<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">epidemiology</journal-id><journal-title-group><journal-title xml:lang="ru">Эпидемиология и Вакцинопрофилактика</journal-title><trans-title-group xml:lang="en"><trans-title>Epidemiology and Vaccinal Prevention</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2073-3046</issn><issn pub-type="epub">2619-0494</issn><publisher><publisher-name>«Numicom» LLC</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.31631/2073-3046-2024-23-2-61-70</article-id><article-id custom-type="elpub" pub-id-type="custom">epidemiology-1971</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ОРИГИНАЛЬНЫЕ СТАТЬИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>ORIGINAL ARTICLES</subject></subj-group></article-categories><title-group><article-title>Мультицентровое агентное моделирование шести волн COVID-19 в Нижегородской области</article-title><trans-title-group xml:lang="en"><trans-title>Multicentral Agent-Based Model of Six Epidemic Waves of COVID-19 in the Nizhny Novgorod Region of Russian Federation</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2075-9634</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хилов</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Hilov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Хилов Александр Владимирович – к. ф.-м. н., м. н. с., ФГБНУ «ФИЦ ИПФ им. А.В. Гапонова-Грехова РАН».</p><p>Нижний Новгород</p><p>Тел. +7 (902) 301-59-15</p></bio><bio xml:lang="en"><p>Aleksandr V. Hilov – junior researcher, A.V. Gaponov-Grekhov Institute of Applied Physics RAS.</p><p>Nizhny Novgorod</p><p>Tel. +7 (902) 301-59-15</p></bio><email xlink:type="simple">alhil@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3629-4712</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Саперкин</surname><given-names>Н. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Saperkin</surname><given-names>N. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Саперкин Николай Валентинович – к. м. н., доцент кафедры эпидемиологии, микробиологии и доказательной медицины, ФГБОУ ВО «ПИМУ» Минздрава России.</p><p>603074, Нижний Новгород, ул. Бурнаковская, 53-76</p><p>Тел. +7 (903) 847-45-89</p></bio><bio xml:lang="en"><p>Nikolaj V. Saperkin – Cand. Sci. (Med.), associate professor, Privolzhsky Research Medical University.</p><p>53-76, Burnakovskaya str., Nizhny Novgorod, 603074</p><p>Tel. +7 (903) 847-45-89</p></bio><email xlink:type="simple">saperkinnv@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3320-1645</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ковалишена</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kovalishena</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ковалишена Ольга Васильевна – д. м. н., профессор, ФГБОУ ВО «ПИМУ» Минздрава России.</p><p>Нижний Новгород</p><p>Тел. +7 (903) 608-39-08</p></bio><bio xml:lang="en"><p>Ol’ga V. Kovalishena – Dr. Sci. (Med.), professor, Privolzhsky Research Medical University.</p><p>Nizhny Novgorod</p><p>Tel. +7 (903) 608-39-08</p></bio><email xlink:type="simple">kovalishena@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Садыкова</surname><given-names>Н. A.</given-names></name><name name-style="western" xml:lang="en"><surname>Sadykova</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Садыкова Наталья Александровна – заместитель Главного государственного санитарного врача по Нижегородской области, Управление Роспотребнадзора по Нижегородской области.</p><p>Нижний Новгород</p><p>Тел. +7 (909) 283-19-15</p></bio><bio xml:lang="en"><p>Natal’ja A. Sadykova – Deputy Chief Sanitary Doctor of the Nizhny Novgorod Region, Federal Service for Supervision of Consumer Rights Protection and Human Welfare, Department in the Nizhny Novgorod Region.</p><p>Nizhny Novgorod</p><p>Tel. +7 (909) 283-19-15</p></bio><email xlink:type="simple">kolmnataly@yandex.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9088-2462</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Перекатова</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Perekatova</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Перекатова Валерия Владимировна – к. ф.