Phenomenological models of three scenarios of local coronavirus epidemics

A. Yu. Perevaryukha

Matematičeskoe modelirovanie, Tome 36 (2024) no. 1, pp. 105-130.

Résumé

The COVID-19 pandemic did not end in the summer of 2023, but moved into the stage of a dynamic confrontation between a mutating pathogen and herd immunity (natural and vaccine). Pandemic influenza strains were guaranteed to die out after three waves. SARS-COV-2 is able to maintain variability in its E and S proteins. The diversity of SARS-COV-2 strains is increasing impulsively (XBB.x in India, XBC in Philippines). Most strains drop out of distribution, but the remaining ones give rise to new branches like BA.2.86 «Pirola». The evolution is reflected by the pulsation in the number of recorded infections, but the frequency and amplitude of the peaks differ in the regions. Regional epidemic scenarios are emerging, and some of them are unusual. Not only the property of the variability of the antigens of the virus leads, after the attenuation of the oscillations in the number of infections, to new repeated outbreaks. For a phenomenological model description of scenarios for the emergence of new waves, we proposed equations with delay as a flexible tool for analyzing complex forms of oscillatory dynamics. The equations were supplemented with special threshold damping functions. In the models, it was possible to obtain scenarios of both collapsing and damping oscillations with the possibility of a new outbreak, which describes the effect of a single extreme wave after increase in length of active infection chains in New York with the sharp J-shaped peak with oscillatory attenuation that stands out sharply among the morbidity oscillations. The wave scenario in Brazil differs significantly from both the primary outbreak in 2020 and the special Japan epidemic scenario in 2022-23 in the form of a series of eight consecutive short peaks with increasing wave amplitude. Since the coronavirus successfully counteracts the immune system, there is an increase in severe cases of reinfection with COVID-19 in a group that is particularly susceptible. An important factor for slowing down the evolution of the virus is heterogeneity of population immunity, when activated T-lymphocytes and produced antibodies in the population are able to respond to a wide range of epitopes from different conservative regions of proteins.

Détail

Keywords: system analysis of epidemic factors, differentiation of regional epidemics, oscillatory modes of infection cases, equations with delay, birth bifurcations and destruction of cyclic trajectories.
Mots-clés : infection chains

Bibliographie

[1] A. V. Lasunskii, “Stability of stationary states in some population models with variable coefficients”, Math. Models and Computer Simulations, 1:2 (2009), 335–342 | DOI | MR

[2] A. Yu. Perevaryukha, “Phenomenological Computational Model for the Development of a Population Outbreak of Insects with Its Bifurcational Completion”, Math. Models and Computer Simulations, 10:4 (2018), 501–511 | DOI | MR | Zbl

[3] V. G. Il'ichev, “Universal stock constants in models of competition”, Math. Models and Computer Simulations, 8:1 (2016), 73–83 | DOI | MR | Zbl

[4] A. Y. Shcheglov, S. V. Netessov, “The Reconstruction of Functional Coefficients for a Quasi-Stable Population Dynamics Model”, Math. Models and Computer Simulations, 14:5 (2022), 808–818 | DOI | DOI | MR

[5] V. D. Perminov, M. A. Kornilina, “Individuum-orientirovannaia model rasprostraneniia epidemii v gorodskikh usloviiakh”, Mat. modelir., 19:5 (2007), 116–127 | Zbl

[6] T. R. Amanbaev, S. J. Antony, “Development of Mathematical Models Taking into Account the Effect of Isolating Individuals in a Population”, Math. Models and Computer Simulations, 14:3 (2022), 466–479 | DOI | DOI | MR

[7] O. Krivorotko, “Agent-based modeling of COVID-19 outbreaks for New York state and UK: parameter identification algorithm”, Infectious Disease Modell, 7 (2022), 30–44 | DOI

[8] V. Petrakova, O. Krivorotko, “Mean field game for modeling of COVID-19 spread”, Journal of Mathematical Analysis and Applications, 514:1 (2022), 126–141 | DOI | MR

