Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

Ugo Avila-Ponce de León; Angel G. C. Pérez; Eric Avila-Vales; Ugo Avila-Ponce de León; Angel G. C. Pérez; Eric Avila-Vales

doi:10.3934/mbe.2023484

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10909-10953. doi: 10.3934/mbe.2023484

Previous Article Next Article

Research article

Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

1.
Programa de Doctorado en Ciencias Biológicas, Universidad Nacional Autónoma de México, Mexico City, Mexico
2.
Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje Catastral 13615, C.P. 97119, Mérida, Yucatán, Mexico

Academic Editor: Yang Kuang

Received: 30 January 2023 Revised: 25 March 2023 Accepted: 05 April 2023 Published: 21 April 2023

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.
- COVID-19,
- vaccination,
- waning immunity,
- stability,
- basic reproduction number
Citation: Ugo Avila-Ponce de León, Angel G. C. Pérez, Eric Avila-Vales. Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10909-10953. doi: 10.3934/mbe.2023484

Related Papers:

Abstract

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

References

[1]	World Health Organization, Classification of Omicron (B.1.1.529): SARS-CoV-2 Variant of Concern. Available from: https://www.who.int/news/item/26-11-2021-classification-of-omicron-(b.1.1.529)-sars-cov-2-variant-of-concern
[2]	Department of Health and Social Care, First UK cases of Omicron variant identified. Available from: https://www.gov.uk/government/news/first-uk-cases-of-omicron-variant-identified.
[3]	D. P. Martin, S. Lytras, A. G. Lucaci, W. Maier, B. Grüning, S. Björn, et al., Selection analysis identifies unusual clustered mutational changes in Omicron lineage BA. 1 that likely impact Spike function, preprint, bioRxiv. https://doi.org/10.1101%2F2022.01.14.476382
[4]	S. Cele, L. Jackson, D. S. Khoury, K. Khan, T. Moyo-Gwete, H. Thandeka, et al., Omicron extensively but incompletely escapes Pfizer BNT162b2 neutralization, Nature, 602 (2021), 654–656. https://doi.org/10.1038/s41586-021-04387-1 doi: 10.1038/s41586-021-04387-1
[5]	M. Li, F. Lou, H. Fan, SARS-CoV-2 variant Omicron: currently the most complete "escapee" from neutralization by antibodies and vaccines, Signal Transduction Targeted Ther., 7 (2022), 28. https://doi.org/10.1038/s41392-022-00880-9 doi: 10.1038/s41392-022-00880-9
[6]	Network for Genomic Surveillance South Africa (NGS-SA), SARS-CoV-2 Sequencing Update 25 November 2021, 2021. Available from: https://www.krisp.org.za/manuscripts/25Nov2021_B.1.1.529_Media.pdf.
[7]	S. He, S. Tang, L. Rong, A discrete stochastic model of the COVID-19 outbreak: Forecast and control, Math. Biosci. Eng., 17 (2020), 2792–2804. http://dx.doi.org/10.3934/mbe.2020153 doi: 10.3934/mbe.2020153
[8]	A. Mourad, F. Mroue, Z. Taha, Stochastic mathematical models for the spread of COVID-19: a novel epidemiological approach, Math. Med. Biol., 39 (2022), 49–76. https://doi.org/10.1093/imammb/dqab019 doi: 10.1093/imammb/dqab019
[9]	F. A. Rihan, H. J. Alsakaji, Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE, Results Phys., 28 (2021), 104658. https://doi.org/10.1016/j.rinp.2021.104658 doi: 10.1016/j.rinp.2021.104658
[10]	H. Wang, N. Yamamoto, Using a partial differential equation with Google Mobility data to predict COVID-19 in Arizona, Math. Biosci. Eng., 17 (2020), 4891–4904. https://doi.org/10.3934/mbe.2020266 doi: 10.3934/mbe.2020266