-м. н., н. с., ФГБНУ «ФИЦ ИПФ им. А.В. Гапонова-Грехова РАН».</p><p>Нижний Новгород</p><p>Тел. +7 (908) 732-34-65</p></bio><bio xml:lang="en"><p>Valerija V. Perekatova – researcher, A.V. Gaponov-Grekhov Institute of Applied Physics RAS.</p><p>Nizhny Novgorod</p><p>Tel. +7 (908) 732-34-65</p></bio><email xlink:type="simple">perekatova.valeriya@ipfran.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0009-5279-095X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Перехожева</surname><given-names>Н. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Perekhozheva</surname><given-names>N. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Перехожева Наталья Владимировна – студентка 6-го курса лечебного факультета, ФГБОУ ВО «ПИМУ» Минздрава России.</p><p>Нижний Новгород</p><p>Тел. +7 (920) 076-86-97</p></bio><bio xml:lang="en"><p>Natal’ja V. Perehozheva – medical student, Privolzhsky Research Medical University.</p><p>Nizhny Novgorod</p><p>Tel. +7 (920) 076-86-97</p></bio><email xlink:type="simple">saburova121281@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4436-2535</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Куракина</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kurakina</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Куракина Дария Андреевна – м. н. с., ФГБНУ «ФИЦ ИПФ им. А.В. Гапонова-Грехова РАН».</p><p>Нижний Новгород</p></bio><bio xml:lang="en"><p>Darija A. Kurakina – junior researcher, A.V. Gaponov-Grekhov Institute of Applied Physics RAS.</p><p>Nizhny Novgorod</p></bio><email xlink:type="simple">daria.kurakina@ipfran.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6804-6369</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кириллин</surname><given-names>М. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Kirillin</surname><given-names>M. Ju.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кириллин Михаил Юрьевич – к. ф.-м. н., с. н. с., ФГБНУ «ФИЦ ИПФ им. А.В. Гапонова-Грехова РАН».</p><p>Нижний Новгород</p><p>Тел. +7 (920) 024-99-42</p></bio><bio xml:lang="en"><p>Mihail Yu. Kirillin – senior researcher, A.V. Gaponov-Grekhov Institute of Applied Physics RAS.</p><p>Nizhny Novgorod</p><p>Tel. +7 (920) 024-99-42</p></bio><email xlink:type="simple">kirillin@ipfran.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБНУ «Федеральный исследовательский центр Институт прикладной физики им. А.В. Гапонова­Грехова Российской академии наук»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>A.V. Gaponov-Grekhov Institute of Applied Physics RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>ФГБОУ ВО «Приволжский исследовательский медицинский университет» Минздрава России</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Privolzhsky Research Medical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Управление Роспотребнадзора по Нижегородской области</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Federal Service for Supervision of Consumer Rights Protection and Human Welfare, Department in the Nizhny Novgorod Region</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>03</day><month>05</month><year>2024</year></pub-date><volume>23</volume><issue>2</issue><fpage>61</fpage><lpage>70</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Хилов А.В., Саперкин Н.В., Ковалишена О.В., Садыкова Н.A., Перекатова В.В., Перехожева Н.В., Куракина Д.А., Кириллин М.Ю., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Хилов А.В., Саперкин Н.В., Ковалишена О.В., Садыкова Н.A., Перекатова В.В., Перехожева Н.В., Куракина Д.А., Кириллин М.Ю.</copyright-holder><copyright-holder xml:lang="en">Hilov A.V., Saperkin N.V., Kovalishena O.V., Sadykova N.A., Perekatova V.V., Perekhozheva N.V., Kurakina D.A., Kirillin M.J.