Multicentral Agent-Based Model of Six Epidemic Waves of COVID-19 in the Nizhny Novgorod Region of Russian Federation

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.

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

2. Pelinovsky E, Kurkin A, Kurkina O et al. Logistic equation and COVID-19. Chaos, Solitons & Fractals. 2020;140:110241.

3. 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.

4. Pelinovsky E, Kokoulina M, Epifanova A, et al. Gompertz model in COVID-19 spreading simulation. Chaos, Solitons & Fractals. 2022;154:111699.

5. 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.

6. 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.

7. 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.

8. 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

9. 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.

10. He S, Peng Y, Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear dynamics. 2020;101:1667–1680.

11. 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

12. 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.

13. 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.

14. 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

15. 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.

16. 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

17. Petrakova V, Krivorotko O. Mean field game for modeling of COVID-19 spread. Journal of Mathematical Analysis and Applications. 2022;514(1):126271.

18. Tembine H. COVID-19: data-driven mean-field-type game perspective. Games. 2020;11(4):51. https://doi.org/10.3390/g11040051

19. 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

20. 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.

21. 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.

22. 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.

23. 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 & Engineering. 2023;9(1): 010302. Doi: 10.18287/JBPE23.09.010302

24. 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 & Engineering. 2023:010306. Doi: 10.18287/JBPE23.09.010306