# Optimization Method for Forecasting Confirmed Cases of COVID-19 in China

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## Abstract

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## 1. Introduction

- We propose an efficient forecasting model to forecast the confirmed cases of the COVID-19 in China for the upcoming ten days based on previously confirmed cases.
- An improved ANFIS model is proposed using a modified FPA algorithm, using SSA.
- We compare the proposed model with the original ANFIS and existing modified ANFIS models, such as PSO, GA, ABC, and FPA.

## 2. Material and Methods

#### 2.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)

#### 2.2. Flower Pollination Algorithm (FPA)

#### 2.3. Salp Swarm Algorithm (SSA)

## 3. The Proposed Method

Algorithm 1 Proposed FPASSA algorithm |

Input: Historical COVID-19 dataset, size of population N, total number of iterations ${t}_{max}$. Divide the data into training and testing sets. Using Fuzzy c-mean method to determine the number of membership functions. Constructing the ANFIS network. Set the initial value for N solutions (X). Set $t=1$. while $t>{t}_{max}$ doCalculate the objective value for each ${X}_{i}$. if $rand>p$ thenApply the Global operators of FPA. elseif $r>0.5$ thenUsing the operators of FPA to update ${X}_{i}$. elseUsing the operators of SSA. end ifend ifend whileReturn the best solution that represents the best configuration for ANFIS. Apply the testing set to the best ANFIS model. Forecasting the COVID-19 for the next ten days. |

## 4. Experiment

#### 4.1. Datasets Description

#### 4.2. Performance Measures

- Root Mean Square Error (RMSE):$$RMSE=\sqrt{\frac{1}{{N}_{s}}\sum _{i=1}^{{N}_{s}}{(YY{P}_{i}-{Y}_{i})}^{2}}$$
- Mean Absolute Error (MAE):$$MAE=\frac{1}{{N}_{s}}\sum _{i=1}^{{N}_{s}}|YY{P}_{i}-{Y}_{i}|$$
- Mean Absolute Percentage Error (MAPE):$$MAPE=\frac{1}{{N}_{s}}\sum _{i=1}^{{N}_{s}}|\frac{Y{P}_{i}-{Y}_{i}}{Y{P}_{i}}|$$
- Root Mean Squared Relative Error (RMSRE):$$RMSRE=\sqrt{\frac{1}{{N}_{s}}\sum _{i=1}^{{N}_{s}}{(\frac{Y{P}_{i}-{Y}_{i}}{Y{P}_{i}})}^{2}}$$
- Coefficient of Determination (${R}^{2}$):$${R}^{2}=1-\frac{{\sum}_{i=1}^{n}{({Y}_{i}-Y{P}_{i})}^{2}}{{\sum}_{i=1}^{n}{({Y}_{i}-{\overline{Y}}_{i})}^{2}}$$

#### 4.3. Parameter Settings

#### 4.4. Performance of FPASSA to Forecast DS1 and DS2

#### 4.5. Influence of FPASSA to Forecast COVID-19

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Date (D/M/Y) | Confirmed | Date (D/M/Y) | Confirmed | Date (D/M/Y) | Confirmed |
---|---|---|---|---|---|

21/1/2020 | 278 | 31/1/2020 | 9720 | 10/2/2020 | 40,554 |

22/1/2020 | 309 | 1/2/2020 | 11,821 | 11/2/2020 | 42,708 |

23/1/2020 | 571 | 2/2/2020 | 14,411 | 12/2/2020 | 44,730 |

24/1/2020 | 830 | 3/2/2020 | 17,283 | 13/2/2020 | 46,550 |

25/1/2020 | 1297 | 4/2/2020 | 20,471 | 14/2/2020 | 48,548 |

26/1/2020 | 1985 | 5/2/2020 | 24,363 | 15/2/2020 | 50,054 |

27/1/2020 | 2741 | 6/2/2020 | 28,060 | 16/2/2020 | 51,174 |

28/1/2020 | 4537 | 7/2/2020 | 31,211 | 17/2/2020 | 70,635 |

29/1/2020 | 5997 | 8/2/2020 | 34,598 | 18/2/2020 | 72,528 |

30/1/2020 | 7736 | 9/2/2020 | 37,251 |

Algorithm | Parameters Setting |
---|---|

ANFIS | $Max.\phantom{\rule{4pt}{0ex}}epochs=100,Error\phantom{\rule{4pt}{0ex}}goal=0,$ |

$Initial\phantom{\rule{4pt}{0ex}}step=0.01,$$Decrease\phantom{\rule{4pt}{0ex}}rate=0.9,$ | |

