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## Discrete Fractional-Order Systems with Applications in Engineering and Natural Sciences

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Research Article | Open Access

Volume 2020 |Article ID 1405764 | https://doi.org/10.1155/2020/1405764

Lianyi Liu, Yan Chen, Lifeng Wu, "Forecasting Confirmed Cases, Deaths, and Recoveries from COVID-19 in China during the Early Stage", Mathematical Problems in Engineering, vol. 2020, Article ID 1405764, 4 pages, 2020. https://doi.org/10.1155/2020/1405764

# Forecasting Confirmed Cases, Deaths, and Recoveries from COVID-19 in China during the Early Stage

Accepted07 Jul 2020
Published29 Jul 2020

#### Abstract

To provide a theoretical basis for the prevention and control of COVID-19 in China, confirmed cases, deaths, and recoveries from COVID-19 in China were predicted using a fractional grey model. The results indicated that the grey model has high forecasting accuracy in the prediction of disease spread.

#### 1. Introduction

The outbreak of the novel coronavirus disease-2019 (COVID-19) caused by SARS-CoV-2 took place in December 2019 in Wuhan, China. This disease can cause severe fever and, in the worst cases, acute respiratory failure syndrome [1]. There were 1016 recorded deaths from this outbreak as of February 10, 2020, in China. It has also spread across other countries, starting with Japan and then Australia, France, and the United States. The SARS-CoV-2 virus continues to evolve in alarming ways, with the spread of COVID-19, putting enormous strain on health systems around the world. There is no indication that China will succeed in beating COVID-19 in the short term. Accurately forecasting the epidemic tendency can provide a theoretical basis for the prevention and control of COVID-19.

Statistical methods are widely used for forecasting of epidemic diseases [2]. Traditional prediction methods often require a large number of data samples, which follow a certain typical distribution. However, because of the limited information available during the early stages of disease transmission, the spreading mechanism of COVID-19 is yet to be fully understood [3]. The grey prediction theory provides a new way to solve the systemic problems that occur in cases of limited information. Thus, the grey prediction theory is more suitable for the prediction of the incidence of COVID-19 in China than other theories.

The rest of the paper is arranged as follows. Section 2 introduces the forecasting model. Section 3 shows in detail the prediction results. Conclusions are drawn in Section 4.

#### 2. Fractional Grey Model

Grey system theory mainly focuses on systems with incomplete or uncertain information [4]. In recent years, grey system theory has been successfully applied to the prediction of infectious diseases [58].

Despite the widespread outbreak of COVID-19, data on this disease in China are limited. Many methods cannot make accurate predictions if the data samples are small. For this reason, the fractional grey model (FGM(1,1)) is used to deal with the forecasting problem with limited samples [9]. The FGM(1,1) model is an optimized form of the grey prediction model. Its detailed modeling process has been described previously [9, 10].

#### 3. Results

In this section, the data are from the National Health Commission of the People’s Republic of China (http://www.nhc.gov.cn/). The Chinese government has made every effort to fight the epidemic and has continued to release relevant data since January 21, 2020. Data released after January 21 were used to test the performance of the forecasts.

A rolling forecast approach was taken in the experiment. Here, the data of every five consecutive days were used as observations to predict the data for the next day. The mean absolute percentage error (MAPE) was used to test the performance of the model. The prediction results of the confirmed cases are presented in Table 1.

 Data Actual values FGM(1,1) MAPE 21-Jan 291 22-Jan 440 23-Jan 571 24-Jan 1287 25-Jan 1975 26-Jan 2744 3207 16.89 27-Jan 4515 3961 12.27 28-Jan 5974 6462 8.17 29-Jan 7711 8362 8.44 30-Jan 9692 9881 1.95 31-Jan 11,791 12,037 2.08 1-Feb 14,380 14,103 1.92 2-Feb 17,205 17,271 0.38 3-Feb 20,438 20,418 0.10 4-Feb 24,324 23,973 1.44 5-Feb 28,018 28,593 2.05 6-Feb 28,985 31,792 9.68 7-Feb 31,774 30,893 2.77 8-Feb 33,738 33,145 1.76 9-Feb 35,982 35,965 0.05 Mean 4.66

As shown in Table 1, the mean MAPE is 4.66%, which meets our expectations for accurate forecasting. The FGM(1,1) model only needs five consecutive days of data to predict the next day’s data. It needs very little data and follows the principle of new information priority. Even for the most uncontrollable first days of the epidemic, FGM(1,1) showed accurate prediction. Since February 28, the predicted MAPE has been less than 10%, which demonstrates the adaptability of the model.