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.epidemvac.ru/jour/article/view/1971">https://www.epidemvac.ru/jour/article/view/1971</self-uri><abstract><p>Актуальность. Полноценное изучение особенностей протекания эпидемии COVID-19 и принятие своевременных и эффективных мер требуют использования статистических моделей, которые способны прогнозировать влияние различных противоэпидемических мероприятий на динамику заболеваемости. В связи с этим представляется целесообразным применение агентных моделей, дающих возможность учитывать различные демографические факторы (например, возрастно-половой состав, социальную активность), ограничительные меры, лабораторные исследования и т.п. Кроме того, функционал такого моделирования также позволяет предусмотреть и влияние случайных факторов, которые обычно не учитываются в традиционно используемых модификациях SIR-моделей. Цель. Усовершенствование предложенной ранее агентной модели [23,24] для моделирования распространения COVID-19 в различных регионах Российской Федерации. На данном этапе произведено моделирование шести волн распространения COVID-19 в Нижегородской области как целого региона, а также в отдельных ее городах с учетом ограничительных мер и вакцинации населения. Материалы и методы. В данной работе представлено развитие ранее предложенной агентной модели с реализацией метода Монте-Карло для численного моделирования распространения COVID-19 с учетом тестирования и вакцинации населения. Статистический анализ выполнен в cреде MATLAB/GNU Octave. Мультицентровая версия модели позволяет более точно смоделировать динамику эпидемического процесса внутри одной области, когда нулевой пациент обычно прибывает в областной административный центр, после чего распространение инфекции за счет маятниковой миграции начинает захватывать периферию области. Результаты. Показано прикладное значение разработанной модели на примере анализа распространения инфекции в Нижегородской области. Смоделированная динамика суточного абсолютного прироста новых выявленных случаев и смертей от COVID-19 хорошо согласовывалась с данными официальной регистрации как для региона в целом, так и для отдельных районов и городов. Заключение. Результаты моделирования позволяют предположить, что фактическое количество заболеваний COVID-19 в 1,5–3,0 раза превышало число зарегистрированных случаев. С помощью разработанной модели также была дана оценка влиянию вакцинопрофилактики. Показано, что при тех же параметрах моделирования, но без вакцинации, третья и четвертая волны пандемии объединились бы в одну со значительным ростом заболеваемости, формированием естественного иммунитета и, как следствие, отсутствием дальнейших волн пандемии, но число смертей превысило бы реальное примерно в 9–10 раз.</p></abstract><trans-abstract xml:lang="en"><p>Relevance. To investigate the characteristics of the COVID-19 pandemic and introduce timely and effective measures, there is a need for models that can predict the impact of various restrictive actions or characteristics of disease itself on COVID-19 spread dynamics. Employing agent-based models can be attractive because they take into consideration different population characteristics (e.g., age distribution and social activity) and restrictive measures, laboratory testing, etc., as well as random factors that are usually omitted in traditional modifications of the SIR-like dynamic models. Aim. Improvement of the previously proposed agent-based model [23,24] for modeling the spread of COVID-19 in various regions of the Russian Federation. At this stage, six waves of the spread of COVID-19 have been modeled in the Nizhny Novgorod region as a whole region, as well as in its individual cities, taking into account restrictive measures and vaccination of the population. Materials and Methods. In this paper we extend a recently proposed agent-based model for Monte Carlo-based numerical simulation of the spread of COVID-19 with consideration of testing and vaccination strategies. Analysis is performed in MATLAB/ GNU Octave. Results. Developed multicentral model allows for more accurate simulation of the epidemic dynamics within one region, when a patient zero usually arrives at a regional center, after which the distribution chains capture the periphery of the region due to pendulum migration. Furthermore, we demonstrate the application of the developed model to analyze the epidemic