[11]	P. Sahoo, H. S. Mondal, Z. Hammouch, T. Abdeljawad, D. Mishra, M. Reza, On the necessity of proper quarantine without lock down for 2019-nCoV in the absence of vaccine, Results Phys., 25 (2021), 104063. https://doi.org/10.1016/j.rinp.2021.104063 doi: 10.1016/j.rinp.2021.104063
[12]	A. Viguerie, G. Lorenzo, F. Auricchio, D. Baroli, T. J. R. Hughes, A. Patton, et al., Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion, Appl. Math. Lett., 111 (2021), 106617. https://doi.org/10.1016/j.aml.2020.106617 doi: 10.1016/j.aml.2020.106617
[13]	K. Hattaf, A new generalized definition of fractional derivative with non-singular kernel, Computation, 8 (2020), 49. https://doi.org/10.3390/computation8020049 doi: 10.3390/computation8020049
[14]	K. Hattaf, On the stability and numerical scheme of fractional differential equations with application to biology, Computation, 10 (2022), 97. https://doi.org/10.3390/computation10060097 doi: 10.3390/computation10060097
[15]	A. A. Hamou, E. Azroul, A. Lamrani Alaoui, Fractional model and numerical algorithms for predicting COVID-19 with isolation and quarantine strategies, Int. J. Appl. Comput. Math., 7 (2021), 142. https://doi.org/10.1007/s40819-021-01086-3 doi: 10.1007/s40819-021-01086-3
[16]	A. Boudaoui, Y. El-hadj Moussa, Z. Hammouch, S. Ullah, A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel, Chaos Solitons Fractals, 146 (2021), 110859. https://doi.org/10.1016/j.chaos.2021.110859 doi: 10.1016/j.chaos.2021.110859
[17]	A. A. hamou, E. Azroul, Z. Hammouch, A. L. alaoui, On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate, preprint, medRxiv: 2021.07.18.21260711. https://doi.org/10.1101/2021.07.18.21260711
[18]	M. Gatto, E. Bertuzzo, L. Mari, S. Miccoli, Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures, Proc. Natl. Acad. Sci., 19 (2020), 10484–10491. https://doi.org/10.1073/pnas.2004978117 doi: 10.1073/pnas.2004978117
[19]	A. L. Bertozzi, E. Franco, G. Mohler, D. Sledge, The challenges of modeling and forecasting the spread of COVID-19, Proc. Natl. Acad. Sci., 117 (2020), 16732–16738. https://doi.org/10.1073/pnas.2006520117 doi: 10.1073/pnas.2006520117
[20]	K. Hattaf, M. I. El-Karimi, A. A. Mohsen, Z. Hajhouji, M. El-Younoussi, N. Yousfi, Mathematical modeling and analysis of the dynamics of RNA viruses in presence of immunity and treatment: A case study of SARS-CoV-2, Vaccines, 11 (2023), 201. https://doi.org/10.3390/vaccines11020201 doi: 10.3390/vaccines11020201
[21]	Y. Yu, Y. Liu, S. Zhao, D. He, A simple model to estimate the transmissibility of the Beta, Delta, and Omicron variants of SARS-COV-2 in South Africa, Math. Biosci. Eng., 19 (2022), 10361–10373. https://doi.org/10.3934/mbe.2022485 doi: 10.3934/mbe.2022485
[22]	W. Yang, J. L. Shaman, COVID-19 pandemic dynamics in South Africa and epidemiological characteristics of three variants of concern (Beta, Delta, and Omicron), Elife, 11 (2022), e78933. https://doi.org/10.7554%2FeLife.78933
[23]	N. Gozzi, M. Chinazzi, J. T. Davis, K. Mu, A. P. Piontti, A. Vespignani, et al., Preliminary modeling estimates of the relative transmissibility and immune escape of the Omicron SARS-CoV-2 variant of concern in South Africa, preprint, medRxiv: 2022.01. 04.22268721. https://doi.org/10.1101/2022.01.04.22268721
[24]	A. Gowrisankar, T. M. C. Priyanka, S. Banerjee, Omicron: A mysterious variant of concern, Eur. Phys. J. Plus, 137 (2022), 1–8. https://doi.org/10.1140/epjp/s13360-021-02321-y doi: 10.1140/epjp/s13360-021-02321-y