The number of deaths due to COVID-19 and the number of people who have recovered are shown in Tables 2 and 3, respectively.

 Data Actual values FGM(1,1) MAPE 22-Jan 9 23-Jan 17 24-Jan 41 25-Jan 56 26-Jan 80 27-Jan 106 109 2.79 28-Jan 132 143 8.63 29-Jan 170 164 3.26 30-Jan 213 212 0.33 31-Jan 259 267 3.22 1-Feb 304 311 2.22 2-Feb 361 351 2.87 3-Feb 425 422 0.78 4-Feb 490 500 2.02 5-Feb 563 559 0.69 6-Feb 636 643 1.16 7-Feb 722 714 1.13 8-Feb 811 813 0.28 9-Feb 908 908 0.05 Mean 2.10
 Data Actual values FGM(1,1) MAPE (%) 24-Jan 38 25-Jan 49 26-Jan 51 27-Jan 60 28-Jan 103 29-Jan 124 129 3.84 30-Jan 171 169 1.00 31-Jan 243 225 7.38 1-Feb 328 318 3.01 2-Feb 475 441 7.09 3-Feb 632 646 2.28 4-Feb 892 843 5.51 5-Feb 1153 1217 5.54 6-Feb 1540 1536 0.25 7-Feb 2050 1975 3.64 8-Feb 2649 2669 0.75 9-Feb 3281 3381 3.05 Mean 3.61

As shown in Tables 2 and 3, the MAPE of the number of deaths and recoveries from COVID-19 was 2.10% and 3.61%, respectively. All the MAPE values of the prediction results were less than 10%, which means that the prediction results met the requirement of highly accurate prediction. Therefore, we took the next step to predict the future number of confirmed, dead, and recovered cases, as shown in Table 4.

 Data Number of confirmed cases Growth rate of confirmed cases (%) Number of deaths Number of recoveries 10-Feb 37,857 5.21 1011 4160 11-Feb 39,742 4.98 1123 5240 12-Feb 41,585 4.64 1244 6582 13-Feb 43,397 4.36 1373 8253 14-Feb 45,186 4.12 1513 10,333

The predictions show that the growth rate of the number of confirmed cases was on the decline, and the number of recoveries was on the rise. Based on the above results, we further predicted the growth rate of confirmed cases. From the existing data, the growth rate showed a straight-line downward trend, so linear regression was used for prediction. The predictive effect is shown in Figure 1. We could draw the conclusion that the inflection point would be reached around February 29, the spread of COVID-19 would be effectively controlled, and the number of people infected would not increase much.

#### 4. Conclusions

The spread of COVID-19 has caused great damage to the world’s health care systems, so it is very necessary to predict the spread of disease in the future. In the early stages of the outbreak, data are limited and not absolutely accurate. The FGM(1,1) model is a good choice at the early stage of disease transmission for the prediction of trends of this new disease. FGM(1,1) is suitable for short-term prediction of time series. Using the characteristics of fractional-order accumulation, the grey model can analyze the rules in short-term data well based on the principle of new information first. Hence, FGM(1,1) could accurately predict the number of confirmed cases, the number of deaths, and the number of recoveries. The predicted results indicate that the spread of COVID-19 will be further suppressed in China, more people will be cured, and infection rates will fall further.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This research was supported by the National Natural Science Foundation of China (71871084), the Scientist Foundation of Hebei Education Department (SQ201027 and ZD202007), and the Excellent Young Scientist Foundation of Hebei Education Department (SLRC2019001).

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