[9] V. Yu. Osipov, S. V. Kuleshov, A. A. Zaitseva, A. Yu. Aksenov, “An approach to localizing the source of the COVID-19 epidemic in Russia based on mathematical modeling”, Informatics and Automation, 2021, no. 5, 1065–1089

[10] I. D. Kolesin, E. M. Zhitkova, “Was There a Period of Latent Development of COVID-19 in St. Petersburg? Mathematical Simulation Results and Facts”, Math. Models and Computer Simulations, 15:6 (2023), 1037–1044 | DOI | DOI | MR | MR

[11] V. Ya. Kisselevskaya-Babinina, A.A. Romanyukha, T.E. Sannikova, “Mathematical Model of COVID-19 Progression: Prediction of Severity and Outcome”, Math. Models and Computer Simulations, 15:6 (2023), 987–998 | DOI | DOI | MR | Zbl

[12] M. Lenart, M. Gorecka, M. Bochenek, E. Barreto-Duran, “SARS-CoV-2 infection impairs NK cell functions via activation of the LLT1-CD161 axis”, Front. Immunol., 14 (2023), 1123155 | DOI

[13] H. Tang, Y. Shao, Y. Huang, “Evolutionary characteristics of SARS-CoV-2 Omicron subvariants adapted to the host”, Sig. Transduct. Target Ther., 8 (2023), 211–221 | DOI

[14] J. P.A. Ioannidis, S. Cripps, M. Tanner, “Forecasting for COVID-19 has failed”, International Journal of Forecasting, 2022, no. 2, 423–438 | DOI

[15] V. Chin, N. I. Samia, R. Marchant, “A case study in model failure? COVID-19 daily deaths and ICU bed utilisation predictions in New York”, European J. of Epidemiology, 35 (2020), 733–742 | DOI

[16] S. Moein, N. Nickaeen, A. Roointan, “Inefficiency of SIR models in forecasting COVID-19 epidemic: a case study of Isfahan”, Scientific Reports, 11 (2021), 4725 | DOI

[17] T. M. Delorey, C. G.K. Ziegler, G. Heimberg, “COVID-19 tissue atlases reveal SARS-CoV-2 pathology and cellular targets”, Nature, 595 (2021), 107–113 | DOI

[18] E. Rocchi, S. Peluso, D. Sisti, M. Carletti, “A New Epidemic Model for the COVID-19 Pandemic: The-SI(R)D Model”, BioMedInformatics, 2022, no. 2, 398–404 | DOI

[19] K. S. Tan, S. W.X. Ong, M. H. Koh, “SARS-CoV-2 Omicron variant shedding during respiratory activities”, International Journal of Infectious Diseases, 131 (2023), 19–25 | DOI

[20] K. D. Lamb, M. M. Luka, M. Saathoff, R. Orton, SARS-CoV-2's evolutionary capacity is mostly driven by host antiviral molecules, https://www.biorxiv.org/content/10.1101/2023.04.07.536037v1

[21] L. Bautista, G. Conesa, R. Caravaca, “COVID-19 effective reproduction number determination: an application, and a review of issues and influential factors”, Epidemiologic Methods, 10 (2021), 20200048 | DOI

[22] G. E. Hutchinson, “Circular causal systems in ecology”, Ann. N.Y. Acad. Sci., 50 (1948), 221–246 | DOI

[23] I. S. Kashchenko, E. M. Glushevskii, “Local dynamics of equation with periodically distributed delay”, Theoret. and Math. Phys., 212 (2022), 1125–1136 | DOI | MR | Zbl

[24] R. Cilia, “SARS-CoV-2-specific CD4+ and CD8+ T cell responses can originate from cross-reactive CMV-specific T cells”, eLife, 11 (2022), e82050 | DOI

[25] A. V. Nikitina, “Study of the spread of viral diseases based on modifications of the SIR model”, Computational Mathematics and Information Technologies, 2020, no. 1, 19–30

[26] A. Y. Perevaryukha, “A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors”, Biophysics, 66 (2021), 327–348 | DOI