spread in the Nizhny Novgorod region of Russian Federation. The simulated dynamics of the daily newly detected cases and COVID-19-related deaths was in good agreement with the official statistical data both for the region as whole and different periphery cities. Conclusions. The results obtained with developed model suggest that the actual number of COVID-19 cases might be 1.5–3.0 times higher than the number of reported cases. The developed model also took into account the effect of vaccination. It is shown that with the same modeling parameters, but without vaccination, the third and fourth waves of the epidemic would be united into one characterized by a huge rise in the morbidity rates and the occurrence of natural individual immunity with the absence of further pandemic waves. Nonetheless, the number of deaths would exceed the real one by about 9–10 times.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>динамика</kwd><kwd>прогнозирование</kwd><kwd>агентное моделирование</kwd><kwd>имитационное моделирование</kwd><kwd>COVID-19</kwd><kwd>эпидемиология</kwd><kwd>надзор</kwd><kwd>методология</kwd></kwd-group><kwd-group xml:lang="en"><kwd>dynamics</kwd><kwd>forecasting</kwd><kwd>agent-based modeling</kwd><kwd>simulation modeling</kwd><kwd>COVID-19</kwd><kwd>epidemiology</kwd><kwd>surveillance</kwd><kwd>methodology</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа профинансирована Министерством науки и высшего образования РФ в рамках государственного задания ИПФ РАН, проект № FFUF­-2021­-0014.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Carletti T., Fanelli D., Piazza F. COVID-19: The unreasonable effectiveness of simple models. Chaos, Solitons &amp; Fractals: X. 2020. N5. P. 100034.</mixed-citation><mixed-citation xml:lang="en">Carletti T, Fanelli D, Piazza F. COVID-19: The unreasonable effectiveness of simple models. Chaos, Solitons &amp; Fractals: X. 2020;5:100034.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Pelinovsky E., Kurkin A., Kurkina O. et al. Logistic equation and COVID-19. Chaos, Solitons &amp; Fractals. 2020. N140.P.110241.</mixed-citation><mixed-citation xml:lang="en">Pelinovsky E, Kurkin A, Kurkina O et al. Logistic equation and COVID-19. Chaos, Solitons &amp; Fractals. 2020;140:110241.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Calatayud J., Jornet M., Mateu J. A stochastic Bayesian bootstrapping model for COVID-19 data. Stochastic Environmental Research and Risk Assessment. 2022. Vol. 36. N9. P. 2907–2917.</mixed-citation><mixed-citation xml:lang="en">Calatayud J, Jornet M, Mateu J. A stochastic Bayesian bootstrapping model for COVID-19 data. Stochastic Environmental Research and Risk Assessment. 2022;36(9):2907– 2917.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Pelinovsky E., Kokoulina M., Epifanova A., et al. Gompertz model in COVID-19 spreading simulation. Chaos, Solitons &amp; Fractals. 2022. N154. P. 111699.</mixed-citation><mixed-citation xml:lang="en">Pelinovsky E, Kokoulina M, Epifanova A, et al. Gompertz model in COVID-19 spreading simulation. Chaos, Solitons &amp; Fractals. 2022;154:111699.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Conde-Gutiérrez R., Colorado D., Hernández-Bautista S. Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México. Nonlinear Dynamics. 2021. Vol. 104. N4. P. 4655–4669.</mixed-citation><mixed-citation xml:lang="en">Conde-Gutiérrez R, Colorado D, Hernández-Bautista S. Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México. Nonlinear Dynamics. 2021;104(4):4655–4669.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Dairi A., Harrou F., Zeroual A, et al. Comparative study of machine learning methods for COVID-19 transmission forecasting. Journal of Biomedical Informatics. 2021. N118. P. 103791.</mixed-citation><mixed-citation xml:lang="en">Dairi A, Harrou F, Zeroual A, et al. Comparative study of machine learning methods for COVID-19 transmission forecasting. Journal of Biomedical Informatics. 2021;118:103791.