[25]	F. Grabowski, M. Kochańczyk, T. Lipniacki, The spread of SARS-CoV-2 variant Omicron with a doubling time of 2.0–3.3 days can be explained by immune evasion, Viruses, 14 (2022), 294. https://doi.org/10.3390/v14020294 doi: 10.3390/v14020294
[26]	F. Özköse, M. Yavuz, M. T. Şenel, R. Habbireeh, Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom, Chaos Solitons Fractals, 157 (2022), 111954.
[27]	F. M. G. Magpantay, M. A. Riolo, M. D. De Celles, A. A. King, P. Rohani, Epidemiological consequences of imperfect vaccines for immunizing infections, SIAM J. Appl. Math., 74 (2014), 1810–1830. https://doi.org/10.1137/140956695 doi: 10.1137/140956695
[28]	A. L. Lloyd, Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics, Theor. Popul. Biol., 60 (2001), 59–71. https://doi.org/10.1006/tpbi.2001.1525 doi: 10.1006/tpbi.2001.1525
[29]	P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
[30]	Johns Hopkins CSSE, 2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository, 2022. Available from: https://github.com/CSSEGISandData/COVID-19.
[31]	C. Appel, D. Beltekian, D. Gavrilov, C. Giattino, J. Hasell, B. Macdonald, et al., Data on COVID-19 (coronavirus) Hospitalizations and Intensive Care by Our World in Data, 2022. Available from: https://github.com/owid/covid-19-data/tree/master/public/data/hospitalizations.
[32]	U. A. P. de Le'on, A. G. C. P'erez, E. Avila-Vales, A data driven analysis and forecast of an SEIARD epidemic model for COVID-19 in Mexico, 5 (2020), 14–28. https://doi.org/10.3934/BDIA.2020002
[33]	J. M. Dan, J. Mateus, Y. Kato, K. M. Hastie, E. D. Yu, C. E. Faliti, et al., Immunological memory to SARS-CoV-2 assessed for up to 8 months after infection, Science, 371 (2021), eabf4063. https://doi.org/10.1126/science.abf4063 doi: 10.1126/science.abf4063
[34]	J. A. Martin, B. E. Hamilton, O. M. JK, A. K. Driscoll, Births: Final data for 2019, Natl. Vital Stat. Rep., 70 (2021). http://dx.doi.org/10.15620/cdc:100472 doi: 10.15620/cdc:100472
[35]	National Center for Health Statistics, Deaths and Mortality, 2022. Available from: https://www.cdc.gov/nchs/fastats/deaths.htm.
[36]	H. Sjödin, A. Wilder-Smith, S. Osman, Z. Farooq, J. Rocklöv, Only strict quarantine measures can curb the coronavirus disease (COVID-19) outbreak in Italy, 2020, Eurosurveillance, 25 (2020), 2000280.
[37]	E. Mathieu, H. Ritchie, E. Ortiz-Ospina, M. Roser, J. Hasell, C. Appel, et al., A global database of COVID-19 vaccinations, Nat. Hum. Behav., 5 (2021), 947–953. https://doi.org/10.1038/s41562-021-01122-8 doi: 10.1038/s41562-021-01122-8
[38]	R. J. Harris, J. A. Hall, A. Zaidi, N. J. Andrews, J. K. Dunbar, G. Dabrera, Effect of vaccination on household transmission of SARS-CoV-2 in England, N. Engl. J. Med., 385 (2021), 759–760. https://doi.org/10.1056/NEJMc2107717 doi: 10.1056/NEJMc2107717
[39]	L. R. Baden, H. M. El-Sahly, B. Essink, K. Kotloff, S. Frey, R. Novak, et al., Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine, N. Engl. J. Med., 384 (2021), 403–416. https://doi.org/10.1056/NEJMoa2035389 doi: 10.1056/NEJMoa2035389
[40]	F. P. Polack, S. J. Thomas, N. Kitchin, J. Absalon, A. Gurtman, S. Lockhart, et al., Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine, N. Engl. J. Med., 383 (2020), 2603–2615. https://doi.org/10.1056/NEJMoa2034577 doi: 10.1056/NEJMoa2034577
[41]	J. Sadoff, G. Gray, A. Vandebosch, V. Cárdenas, G. Shukarev, B. Grinsztejn, et al., Safety and efficacy of single-dose Ad26. COV2. S vaccine against Covid-19, N. Engl. J. Med., 384 (2021), 2187–2201. https://doi.org/10.1056/NEJMoa2101544 doi: 10.1056/NEJMoa2101544
