# CBRR Model for Predicting the Dynamics of the COVID-19 Epidemic in Real Time

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Related Works

#### 2.2. Preliminary Insight on Recurrent Relations

#### 2.3. Case-Based Rate Reasoning Method

## 3. Results

#### 3.1. Modeling for the USA

#### 3.2. Modeling for Russia

#### Simulation Results for Russia

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Layne, S.P.; Hyman, J.M.; Morens, D.M.; Taubenberger, J.K. New coronavirus outbreak: Framing questions for pandemic prevention. Sci. Transl. Med.
**2020**, 12, eabb1469. [Google Scholar] [CrossRef] [PubMed] [Green Version] - The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team. Vital surveillances: The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases (COVID-19)-China 2020. China CDC Wkly.
**2020**, 2, 113–122. [Google Scholar] [CrossRef] - Wu, J.T.; Leung, K.; Leung, G.M. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: A modelling study. Lancet
**2020**, 395, 689–697. [Google Scholar] [CrossRef] [Green Version] - MIDAS Coordination Center. Models of Infectious Disease Agent Study (University of Pittsburgh, 2020). Available online: https://midasnetwork.us/ (accessed on 23 June 2020).
- Kondratyev, M.A. Forecasting methods and models of disease spread. Comput. Res. Model.
**2013**, 5, 863–882. [Google Scholar] [CrossRef] - Mandal, M.; Jana, S.; Nandi, S.; Khatua, A.; Adak, S.; Kar, T.K. A model based study on the dynamics of COVID-19: Prediction and control. Chaos Solitons Fractals
**2020**, 136, 109889. [Google Scholar] [CrossRef] [PubMed] - Bekirosab, S.; Kouloumpou, D. SBDiEM: A new mathematical model of infectious disease dynamics. Chaos Solitons Fractals
**2020**, 136, 109828. [Google Scholar] [CrossRef] - Barmparis, G.D.; Tsironis, G.P. Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach. Chaos Solitons Fractals
**2020**, 135, 109842. [Google Scholar] [CrossRef] - Kissler, S.M.; Tedijanto, C.; Goldstein, E.; Grad, Y.H.; Lipsitch, M. Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period. Science
**2020**, 368, 860–868. [Google Scholar] [CrossRef] - Fanelli, D.; Piazza, F. Analysis and forecast of COVID-19 spreading in China, Italy and France. Chaos Solitons Fractals
**2020**, 134, 109761. [Google Scholar] [CrossRef] - López, L.; Rodó, X. The end of social confinement and COVID-19 re-emergence risk. Nat. Hum. Behav.
**2020**, 4, 746–755. [Google Scholar] [CrossRef] - Otunuga, O.M.; Ogunsolu, M.O. Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment. Infect. Dis. Model.
**2020**, 5, 61–90. [Google Scholar] [CrossRef] [PubMed] - Cooper, I.; Mondal, A.; Antonopoulos, C.G. A SIR model assumption for the spread of COVID-19 in different communities. Chaos Solitons Fractals
**2020**, 139, 110057. [Google Scholar] [CrossRef] [PubMed] - Singh, R.K.; Rani, M.; Bhagavathula, A.S.; Sah, R.; Rodriguez-Morales, A.J.; Kalita, H.; Nanda, C.; Sharma, S.; Sharma, Y.D.; Rabaan, A.A.; et al. Prediction of the COVID-19 pandemic for the top 15 affected countries: Advanced autoregressive integrated moving average (ARIMA) model. JMIR Public Health Surveill.
**2020**, 6, e19115. [Google Scholar] [CrossRef] - Sharma, V.K.; Nigam, U. Modeling and forecasting of Covid-19 growth curve in India. MedRxiv
**2020**. [Google Scholar] [CrossRef] - Zhang, T.; Ma, Y.; Xiao, X.; Lin, Y.; Zhang, X.; Yin, F.; Li, X. Dynamic bayesian network in infectious diseases surveillance: A simulation study. Sci. Rep.
**2019**, 9, 10376. [Google Scholar] [CrossRef] - Akhtar, M.; Kraemer, M.U.G.; Gardner, L.M. A dynamic neural network model for predicting risk of Zika in real time. BMC Med.
**2019**, 17, 171. [Google Scholar] [CrossRef] [Green Version] - Schmidt, R.; Waligora, T. Influenza forecast: Case-based reasoning or statistics? In Lecture Notes in Computer Science, Proceedings of the 11th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, Vietri sul Mare, Italy, 12–14 September 2007; Apolloni, B., Howlett, R.J., Jain, L., Eds.; Springer: Berlin/Heidelberg, Germany, 2007; Volume 4692, pp. 287–294. [Google Scholar] [CrossRef]
- Viboud, C.; Boelle, P.Y.; Carrat, F.; Valleron, A.J.; Flahault, A. Prediction of the spread of influenza epidemics by the method of analogues. Am. J. Epidemiol.
**2003**, 158, 996–1006. [Google Scholar] [CrossRef] [Green Version] - Relich, M.; Pawlewski, P. A case-based reasoning approach to cost estimation of new product development. Neurocomputing
**2018**, 272, 40–45. [Google Scholar] [CrossRef] - Kaedi, M.; Ghasem-Aghaee, N. Improving case-based reasoning in solving optimization problems using Bayesian optimization algorithm. Intell. Data Anal.
**2012**, 16, 199–210. [Google Scholar] [CrossRef] - Teles, P. Predicting the evolution of SARS-Covid-2 in portugal using an adapted SIR model previously used in south Korea for the MERS outbreak. MedRxiv
**2020**. [Google Scholar] [CrossRef] - COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. Available online: https://coronavirus.jhu.edu/map.html (accessed on 4 August 2020).
- Popkov, Y.; Popkov, A.; Dubnov, Y.; Solomatine, D. Entropy-randomized forecasting of stochastic dynamic regression models. Mathematics
**2020**, 8, 1119. [Google Scholar] [CrossRef] - Zakharov, V.; Balykina, Y. Predicting the dynamics of the coronavirus (COVID-19) epidemic based on the case-based reasoning approach. Appl. Math. Comput. Sci. Control Process.
**2020**, 3, 249–259. [Google Scholar] - Coronavirus Epidemic in Russia. Dynamics Modeling and Forecasting. Available online: http://hdl.handle.net/11701/18124 (accessed on 7 September 2020).
- The Coronavirus Epidemic in Russia. Intelligent Logistics Center Analytical Notes. Available online: http://www.apmath.spbu.ru/cil/ (accessed on 20 September 2020).