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Alali Y., Harrou F., Sun Y. A proficient approach to forecast COVID-19 spread via optimized dynamic machine learning models. Scientific Reports. 2022. Vol. 12. N1. P. 2467.</mixed-citation><mixed-citation xml:lang="en">Alali Y, Harrou F, Sun Y. A proficient approach to forecast COVID-19 spread via optimized dynamic machine learning models. Scientific Reports. 2022;12(1):2467.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Pavlyutin M., Samoyavcheva M., Kochkarov R., et al. COVID-19 spread forecasting, mathematical methods vs. machine learning, Moscow case. Mathematics. 2022. Vol. 10. N2. P. 195. https://doi.org/10.3390/math10020195</mixed-citation><mixed-citation xml:lang="en">Pavlyutin M, Samoyavcheva M, Kochkarov R, et al. COVID-19 spread forecasting, mathematical methods vs. machine learning, Moscow case. Mathematics. 2022;10(2):195. https://doi.org/10.3390/math10020195</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character. 1927. Vol. 115. N772. P. 700–721.</mixed-citation><mixed-citation xml:lang="en">Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character. 1927;115(772):700–721.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">He S., Peng Y., Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear dynamics. 2020. Vol. 101. P. 1667–1680.</mixed-citation><mixed-citation xml:lang="en">He S, Peng Y, Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear dynamics. 2020;101:1667–1680.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Kamrujjaman M., Saha P., Islam M.S., et al. Dynamics of SEIR model: a case study of COVID-19 in Italy. Results in Control and Optimization. 2022. N7. P. 100119. https://doi.org/10.1016/j.rico.2022.100119</mixed-citation><mixed-citation xml:lang="en">Kamrujjaman M, Saha P, Islam MS, et al. Dynamics of SEIR model: a case study of COVID-19 in Italy. Results in Control and Optimization. 2022;7:100119. https://doi.org/10.1016/j.rico.2022.100119</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Poonia R.C., Saudagar A.K.J., Altameem A., et al. An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect. Life (Basel). 2022. Vol. 12. N5. P. 647. doi: 10.3390/life12050647.</mixed-citation><mixed-citation xml:lang="en">Poonia RC, Saudagar AKJ, Altameem A, et al. An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect. Life (Basel). 2022;12(5):647. doi: 10.3390/life12050647.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Ying F., O’Clery N. Modelling COVID-19 transmission in supermarkets using an agent-based model. PLoS One. 2021. Vol. 16. N4. P. e0249821. doi: 10.1371/journal.pone.0249821.</mixed-citation><mixed-citation xml:lang="en">Ying F, O’Clery N. Modelling COVID-19 transmission in supermarkets using an agent-based model. PLoS One. 2021;16(4):e0249821. doi: 10.1371/journal.pone.0249821.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Gomez J., Prieto J., Leon E., Rodríguez A. INFEKTA - An agent-based model for transmission of infectious diseases: The COVID-19 case in Bogotá, Colombia. PloS One. 2021. Vol. 16. N2. P. e0245787. doi: 10.1371/journal.pone.0245787</mixed-citation><mixed-citation xml:lang="en">Gomez J, Prieto J, Leon E, Rodríguez A. INFEKTA - An agent-based model for transmission of infectious diseases: The COVID-19 case in Bogotá, Colombia. PloS One. 2021;16(2):e0245787. doi: 10.1371/journal.pone.0245787</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Tatapudi H., Das T.K. Impact of school reopening on pandemic spread: A case study using an agent-based model for COVID-19. Infectious Disease Modelling. 2021. Vol. 6. P. 839–847.</mixed-citation><mixed-citation xml:lang="en">Tatapudi H, Das TK. Impact of school reopening on pandemic spread: A case study using an agent-based model for COVID-19. Infectious Disease Modelling. 2021;6:839–847.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Рыкованов Г.Н., Лебедев С.Н., Зацепин О.В. и др. Агентный подход к моделированию эпидемии COVID-19 в России. Вестник РАН. 2022. Т. 92, №4. С. 479–487. Doi: 10.31857/S0869587322080138</mixed-citation><mixed-citation xml:lang="en">Rykovanov GN, Lebedev SN, Zatsepin OV, et al. Agentnyj podhod k modelirovaniju jepidemii COVID-19 v Rossii. Vestnik RAN. 2022;92(4):479–487.