[42]	UK Health Security Agency, SARS-CoV-2 Variants of Concern And Variants Under Investigation In England, 2022. Available from: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1050236/technical-briefing-34-14-january-2022.pdf.
[43]	S. A. Buchan, H. Chung, K. A. Brown, P. C. Austin, D. B. Fell, J. B. Gubbay, et al., Estimated effectiveness of COVID-19 vaccines against Omicron or Delta symptomatic infection and severe outcomes, 5 (2022), e2232760. https://doi.org/10.1001/jamanetworkopen.2022.32760
[44]	C. N. Ngonghala, J. R. Knitter, L. Marinacci, M. H. Bonds, A. B. Gumel, Assessing the impact of widespread respirator use in curtailing COVID-19 transmission in the USA, R. Soc. Open Sci., 8 (2021), 210699. https://doi.org/10.1098/rsos.210699 doi: 10.1098/rsos.210699
[45]	A. Pak, O. A. Adegboye, A. I. Adekunle, K. M. Rahman, E. S. McBryde, D. P. Eisen, Economic consequences of the COVID-19 outbreak: the need for epidemic preparedness, Front. Public Health, 8 (2020), 241. https://doi.org/10.3389/fpubh.2020.00241 doi: 10.3389/fpubh.2020.00241
[46]	Y. Shang, H. Li, R. Zhang, Effects of pandemic outbreak on economies: Evidence from business history context, Front. Public Health, 9 (2021), 632043. https://doi.org/10.3389/fpubh.2021.632043 doi: 10.3389/fpubh.2021.632043
[47]	Centers for Disease Control and Prevention, COVID Data Tracker, 2022. Available from: https://covid.cdc.gov/covid-data-tracker/.
[48]	Centers for Disease Control and Prevention, COVID-19 Data Review: Update on COVID-19–Related Mortality, 2022. Available from: https://www.cdc.gov/coronavirus/2019-ncov/science/data-review/index.html.
[49]	E. Callaway, Fast-evolving COVID variants complicate vaccine updates, Nature, 607 (2022), 18–19. https://doi.org/10.1038/d41586-022-01771-3 doi: 10.1038/d41586-022-01771-3
[50]	S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178–196. https://doi.org/10.1016/j.jtbi.2008.04.011 doi: 10.1016/j.jtbi.2008.04.011
[51]	D. Kirschner, Uncertainty and Sensitivity Functions and Implementation, 2007. Available from: http://malthus.micro.med.umich.edu/lab/usadata/.
[52]	World Health Organization, Update on Omicron, 2021. Available from: https://www.who.int/news/item/28-11-2021-update-on-omicron.
[53]	V. C. Lucia, A. Kelekar, N. M. Afonso, COVID-19 vaccine hesitancy among medical students, J. Public Health, 43 (2021), 445–449. https://doi.org/10.1093/pubmed/fdaa230 doi: 10.1093/pubmed/fdaa230
[54]	S. Machingaidze, C. S. Wiysonge, Understanding COVID-19 vaccine hesitancy, Nat. Med., 27 (2021), 1338–1339. https://doi.org/10.1038/s41591-021-01459-7 doi: 10.1038/s41591-021-01459-7
[55]	C. E. Bonnema, I. van Woerden, J. R. Steinberg, E. Nguyen, C. M. Oliphant, K. W. Cleveland, et al., Understanding COVID-19 vaccine hesitancy among students in health professions: A cross-sectional analysis, J. Allied Health, 50 (2021), 314–320.
[56]	A. Coustasse, C. Kimble, K. Maxik, COVID-19 and vaccine hesitancy: A challenge the United States must overcome, J. Ambulatory Care Manage., 44 (2021), 71–75. https://doi.org/10.1097/JAC.0000000000000360 doi: 10.1097/JAC.0000000000000360
[57]	M. Anderson, The Associated Press, Only 40% of Fully Vaccinated Americans Have Received a Booster Shot, CDC Says, 2022. Available from: https://fortune.com/2022/01/25/40-percent-fully-vaccinated-americans-booster-shot-cdc-report/.
[58]	C. K. Johnson, Omicron Has Caused Higher Increase in U.S. Daily Death Count Than Delta Cariant, 2022. Available from: https://www.pbs.org/newshour/health/omicron-has-caused-higher-increase-in-u-s-daily-death-count-than-delta-variant.
