# COVID-19 Outbreak Prediction with Machine Learning

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

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#### 2.1. Evolutionary Algorithms

#### 2.1.1. Genetic Algorithm (GA)

#### 2.1.2. Particle Swarm Optimization (PSO)

- Each particle independently looks for the optimal point.
- Each particle moves at the same speed at each step.
- Each particle remembers its best position in the space.
- The particles work together to inform each other of the places they are looking for.
- Each particle is in contact with its neighboring particles.
- Every particle is aware of the particles that are in the neighborhood.
- Every particle is known as one of the best particles in its neighborhood.

#### 2.1.3. Grey Wolf Optimizer (GWO)

#### 2.2. Machine Learning (ML)

^{t}be a time-series vector, in which x

_{t}is the outbreak at time point t and T is the set of all equidistant time points. To train ML methods effectively, we defined two scenarios, listed in Table 2.

#### 2.2.1. Multi-Layered Perceptron (MLP)

_{p}enters the cell from the previous cell p (Equation (19)). w

_{pc}is the weight of the input b

_{p}with respect to cell c and a

_{c}is the sum of the multiplications of the inputs and their weights [86]:

_{c}is applied to a

_{c}. Accordingly, b

_{c}can be calculated as Equation (20) [85]:

_{cn}is the weight of the b

_{cn}which is the output of c to n. W is the collection of all of the weights of the neural network in a set. For input x and output y, h

_{w}(x) is the output of the neural network. The main goal is to learn these weights to reduce the error values between y and h

_{w}(x). That is, the goal is to minimize the cost function Q(W), Equation (21) [86]:

#### 2.2.2. Adaptive Neuro Fuzzy Inference System (ANFIS)

- A fuzzy separator to cluster input–output data within multiple classes.
- A neural network for each class.
- Training neural networks with output–input data in the corresponding classes.

#### 2.2.3. Evaluation Criteria

## 3. Results

#### Machine Learning Results

#### Comparing the Fitted Models

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

MLP | Multi-layered perceptron |

ANFIS | Adaptive network-based fuzzy inference system |

SIR | Susceptible–infected–recovered |

CDR | Call data record |

CART | Classification and regression tree |

EA | Evolutionary algorithms |

GA | Genetic algorithm |

PSO | Particle swarm optimization |

MF | Membership function |

GWO | Grey wolf optimization |

MSE | Mean square error |

RMSE | Root mean square error |

AI | Artificial intelligence |

ANN | Artificial neural network |

Tri. | Triangular |

Gauss. | Gaussian |

Trap. | Trapezoidal |

ML | Machine learning |

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**Figure 1.**Italy’s COVID-19 outbreak: the actual number of confirmed infections vs. epidemiological model.

**Figure 27.**An overview of the current state of the COVID-19 outbreak including daily cases for the four countries of the study (source: World Health Organization).

Authors | Journal | Outbreak Infection | Machine Learning |
---|---|---|---|

[39] | Transboundary and Emerging Diseases | Swine fever | Random Forest |

[35] | Geospatial Health | Dengue fever | Neural Network |

[42] | BMC Research Notes | Influenza | Random Forest |

[41] | Journal of Public Health Medicine | Dengue/Aedes | Bayesian Network |

[38] | Informatica | Dengue | LogitBoost |

[8] | Global Ecology and Biogeography | H1N1 flu | Neural Network |

[34] | Current Science | Dengue | Adopted multi-regression and Naïve Bayes |

[36] | Environment International | Oyster norovirus | Neural Network |

[37] | Water Research | Oyster norovirus | Genetic programming |

[43] | Infectious Disease Modelling | Dengue | Classification and regression tree (CART) |

Inputs | Input Number | Output | |
---|---|---|---|

Scenario 1 | x_{t−1}, x_{t−7}, x_{t−14}, and x_{t−21} | Four inputs | x_{t} (outbreak) |

Scenario 2 | x_{t−1}, x_{t−2}, x_{t−3}, x_{t−4}, and x_{t−5} | Five inputs | x_{t} (outbreak) |

Country | Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 82 s | 1028.98 | 0.996 |

PSO | 1000 | 500 | 36 s | 3358.1 | 0.997 | |

GWO | 500 | 1000 | 14 s | 187.15 | 0.999 | |

China | GA | 300 | 500 | 79 s | 42,160.4 | 0.982 |

PSO | 1000 | 500 | 35 s | 2524.44 | 0.994 | |

GWO | 500 | 1000 | 13 s | 2270.58 | 0.995 | |

Iran | GA | 300 | 500 | 81 s | 1267.04 | 0.992 |

PSO | 1000 | 500 | 36 s | 628.62 | 0.997 | |

GWO | 500 | 1000 | 13 s | 392.88 | 0.996 | |

USA | GA | 300 | 500 | 82 s | 1028.98 | 0.999 |

PSO | 1000 | 500 | 38 s | 350.33 | 0.999 | |

GWO | 500 | 1000 | 15 s | 22.35 | 0.999 | |

Germany | GA | 300 | 500 | 86 s | 5339.5 | 0.983 |

PSO | 1000 | 500 | 39 s | 555.32 | 0.997 | |

GWO | 500 | 1000 | 16 s | 55.54 | 0.999 |

Country | Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 92 s | 3774.06 | 0.845 |