[27] I. V. Trofimova, A. Y. Perevaryukha, A. B. Manvelova, “Adequacy of Interpretation of Monitoring Data on Biophysical Processes in Terms of the Theory of Bifurcations and Chaotic Dynamics”, Technical Physics Letters, 48 (2022), 305–310 | DOI

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

[29] A. V. Shabunin, “Hybrid SIRS-model of the spread of infections”, Applied nonlinear dynamics, 30:6 (2022), 717–731

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

[31] A. V. Zaykovskaya, A. V. Gladysheva, M. Y. Kartashov, “Izucheniye v usloviyakh in vitro biologicheskikh svoystv shtammov koronavirusa SARS-COV-2, otnosyashchikhsya k razlichnym geneticheskim variantam”, Problemy osobo opasnykh infektsiy, 2022, no. 1, 94–100

[32] V. I. Vechorko, O. V. Averkov, A. A. Zimin, “Novyy shtamm SARS-COV-2 Omikron klinika, lecheniye, profilaktika (obzor literatury)”, Kardiovaskulyarnaya terapiya i profilaktika, 2022, no. 6, 89–98

[33] S. J. Silva, K. Pardee, L. Pena, A. Kohl, “Recent insights into SARS-COV-2 omicron variant”, Reviews in Medical Virology, 33 (2022), e2373 | DOI

[34] F. Juul, H. C. Jodal, I. Barua, “Mortality in Norway and Sweden during the COVID-19 pandemic”, Scandinavian J. of Public Health, 50 (2022), 38–45 | DOI

[35] N. Brusselaers, D. Steadson, K. Bjorklund, “Evaluation of science advice during the COVID-19 pandemic in Sweden”, Humanities Social Sci. Communications, 9 (2022), 91 | DOI

[36] C. Phetsouphanh, D. R. Darley, D. B. Wilson, “Immunological dysfunction persists for 8 months following initial mild-to-moderate SARS-CoV-2 infection”, Nature Immunology, 2022, 210–216 | DOI

[37] H. Oshitani, “COVID lessons from Japan: the right messaging empowers citizens”, Nature, 605 (2022), 589 | DOI

[38] A. Y. Popova, E. B. Ezhlova, A. A. Melnikova, N. S. Bashketova, “Populiatsionnyi immunitet k SARS-CoV-2 sredi naseleniia Sankt-Peterburga v period epidemii COVID-19”, Problemy osobo opasnykh infektsii, 2020, no. 3, 124–130

[39] L. Corey, C. Beyrer, M. Cohen, “SARS-CoV-2 variants in patients with immunosuppression”, The New England Journal of Medicine, 385 (2021), 562–566 | DOI

[40] C. M. Arieta, Y. J. Xie, D. A. Rothenberg, “The T-cell-directed vaccine BNT162b4 encoding conserved non-spike antigens protects animals from severe SARS-CoV-2 infection”, Cell, 2023, 2023.04.007

[41] L. Bull-Otterson, S. Baca, S. Saydah, “Post COVID Conditions Among Adult COVID-19 Survivors Aged 18-64 and65 Years - United States, March 2020-November 2021”, MMWR Morb. Mortal Rep, 71 (2022), 713–717 | DOI

[42] E. L. Shrock, R. T. Timms, “Germline-encoded amino acid-binding motifs drive immune-dominant public antibody responses”, Science, 380 (2023), 798–816 | DOI

[43] P. V. Markov, M. Ghafari, M. Beer, “The evolution of SARS-CoV-2”, Nature Reviews Microbiology, 21 (2023), 195–210 | DOI

[44] D. M. Patrick, M. Petric, D. M. Skowronski, R. Guasparini, “An outbreak of human coronavirus OC43 infection and serological cross-reactivity with SARS coronavirus”, Canadian J. Infectious Diseases and Medical Microbiology, 17 (2006), 330–336 | DOI

[45] A. Y. Perevaryukha, “An iterative continuous-event model of the population outbreak of a phytophagous hemipteran”, Biophysics, 61:2 (2016), 334–341 | DOI