# Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Developing a System Dynamic Model

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- The recovered population do not become susceptible again.
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- The symptomatic are immediately isolated and cannot infect the susceptible.
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- Population is not affected by birth and death rates.
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- The incubation period for all infected individuals is 6 days.

#### 2.2. Data Collection

#### 2.3. The Estimation and Prediction Scheme

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- The first training time frame (AC) included periods of relative stability in daily new cases, as well as periods of rise and fall in incidence. This corresponds to the first 300 days of the pandemic development in Karaganda from 10 March 2020 to 5 January 2021.
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- The next training time frame (AD) was 400 days from the first recorded COVID-19 incident in the city (from 10 March 2020 to 15 April 2021, see Figure 2a). This period includes the first wave and the beginning of the second wave from about 361 days.
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- The third training time frame (AF) was 500 days, from 10 March 2020 to 24 July 2021. In this period, there were two waves of morbidity and the rise of the third—the most “powerful” wave.

_{t}is the actual data, F

_{t}is the forecast data at time t and n is the number of forecast days.

## 3. Results

## 4. Discussion

#### 4.1. The Findings and Their Implications

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- Estimation of model parameters improved due to the increase in sample size.
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- Three scenarios of the development of the situation were proposed—optimistic, pessimistic and most probable—which is especially important for regulators when developing various response measures.
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- The duration of forecasting with acceptable accuracy was 100 days, which significantly exceeds some of the literature data [61]. When compared with the information from Table 3, it is obvious that the results obtained by us in terms of the duration and accuracy of the forecast surpass those of the indicated models. The already-mentioned review [9] demonstrates the high prediction accuracy of machine-learning models. However, the duration of forecasting in these works was no more than 14 days. Under the optimistic scenario, the quality of long-term forecasting of our model can be assessed as high and good.

#### 4.2. Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Forecasting total cases (left) and evaluation of forecasting accuracy APE (right). (

**a**,

**b**) First testing time frame; (

**c**,

**d**) second testing time frame; (

**e**,

**f**) third testing time frame. Green line—optimistic scenario; orange line—pessimistic scenario and red line—most likely scenario.

**Figure 6.**Transmission rate normality checking on the various testing time frames. (

**a**) First testing time frame, 300–400 days (Shapiro–Wilk test, p = 0.00063). (

**b**) Second testing time frame, 400–500 days (Shapiro–Wilk test, p = 0.049). (

**c**) Third testing time frame, 500–600 days (Shapiro–Wilk test, p = 0.00382).

Training Time Frame, Day | 1–300 | 1–400 | 1–500 |
---|---|---|---|

β (mean, SD) | 0.17 (0.075) | 0.177 (0.074) | 0.182 (0.073) |

MAPE (%) | ||||
---|---|---|---|---|

Duration of Forecasting | 25 Days | 50 Days | 75 Days | 100 Days |

(a) First testing time frame | ||||

Optimistic scenario | 2.235 | 3.712 | 5.986 | 6.697 |

Pessimistic scenario | 4.481 | 9.400 | 19.781 | 30.569 |

Most likely scenario | 3.004 | 6.320 | 11.897 | 16.629 |

(b) Second testing time frame | ||||

Optimistic scenario | 6.209 | 14.119 | 25.059 | 33.154 |

Pessimistic scenario | 16.532 | 40.448 | 83.038 | 108.475 |

Most likely scenario | 10.405 | 26.836 | 46.881 | 59.193 |

(c) Third testing time frame | ||||

Optimistic scenario | 5.648 | 22.237 | 38.360 | 50.641 |

Pessimistic scenario | 29.947 | 65.941 | 83.094 | 93.817 |

Most likely scenario | 14.143 | 37.537 | 54.659 | 66.829 |

S. No. | References | Forecasting Techniques | Duration of Forecasting | MAPE Score |
---|---|---|---|---|

1 | Gupta, R.; et al., 2020 [62] | SEIR and regression models | 20 days | SEIR: 25.533, Regression: 21.889 |

2 | Khan, F.M.; Gupta, R., 2020 [63] | ARIMA and NAR | 50 days | ARIMA: 362.1761 |

3 | Sujath, R.; et al., 2020 [64] | LR, MLP and VAR | 69 days | LR: 1745454.432, MLP: 80.057, VAR: 43289.290 |

4 | Tiwari, S.; et al., 2020 [65] | Time series forecasting using Weka | 24 days | 55.489 |

5 | Tomar, A.; Gupta, N., 2020 [66] | LSTM | 25 days | 63.357 |

6 | Salgotra, R.; et al., 2020 [67] | Genetic programming-based model (GP) (GEP model) | 10 days | 7.827 |

7 | Sunori, S.K.; et al., 2021 [68] | Exponential growth model and ML-based LR model | 33 days | LR: 662.441, Exponential: 2096.000 |

8 | Mr. Sudip Ghosh, 2020 [69] | Least square fit- ted model | 35 days | 39.816 |

Time Frame, Day | 300–400 | 400–500 | 500–600 | |
---|---|---|---|---|

Actual data | β (mean, SD) | 0.195 (0.071) | 0.200 (0.061) | 0.204 (0.065) |

Model data | β (mean, SD) | 0.17 (0.075) | 0.177 (0.074) | 0.182 (0.073) |

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**MDPI and ACS Style**

Koichubekov, B.; Takuadina, A.; Korshukov, I.; Turmukhambetova, A.; Sorokina, M.
Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan. *Healthcare* **2023**, *11*, 752.
https://doi.org/10.3390/healthcare11050752

**AMA Style**

Koichubekov B, Takuadina A, Korshukov I, Turmukhambetova A, Sorokina M.
Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan. *Healthcare*. 2023; 11(5):752.
https://doi.org/10.3390/healthcare11050752

**Chicago/Turabian Style**

Koichubekov, Berik, Aliya Takuadina, Ilya Korshukov, Anar Turmukhambetova, and Marina Sorokina.
2023. "Is It Possible to Predict COVID-19? Stochastic System Dynamic Model of Infection Spread in Kazakhstan" *Healthcare* 11, no. 5: 752.
https://doi.org/10.3390/healthcare11050752