**Figure 1.**Steps for constructing the forecast trajectory of the coronavirus epidemic dynamics based on the Case-Based Rate Reasoning (CBRR) approach.

**Figure 3.**Growth rate over the considered time period in the USA (real-world data and model forecast). Red dotted lines correspond to the growth rates of 5% and 2%.

**Figure 4.**Total number of confirmed cases in the Russian Federation (RF) (real-world data and model forecast).

**Figure 5.**Growth rate over the considered time period in the RF (real-world data and model forecast). Red dotted lines correspond to the growth rates of 5% and 2%.

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**MDPI and ACS Style**

Zakharov, V.; Balykina, Y.; Petrosian, O.; Gao, H.
CBRR Model for Predicting the Dynamics of the COVID-19 Epidemic in Real Time. *Mathematics* **2020**, *8*, 1727.
https://doi.org/10.3390/math8101727

**AMA Style**

Zakharov V, Balykina Y, Petrosian O, Gao H.
CBRR Model for Predicting the Dynamics of the COVID-19 Epidemic in Real Time. *Mathematics*. 2020; 8(10):1727.
https://doi.org/10.3390/math8101727

**Chicago/Turabian Style**

Zakharov, Victor, Yulia Balykina, Ovanes Petrosian, and Hongwei Gao.
2020. "CBRR Model for Predicting the Dynamics of the COVID-19 Epidemic in Real Time" *Mathematics* 8, no. 10: 1727.
https://doi.org/10.3390/math8101727