[59]	J. Oh, C. Apio, T. Park, Mathematical modeling of the impact of Omicron variant on the COVID-19 situation in South Korea, Genomics Inf., 20 (2022), e22. https://doi.org/10.5808%2Fgi.22025
[60]	M. A. Khan, A. Atangana, Mathematical modeling and analysis of COVID-19: A study of new variant Omicron, Phys. A Stat. Mech. Appl., 599 (2022), 127452. https://doi.org/10.1016/j.physa.2022.127452 doi: 10.1016/j.physa.2022.127452
[61]	B. G. Wang, Z. C. Wang, Y. Wu, Y. Xiong, J. Zhang, Z. Ma, A mathematical model reveals the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant, Nonlinear Dyn., 111 (2023), 3937–3952. https://doi.org/10.1007/s11071-022-07985-4 doi: 10.1007/s11071-022-07985-4
[62]	G. González-Parra, A. J. Arenas, Mathematical modeling of SARS-CoV-2 Omicron wave under vaccination effects, Computation, 11 (2023), 36. https://doi.org/10.3390/computation11020036 doi: 10.3390/computation11020036
[63]	C. N. Ngonghala, H. B. Taboe, S. Safdar, A. B. Gumel, Unraveling the dynamics of the Omicron and Delta variants of the 2019 coronavirus in the presence of vaccination, mask usage, and antiviral treatment, Appl. Math. Modell., 114 (2023), 447–465. https://doi.org/10.1016/j.apm.2022.09.017 doi: 10.1016/j.apm.2022.09.017
[64]	S. Safdar, C. N. Ngonghala, A. Gumel, Mathematical assessment of the role of waning and boosting immunity against the BA. 1 Omicron variant in the United States, Math. Biosci. Eng., 20 (2023), 179–212. https://doi.org/10.3934/mbe.2023009 doi: 10.3934/mbe.2023009
[65]	U. A. P. de León, E. Avila-Vales, K. Huang, Modeling the transmission of the SARS-CoV-2 delta variant in a partially vaccinated population, Viruses, 14 (2022), 158. https://doi.org/10.3390/v14010158 doi: 10.3390/v14010158
[66]	F. J. Aguilar-Canto, U. A. P. de León, E. Avila-Vales, Sensitivity theorems of a model of multiple imperfect vaccines for COVID-19, Chaos Solitons Fractals, 156 (2022), 111844. https://doi.org/10.1016/j.chaos.2022.111844 doi: 10.1016/j.chaos.2022.111844
[67]	U. A. P. de León, E. Avila-Vales, K. Huang, Modeling COVID-19 dynamic using a two-strain model with vaccination, Chaos Solitons Fractals, 157 (2022), 111927. https://doi.org/10.1016/j.chaos.2022.111927 doi: 10.1016/j.chaos.2022.111927
[68]	N. Andrews, J. Stowe, F. Kirsebom, S. Toffa, T. Rickeard, E. Gallagher, et al., Effectiveness of COVID-19 vaccines against the Omicron (B.1.1.529) variant of concern, preprint, medRxiv. https://doi.org/10.1101/2021.12.14.21267615
[69]	C. Willyard, What the Omicron wave is revealing about human immunity, Nature, 602 (2022), 22–25. https://doi.org/10.1038/d41586-022-00214-3 doi: 10.1038/d41586-022-00214-3
[70]	T. K. Burki, Fourth dose of COVID-19 vaccines in Israel, Lancet Respir. Med., 10 (2022), e19. https://doi.org/10.1016/S2213-2600(22)00010-8 doi: 10.1016/S2213-2600(22)00010-8
[71]	J. Chen, G. W. Wei, Omicron BA. 2 (B. 1.1. 529.2): High potential to becoming the next dominating variant, J. Phys. Chem. Lett., 13 (2022), 3840–3849. https://doi.org/10.1021/acs.jpclett.2c00469 doi: 10.1021/acs.jpclett.2c00469
[72]	Y. Yu, Y. Liu, S. Zhao, D. He, A simple model to estimate the transmissibility of SARS-CoV-2 Beta, Delta and Omicron variants in South Africa, Delta Omicron Variants S. Afr., 2021 (2021). http://dx.doi.org/10.2139/ssrn.3989919 doi: 10.2139/ssrn.3989919

mbe-20-06-484-Supplementary.pdf

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)