis. 225, 1118-1124 (2022). doi: 10.1101/2021.10.02.21264267
  24. Cevik M. SARS-CoV-2, SARS-CoV, and MERS-CoV viral load dynamics, duration of viral shedding, and infectiousness: a systematic review and meta-analysis. Lancet Microbe, 2 (1), e13-e22 (2021). doi: 10.1016/S2666-5247(20)30172-5
  25. Puhach O., Meyer B., and Eckerle I. SARS-CoV-2 viral load and shedding kinetics. Nat. Rev. Microbiol., 21, 147161 (2023). doi: 10.1038/s41579-022-00822-w
  26. Tsang K., Perera R., and Fang J. Reconstructing antibody dynamics to estimate the risk of influenza virus infection. Nat. Commun., 13, 1557-1568 (2022). doi: 10.1038/s41467-022-29310-8
  27. Wilke C. O. The biophysical landscape of viral evolution. Proc. Natl. Acad. Sci. USA, 121, e2409667121 (2024). doi: 10.1073/pnas.2409667121
  28. Hay J. A. Quantifying the impact of immune history and variant on SARS-CoV-2 viral kinetics and infection rebound: A retrospective cohort study. eLfe, 11, e81849 (2022). doi: 10.7554/eLife.81849
  29. Bacaër N. The model of Kermack and McKendrick for the plague epidemic in Bombay and the type reproduction number with seasonality. J. Math. Biol., 64, 403—422 (2012). doi: 10.1007/s00285-011-0417-5.
  30. Kermack W. O. and McKendrick A. G. A contribution to the mathematical theory ofepidemics. Papers Math. Phys., 115, 700-721 (1927). doi: 10.1098/rspa.1927.0118
  31. Bakare E., Nwagwo A., and Danso-Addo E. Optimal Control Analysis of an SIR Epidemic Model with Constant Recruitment. Int. J. Appl. Math. Res., 3, 273-285 (2014). doi: 10.14419/ijamr.v3i3.2872
  32. Nikitina A. V., Lyapunov I. A., and Dudnikov E. A. Study of the spread of viral diseases based on modifications of the SIRmodel. Comput. Math. Inform. Technol., 4 (1), 1930 (2020). doi: 10.23947/2587-8999-2020-1-1-19-30
  33. Almeida R., Cruz B., and Martins N. An epidemiological MSEIR model described by the Caputo fractional derivative. Int. J. Dynam. Control., 7, 776-784 (2019). doi: 10.1007/s40435-018-0492-1
  34. Drake J., Bakach I., and Just M. Transmission models of historical Ebola outbreaks. Emerg. Inf. Dis., 21, 14471459 (2015). doi: 10.3201/eid2108.141613
  35. Spyrou M.A., Keller M., and Tukhbatova R. Phylogeography of the second plague pandemic revealed through analysis of historical Yersinia pestis genomes. Nat. Commun. , 10, 4470-4478 (2019). doi: 10.1038/s41467-019-12154-0
  36. Chin V., Samia I., and Marchant R. A case study in model failure? COVID-19 daily deaths and ICU bed utilisation predictions in New York state. Eur. J. Epidemiol. ,35,733742 (2020). doi: 10.1007/s10654-020-00669-6
  37. Moein S., Nickaeen N. and Roointan A. Inefficiency of SIR models in forecasting CO VID-19 epidemic: a case study of Isfahan. Sci. Rep., 11,4725-4733 (2021). doi: 10.1038/s41598-021-84055-6
  38. Rocchi E., Peluso S., Sisti D., and Carletti M. New epidemic model for the CO VID-19 pandemic: The 0-SI(R)D model. BioMedInformatics, 2 (3), 398-404 (2022). doi: 10.3390/biomedinformatics2030025
  39. Swadling L. and Maini K. T cells in COVID-19 - united in diversity. Nature Immunol., 21, 1307-1308 (2020). doi: 10.1038/s41590-020-0798-y
  40. Ghafari M., Hall M., and Golubchik T. Prevalence of persistent SARS-CcV-2 in a large community surveillance study. Nature, 626, 1094-1101 (2024). doi: 10.1038/s41586-024-07029-4
  41. Billong S., Kouamou G., Bouetou T., and Tagoudjeu J. A hybrid epidemiological model based on individual dynamics. J. Algorithms Comput. Technol., 17, 345-349, 2023. doi: 10.1177/17483026231186009
  42. Paxson W. and Shen B. A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis. Chaos, Solitons and Fractals, 173, e113610 (2023). doi: 10.1016/j.chaos.2023.113610
  43. Choi H. and Hwang M., Evolution of a Distinct SARS-CoV-2 Lineage Identified during an Investigation of a Hospital Outbreak. Viruses, 16 (2), 337-343 (2024) doi: 10.3390/v16030337
