Simulation of the First and the Second Waves of COVID-19 Spreading in Russian Federation Regions Using an Agent-Based Model

Mikhail Kirillin
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Aleksandr Khilov (Login required)
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Valeriya Perekatova
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Ekaterina Sergeeva
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Daria Kurakina
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Ilya Fiks
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Nikolay Saperkin
Institute of Applied Physics RAS, Nizhny Novgorod, Russia
Privolzhsky Research Medical University, Nizhny Novgorod, Russia

Ming Tang
East China Normal University, Shanghai, China

Yong Zou
East China Normal University, Shanghai, China

Elbert Macau
Universidade Federal de São Paulo, Brasil

Efim Pelinovsky
Institute of Applied Physics RAS, Nizhny Novgorod, Russia
National Research University – Higher School of Economics, Nizhny Novgorod, Russia

Paper #3568 received 02 Dec 2022; revised manuscript received 21 Dec 2022; accepted for publication 21 Dec 2022; published online 13 Feb 2023.

DOI: 10.18287/JBPE23.09.010302


The COVID-19 pandemics remains one of the largest global challenges. Necessity of effective systemic aids for the minimization of losses leads to the requirement of adequate models allowing to predict the impact of different factors on the spread of the disease. Agent-based simulation models provide a suitable solution with the possibility to accurately account for such factors as age structure of a population, characteristics of isolation, self-isolation strategies and testing strategies, presence of super-spreaders etc. In this paper we report on the results of simulating the spread of COVID-19 in several representative regions of Russia using an agent-based model with a general pool combined with the simulation of population testing strategy. The model accounts for the following key epidemiologic characteristics: population age distribution, reproducibility rate, distributions of infectivity period, a period of clinical manifestation, and age-dependent probability of critical disease. It is demonstrated that the daily epidemiologic curves can be predicted well for different territories with the same model parameters, except for the initial number of infected agents and region-dependent testing as well as isolation strategies, which are considered to be tuning parameters of the model. The developed approach can be further expanded to other regions of different countries, while the determined model parameters could be used as starting values for such simulations.


dynamics and control of epidemics; COVID-19; agent-based modeling

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1. T. Carletti, D. Fanelli, and F. Piazza, “COVID-19: The unreasonable effectiveness of simple models,” Chaos, Solitons & Fractals: X 5, 100034 (2020).

2. E. Pelinovsky, A. Kurkin, O. Kurkina, M. Kokoulina, and A. Epifanova, “Logistic equation and COVID-19,” Chaos, Solitons & Fractals 140, 110241 (2020).

3. K. Wu, D. Darcet, Q. Wang, and D. Sornette, “Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world,” Nonlinear Dynamics 101, 1561–1581 (2020).

4. A. Cunha, F. da C. Batista, P. R. de L. Gianfelice, R. S. Oyarzabal, J. M. V. Grzybowski, and E. E. N. Macau, “epidWaves: A code for fitting multi-wave epidemic models,” Software Impacts 14, 100391 (2022).

5. E. Pelinovsky, M. Kokoulina, A. Epifanova, A. Kurkin, O. Kurkina, M. Tang, E. Macau, and M. Kirillin, “Gompertz model in COVID-19 spreading simulation,” Chaos, Solitons & Fractals 154, 111699 (2022).

6. H. S. Burkom, S. P. Murphy, and G. Shmueli, “Automated time series forecasting for biosurveillance,” Statistics in Medicine 26(22), 4202–4218 (2007).

7. J. C. Brillman, T. Burr, D. Forslund, E. Joyce, R. Picard, and E. Umland, “Modeling emergency department visit patterns for infectious disease complaints: results and application to disease surveillance,” BMC Medical Informatics and Decision Making 5(1), 4 (2005).

8. D. Lai, “Monitoring the SARS epidemic in China: a time series analysis,” Journal of Data Science 3(3), 279–293 (2005).

9. J. Díaz-Hierro, J. J. Martín Martín, Á. Vilches Arenas, M. P. López Del Amo González, J. M. Patón Arévalo, and C. Varo González, “Evaluation of time-series models for forecasting demand for emergency health care services,” Emergencias 24(3), 181–188 (2012).

10. S. Unkel, C. P. Farrington, P. H. Garthwaite, C. Robertson, and N. Andrews, “Statistical methods for the prospective detection of infectious disease outbreaks: a review,” Journal of the Royal Statistical Society: Series A (Statistics in Society) 175(1), 49–82 (2012).

11. R. Kiang, F. Adimi, V. Soika, J. Nigro, P. Singhasivanon, J. Sirichaisinthop, S. Leemingsawat, C. Apiwathnasorn, and S. Looareesuwan, “Meteorological, environmental remote sensing and neural network analysis of the epidemiology of malaria transmission in Thailand,” Geospatial Health 1(1), 71–84 (2006).