[in Russ] Doi: 10.31857/S0869587322080138</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Petrakova V., Krivorotko O. Mean field game for modeling of COVID-19 spread. Journal of Mathematical Analysis and Applications. 2022. Vol. 514. N1. P. 126271.</mixed-citation><mixed-citation xml:lang="en">Petrakova V, Krivorotko O. Mean field game for modeling of COVID-19 spread. Journal of Mathematical Analysis and Applications. 2022;514(1):126271.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Tembine H. COVID-19: data-driven mean-field-type game perspective. Games. 2020. Vol. 11. N4. P. 51. https://doi.org/10.3390/g11040051</mixed-citation><mixed-citation xml:lang="en">Tembine H. COVID-19: data-driven mean-field-type game perspective. Games. 2020;11(4):51. https://doi.org/10.3390/g11040051</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Ghilli D., Ricci C., Zanco G. A mean field game model for COVID-19 with human capital accumulation. Economic Theory. 2023. N3. P. 1–28. https://doi.org/10.1007/s00199-023-01505-0</mixed-citation><mixed-citation xml:lang="en">Ghilli D, Ricci C, Zanco G. A mean field game model for COVID-19 with human capital accumulation. Economic Theory. 2023. P. 1–28. https://doi.org/10.1007/s00199-023-01505-0</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Hernández-Hernández A.M., Huerta-Quintanilla R. Managing school interaction networks during the COVID-19 pandemic: Agent-based modeling for evaluating possible scenarios when students go back to classrooms. PLoS One. 2021. Vol. 16. N8. P. e0256363.</mixed-citation><mixed-citation xml:lang="en">Hernández-Hernández AM, Huerta-Quintanilla R. Managing school interaction networks during the COVID-19 pandemic: Agent-based modeling for evaluating possible scenarios when students go back to classrooms. PLoS One. 2021;16(8):e0256363.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Hunter E., Kelleher J.D. Validating and testing an agent-based model for the spread of COVID-19 in Ireland. Algorithms. 2022. Vol. 15. N8. P. 270.</mixed-citation><mixed-citation xml:lang="en">Hunter E, Kelleher J D. Validating and testing an agent-based model for the spread of COVID-19 in Ireland. Algorithms. 2022;15(8):270.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Hunter E., Mac Namee B., Kelleher J.D. A Model for the spread of infectious diseases in a region. International journal of environmental research and public health. 2020. Vol. 17. N9. P. 3119.</mixed-citation><mixed-citation xml:lang="en">Hunter E, Mac Namee B, Kelleher JD. A Model for the spread of infectious diseases in a region. International journal of environmental research and public health. 2020;17(9):3119.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Kirillin M., Khilov A., Perekatova V., et al. Simulation of the first and the second waves of COVID-19 spreading in Russian Federation regions using an agent-based model. Journal of Biomedical Photonics &amp; Engineering. 2023. Vol. 9. N1. P. 010302. doi: 10.18287/JBPE23.09.010302</mixed-citation><mixed-citation xml:lang="en">Kirillin M, Khilov A, Perekatova V, et al. Simulation of the first and the second waves of COVID-19 spreading in Russian Federation regions using an agent-based model. Journal of Biomedical Photonics &amp; Engineering. 2023;9(1): 010302. Doi: 10.18287/JBPE23.09.010302</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Kirillin M., Khilov A., Perekatova V., et al. Multicentral agent-based model of four waves of COVID-19 spreading in Nizhny Novgorod region of Russian Federation. Journal of Biomedical Photonics &amp; Engineering. 2023. P. 010306. doi: 10.18287/JBPE23.09.010306</mixed-citation><mixed-citation xml:lang="en">Kirillin M, Khilov A, Perekatova V, et al. Multicentral agent-based model of four waves of COVID-19 spreading in Nizhny Novgorod region of Russian Federation. Journal of Biomedical Photonics &amp; Engineering. 2023:010306. Doi: 10.18287/JBPE23.09.010306</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