  44. Mikhailov V. V. and Spesivtsev A. V. Evaluation of the dynamics ofphytomass in the Tundra zone using a fuzzy-opportunity approach. Intelligent distributed computing XIII (ISC 2019), Studies in Computational Intelligence, 868, 449-454 (2020). doi: 10.1007/978-3-030-32258-8_53
  45. Переварюха А. Ю. Итерационная непрерывно-событийная модель вспышки численности полужесткокрылого фитофага. Биофизика, 61 (2), 395-404 (2016). doi: 10.31857/S0006302923050277
  46. Perevaryukha A. Y. Scenario modeling of regional epidemics of SARS-COV-2 and analysis of immunological aspects of new expected COVID waves. Tech. Phys., 68, 205-217 (2023). doi: 10.1134/S1063784223060038
  47. Cao Y., Wang J., and Jian F. Omicron escapes the majority of existing SARS-CoV-2 neutralizing antibodies. Nature, 602, 657-663 (2022). doi: 10.1038/s41586-021-04385-3
  48. Perevaryukha A. Y. Modeling abrupt changes in population dynamics with two threshold states. Cybern. Syst. Anal. ,52, 623-630 (2016). doi: 10.1007/s10559-016-9864-8
  49. Perevaryukha A. Y. Hybrid model of bioresourses’ dynamics: Equilibrium, cycle, and transitional chaos. Aut. Conrol Comp. Sci., 45, 223-232 (2011). doi: 10.3103/S0146411611040067
  50. Perevaryukha A. Y. Uncertainty of asymptotic dynamics in bioresource management simulation. J. Comput. Syst. Sci. Int., 50, 491-498 (2011). doi: 10.1134/S1064230711010151
  51. Jian E, Feng L., and Yang S. Convergent evolution of SARS-CoV-2 XBB lineages on receptor-binding domain 455-456 synergistically enhances antibody evasion and ACE2 binding. PLoSPathogens, 19 (12), e1011868 (2023). doi: 10.1371/journal.ppat.1011868
  52. Cui J. and Li F. Origin and evolution of pathogenic coronaviruses. Nat. Rev. Microbiol., 17, 181-192 (2019). doi: 10.1038/s41579-018-0118-9
  53. Lu G. Molecular basis of binding between novel human coronavirus MERS-CoV and its receptor CD26. Nature, 500, 227-231 (2013). doi: 10.1038/nature12328
  54. Ferretti L., Wymant C., and Petrie J. Digital measurement of SARS-CoV-2 transmission risk from 7 million contacts. Nature, 626, 145-150 (2024). doi: 10.1038/s41586-023-06952-2
  55. Fabiano N. and Radenovic S. On covid-19 diffusion in italy: data analysis and possible outcome. Military Technical Courier, 69 (1), 15-21 (2021). doi: 10.5937/vcjtehg68-25948
  56. Carreño J., Alshammary H., and Tcheou J. Activity of convalescent and vaccine serum against SARS-CoV-2 Omicron. Nature, 602, 682-688 (2022). doi: 10.1038/s41586-022-04399-5
  57. Perevaryukha A. Y. Cyclic and unstable chaotic dynamics in models of two populations of sturgeon fish. Numer. Analys. Appl., 5, 254-264 (2012). doi: 10.1134/S199542391203007X
  58. Mikhailov V. V. and Trofimova I. V. Computational modeling of the nonlinear metabolism rate as a trigger mechanism of extreme dynamics of invasion processes. Tech. Phys. Lett., 48, 301-304 (2022). doi: 10.1134/S1063785022110013
  59. Trofimova I. V., Perevaryukha A. Y., and Manvelova A. B. Adequacy of interpretation of monitoring data on biophysical processes in terms of the theory of bifurcations and chaotic dynamics. Tech. Phys. Lett., 48, 305-310 (2022). doi: 10.1134/S1063785022110025
  60. Perevaryukha A. Y. Predicative computing structures and hybrid automates in modeling invasive processes and epidemic COVID waves. Tech. Phys., 68, 8-17 (2023). doi: 10.1134/S1063784223010048
  61. Borisova T. Y. On the physicochemical method of analysis of the formation of secondary immunodeficiency as a bioindicator of the state of ecosystems using the example of seabed biota of the Caspian Sea. Tech. Phys. Lett., 48, 251-257 (2022). doi: 10.1134/S1063785022090012
  62. Mikhailov V. V., Perevaryukha A. Y., and Trofimova I. V. Principles of simulation of invasion stages with allowance for solar cycles. Tech. Phys. Lett., 49, 97-105 (2023). doi: 10.1134/S1063785023700049
  63. Perevaryukha A. Y. Continuous model for the devastating oscillation dynamics of local forest pest populations in Canada. Cybern. Syst. Anal., 55, 141-152 (2019). doi: 10.1007/s10559-019-00119-6

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