12. W. O. Kermack, A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London. Series A 115(772), 700-721 (1927).

13. Z. Zhao, X. Li, F. Liu, G. Zhu, C. Ma, and L. Wang, “Prediction of the COVID-19 spread in African countries and implications for prevention and controls: A case study in South Africa, Egypt, Algeria, Nigeria, Senegal and Kenya,” Science of The Total Environment 729, 138959 (2020).

14. N. Ghaffarzadegan, H. Rahmandad, “Simulation-based estimation of the early spread of COVID-19 in Iran: actual versus confirmed cases,” System Dynamics Review 36(1), 101–129 (2020).

15. S. Annas, M. I. Pratama, M. Rifandi, W. Sanusi, and S. Side, “Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia,” Chaos, Solitons & Fractals 139, 110072 (2020).

16. L. López, X. Rodo, “A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: simulating control scenarios and multi-scale epidemics,” Results in Physics 21, 103746 (2021).

17. X. Yu, G. Qi, and J. Hu, “Analysis of second outbreak of COVID-19 after relaxation of control measures in India,” Nonlinear Dynamics 106, 1149–1167 (2020).

18. S. Kurmi, U. Chouhan, “A multicompartment mathematical model to study the dynamic behaviour of COVID-19 using vaccination as control parameter,” Nonlinear Dynamics 109(3), 2185–2201 (2022).

19. Y. Fang, Y. Nie, and M. Penny, “Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: A data-driven analysis,” Journal of Medical Virology 92(6), 645–659 (2020).

20. A. Temerev, L. Rozanova, O. Keiser, and J. Estill, “Geospatial model of COVID-19 spreading and vaccination with event Gillespie algorithm,” Nonlinear Dynamics 109(3), 239–248 (2022).

21. C. Siettos, C. Anastassopoulou, L. Russo, C. Grigoras, and E. Mylonakis, “Modeling the 2014 Ebola virus epidemic–agent-based simulations, temporal analysis and future predictions for Liberia and Sierra-Leone,” PLoS Currents 7, (2015).

22. H. Arduin, M. Domenech de Cellès, D. Guillemot, L. Watier, and L. Opatowski, “An agent-based model simulation of influenza interactions at the host level: insight into the influenza-related burden of pneumococcal infections,” BMC Infectious Diseases 17(1), 382 (2017).

23. J. T. Tuomisto, J. Yrjölä, M. Kolehmainen, J. Bonsdorff, J. Pekkanen, and T. Tikkanen, “An agent-based epidemic model REINA for COVID-19 to identify destructive policies,” medRxiv: 20047498 (2020).

24. N. Hoertel, M. Blachier, C. Blanco, M. Olfson, M. Massetti, F. Limosin, and H. Leleu, “Facing the COVID-19 epidemic in NYC: a stochastic agent-based model of various intervention strategies,” medRxiv: 20076885 (2020).

25. J. R. Koo, A. R. Cook, M. Park, Y. Sun, H. Sun, J. T. Lim, C. Tam, and B. L. Dickens, “Interventions to mitigate early spread of SARS-CoV-2 in Singapore: A modelling study,” The Lancet Infectious Diseases 20(6), 678–688 (2020).

26. G. España, S. Cavany, “NotreDame-FRED COVID-19 forecasts,” GitHub (accessed 18 November 2022). [].

27. N. M. Ferguson, D. Laydon, G. Nedjati-Gilani, N. Imai, K. Ainslie, M. Baguelin, S. Bhatia, A. Boonyasiri, Z. Cucunubá, G. Cuomo-Dannenburg, A. Dighe, I. Dorigatti, H. Fu, K. Gaythorpe, W. Green, A. Hamlet, W. Hinsley, L. C. Okell, S. van Elsland, H. Thompson, R. Verity, E. Volz, H. Wang, Y. Wang, P. G. T. Walker, C. Walters, P. Winskill, C. Whittaker, C. A. Donnelly, S. Riley, and A. C. Ghani, “Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand,” Imperial College London (2020).

28. S. L. Chang, N. Harding, C. Zachreson, O. M. Cliff, and M. Prokopenko, “Modelling transmission and control of the COVID-19 pandemic in Australia,” Nature Communications 11, 5710 (2020).

29. D. Kai, G.-P. Goldstein, A. Morgunov, V. Nangalia, and A. Rotkirch, “Universal masking is urgent in the COVID-19 pandemic: SEIR and agent based models, empirical validation, policy recommendations, arXiv:2004.13553 (2020).