$Increase\phantom{\rule{4pt}{0ex}}rate=1.1$ | |

GA-ANFIS | $Crossover\phantom{\rule{4pt}{0ex}}type=1,$ |

PSO-ANFIS | $wMax=0.9,\phantom{\rule{4pt}{0ex}}wMin=0.2,\phantom{\rule{4pt}{0ex}}C1=2,\phantom{\rule{4pt}{0ex}}C2=2$ |

$cp=1,$ | |

$mp=0.01$ | |

ABC-ANFIS | $a=1,employed\phantom{\rule{4pt}{0ex}}bees=N/2,onlooker\phantom{\rule{4pt}{0ex}}bees=N/2$ |

FPA-ANFIS | $Standard\phantom{\rule{4pt}{0ex}}gamma=1.5,\phantom{\rule{4pt}{0ex}}Swich\phantom{\rule{4pt}{0ex}}probablity=0.8$ |

FPASSA-ANFIS | $Standard\phantom{\rule{4pt}{0ex}}gamma=1.5,\phantom{\rule{4pt}{0ex}}Swich\phantom{\rule{4pt}{0ex}}probablity=0.8,{C}_{2}$∈ [0, 1], ${C}_{3}$ ∈ [0, 1] |

Dataset | Method | RMSE | MAE | MAPE | RMSRE | R2 | Time |
---|---|---|---|---|---|---|---|

DS1 | ANFIS | 952 | 570 | 37.61 | 0.551 | 0.969 | - |

PSO | 798 | 494 | 34.13 | 0.510 | 0.978 | 25.43 | |

GA | 766 | 480 | 35.44 | 0.530 | 0.98 | 28.70 | |

ABC | 878 | 564 | 39.79 | 0.593 | 0.972 | 49.27 | |

FPA | 618 | 411 | 37.69 | 0.570 | 0.979 | 24.58 | |

FPASSA | 609 | 391 | 32.58 | 0.497 | 0.986 | 24.55 | |

DS2 | ANFIS | 718 | 405 | 64.20 | 1.198 | 0.858 | - |

PSO | 620 | 353 | 52.07 | 0.870 | 0.892 | 31.64 | |

GA | 622 | 362 | 87.91 | 3.216 | 0.902 | 34.83 | |

ABC | 696 | 433 | 53.30 | 1.101 | 0.887 | 60.87 | |

FPA | 622 | 371 | 80.55 | 3.152 | 0.898 | 30.42 | |

FPASSA | 619 | 367 | 45.02 | 0.887 | 0.909 | 30.39 |

Method | RMSE | MAE | MAPE | RMSRE | R2 | Time |
---|---|---|---|---|---|---|

ANN | 8750 | 5413 | 13.09 | 0.204 | 0.8991 | - |

KNN | 12,100 | 7671 | 8.32 | 0.130 | 0.7710 | - |

SVR | 7822 | 5354 | 8.40 | 0.080 | 0.8910 | - |

ANFIS | 7375 | 5523 | 5.32 | 0.09 | 0.9032 | - |

PSO | 6842 | 4559 | 5.12 | 0.08 | 0.9492 | 24.18 |

GA | 7194 | 4963 | 5.26 | 0.08 | 0.9575 | 27.02 |

ABC | 8327 | 6066 | 6.86 | 0.10 | 0.7906 | 46.80 |

FPA | 6059 | 4379 | 5.04 | 0.07 | 0.9439 | 23.41 |

FPASSA | 5779 | 4271 | 4.79 | 0.07 | 0.9645 | 23.30 |

Data | Confirmed Cases (Expected) |
---|---|

19/2/2020 | 74,406 |

20/2/2020 | 76,215 |

21/2/2020 | 78,728 |

22/2/2020 | 80,332 |

23/2/2020 | 81,617 |

24/2/2020 | 83,858 |

25/2/2020 | 86,115 |

26/2/2020 | 90,794 |

27/2/2020 | 95,695 |

28/2/2020 | 99,453 |

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## Share and Cite

**MDPI and ACS Style**

Al-qaness, M.A.A.; Ewees, A.A.; Fan, H.; Abd El Aziz, M.
Optimization Method for Forecasting Confirmed Cases of COVID-19 in China. *J. Clin. Med.* **2020**, *9*, 674.
https://doi.org/10.3390/jcm9030674

**AMA Style**

Al-qaness MAA, Ewees AA, Fan H, Abd El Aziz M.
Optimization Method for Forecasting Confirmed Cases of COVID-19 in China. *Journal of Clinical Medicine*. 2020; 9(3):674.
https://doi.org/10.3390/jcm9030674

**Chicago/Turabian Style**

Al-qaness, Mohammed A. A., Ahmed A. Ewees, Hong Fan, and Mohamed Abd El Aziz.
2020. "Optimization Method for Forecasting Confirmed Cases of COVID-19 in China" *Journal of Clinical Medicine* 9, no. 3: 674.
https://doi.org/10.3390/jcm9030674