30. J. A. Moreno López, B. Arregui García, P. Bentkowski, L. Bioglio, F. Pinotti, P.-Y. Boëlle, A. Barrat, V. Colizza, and C. Poletto, “Anatomy of digital contact tracing: Role of age, transmission setting, adoption, and case detection,” Science Advances 7(15), eabd8750 (2021).

31. Md. S. Shamil, F. Farheen, N. Ibtehaz, I. M. Khan, and M. S Rahman, “An Agent-Based Modeling of COVID-19: Validation, Analysis, and Recommendations,” Cognitive Computation (2021).

32. A. Aleta, D. Martin-Corral, A. Pastore y Piontti, M. Ajelli, M. Litvinova, M. Chinazzi, N. E. Dean, M. E. Halloran, I. M. Longini, S. Merler, A. Pentland, A. Vespignani, E. Moro, and Y. Moreno, “Modeling the impact of social distancing, testing, contact tracing and household quarantine on second-wave scenarios of the COVID-19 epidemic,” medRxiv:20092841 (2020).

33. P. C. L. Silva, P. V. C. Batista, H. S. Lima, M. A. Alves, F. G. Guimarães, and R. C. P. Silva, “COVID-ABS: An agent-based model of COVID-19 epidemic to simulate health and economic effects of social distancing interventions,” Chaos, Solitons & Fractals 139, 110088 (2020).

34. P. Keskinocak, B. E. Oruc, A. Baxter, J. Asplund, and N. Serban, “The impact of social distancing on COVID19 spread: State of Georgia case study,” PLoS One 15(10), e0239798 (2020).

35. P. T. Gressman, J. R. Peck, “Simulating COVID-19 in a university environment,” Mathematical Biosciences 328, 108436 (2020).

36. F. Ying, N. O’Clery, “Modelling COVID-19 transmission in supermarkets using an agent-based model,” PLoS One 16(4), e0249821 (2021).

37. A. Truszkowska, B. Behring, J. Hasanyan, L. Zino, S. Butail, E. Caroppo, Z. Jiang, A. Rizzo, and M. Porfiri, “High-Resolution Agent-Based Modeling of COVID-19 Spreading in a Small Town,” Advanced Theory and Simulations 4(3), 2000277 (2021).

38. C. Cheng, D. Zhang, D. Dang, J. Geng, P. Zhu, M. Yuan, R. Liang, H. Yang, Y. Jin, J. Xie, S. Chen, and G. Duan, “The incubation period of COVID-19: a global meta-analysis of 53 studies and a Chinese observation study of 11 545 patients,” Infectious Diseases of Poverty 10(1), 119 (2021).

39. W. Dhouib, J. Maatoug, I. Ayouni, N. Zammit, R. Ghammem, S. B. Fredj, and H. Ghannem, “The incubation period during the pandemic of COVID-19: a systematic review and meta-analysis,” Systematic Reviews 10, 101 (2021).

40. S. Paul, E. Lorin, “Distribution of incubation periods of COVID-19 in the Canadian context,” Scientific Reports 11(1), 12569 (2021).

41. H. Xin, J. Y. Wong, C. Murphy, A. Yeung, S. Taslim Ali, P. Wu, and B. J. Cowling, “The Incubation Period Distribution of Coronavirus Disease 2019: A Systematic Review and Meta-analysis,” Clinical Infectious Diseases 73(12), 2344–2352 (2021).

42. M. Kirillin, E. Sergeeva, A. Khilov, D. Kurakina, and N. Saperkin, “Monte Carlo simulation of the covid-19 spread in early and peak stages in different regions of the Russian Federation using an agent-based modelling,” in Saratov Fall Meeting, Chinese-Russian workshop on Biophotonics and Bioimaging-2020 1, 71–74 (2020).

43. Coronavirus-monitor – interactive map of COVID-19 spread and statistics (accessed 06 April 2021). [, in Russian].

44. Newsletter on the situation and measures taken to prevent the spread of diseases caused by the new coronavirus, (accessed 06 April 2021). [ news_details.php?ELEMENT_ID=19030&sphrase_id=4390258, in Russian].

45. E. Mathieu, H. Ritchie, L. Rodés-Guirao, C. Appel, D. Gavrilov, C. Giattino, J. Hasell, B. Macdonald, S. Dattani, D. Beltekian, E. Ortiz-Ospina, and M. Roser, “Coronavirus Pandemic (COVID-19),” Our World in Data (accessed 19 April 2022). [].

46. E. Dong, H. Du, and L. Gardner, “An interactive web-based dashboard to track COVID-19 in real time,” Lancet Infectious Diseases 20(5), 533–534 (2020).

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