PSO | 1000 | 500 | 42 s | 3645.76 | 0.844 | |

GWO | 500 | 1000 | 16 s | 3642.44 | 0.844 | |

China | GA | 300 | 500 | 91 s | 7188.95 | 0.981 |

PSO | 1000 | 500 | 39 s | 6644.16 | 0.982 | |

GWO | 500 | 1000 | 14 s | 5039.48 | 0.982 | |

Iran | GA | 300 | 500 | 96 s | 3330.45 | 0.943 |

PSO | 1000 | 500 | 45 s | 2072.71 | 0.944 | |

GWO | 500 | 1000 | 18 s | 1981.97 | 0.944 | |

USA | GA | 300 | 500 | 88 s | 850.22 | 0.745 |

PSO | 1000 | 500 | 40 s | 596.69 | 0.746 | |

GWO | 500 | 1000 | 17 s | 592.48 | 0.746 | |

Germany | GA | 300 | 500 | 93 s | 1118.77 | 0.758 |

PSO | 1000 | 500 | 47 s | 964.46 | 0.759 | |

GWO | 500 | 1000 | 20 s | 951.63 | 0.759 |

Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 98 s | 8325.33 | 0.634 |

PSO | 1000 | 500 | 51 s | 8818.2 | 0.634 | |

GWO | 500 | 1000 | 20 s | 9296.59 | 0.634 | |

China | GA | 300 | 500 | 96 s | 40,828.2 | 0.847 |

PSO | 1000 | 500 | 42 s | 43,835.37 | 0.847 | |

GWO | 500 | 1000 | 17 s | 42,714.93 | 0.847 | |

Iran | GA | 300 | 500 | 102 s | 4929.97 | 0.757 |

PSO | 1000 | 500 | 59 s | 8775.56 | 0.757 | |

GWO | 500 | 1000 | 22 s | 8995.52 | 0.756 | |

USA | GA | 300 | 500 | 94 s | 889.15 | 0.538 |

PSO | 1000 | 500 | 37 s | 1130.33 | 0.538 | |

GWO | 500 | 1000 | 15 s | 1135.12 | 0.538 | |

Germany | GA | 300 | 500 | 95 s | 1552.22 | 0.548 |

PSO | 1000 | 500 | 45 s | 1966.81 | 0.548 | |

GWO | 500 | 1000 | 21 s | 1878.67 | 0.548 |

Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 102 s | 6710.01 | 0.976 |

PSO | 1000 | 500 | 54 s | 5102.4 | 0.953 | |

GWO | 500 | 1000 | 26 s | 1272.1 | 0.982 | |

China | GA | 300 | 500 | 100 s | 7921.33 | 0.992 |

PSO | 1000 | 500 | 46 s | 4328.71 | 0.993 | |

GWO | 500 | 1000 | 20 s | 3710.16 | 0.993 | |

Iran | GA | 300 | 500 | 105 s | 6771.74 | 0.995 |

PSO | 1000 | 500 | 62 s | 822.09 | 0.998 | |

GWO | 500 | 1000 | 24 s | 310.02 | 0.998 | |

USA | GA | 300 | 500 | 98 s | 754.6 | 0.931 |

PSO | 1000 | 500 | 38 s | 791.92 | 0.853 | |

GWO | 500 | 1000 | 19 s | 307.58 | 0.938 | |

Germany | GA | 300 | 500 | 101 s | 7577 | 0.904 |

PSO | 1000 | 500 | 49 s | 752.95 | 0.923 | |

GWO | 500 | 1000 | 26 s | 472.62 | 0.946 |

Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 112 s | 7973.11 | 0.993 |

PSO | 1000 | 500 | 61 s | 4827.08 | 0.996 | |

GWO | 500 | 1000 | 34 s | 324.33 | 0.998 | |

China | GA | 300 | 500 | 113 s | 15,697.84 | 0.971 |

PSO | 1000 | 500 | 59 s | 3611.15 | 0.995 | |

GWO | 500 | 1000 | 34 s | 2429.45 | 0.995 | |

Iran | GA | 300 | 500 | 120 s | 5852.66 | 0.995 |

PSO | 1000 | 500 | 88 s | 3809.76 | 0.997 | |

GWO | 500 | 1000 | 39 s | 250.2 | 0.999 | |

USA | GA | 300 | 500 | 110 s | 37,766.56 | 0.875 |

PSO | 1000 | 500 | 49 s | 678.36 | 0.979 | |

GWO | 500 | 1000 | 25 s | 118.24 | 0.991 | |

Germany | GA | 300 | 500 | 116 s | 1709.06 | 0.744 |

PSO | 1000 | 500 | 59 s | 1812.78 | 0.967 | |

GWO | 500 | 1000 | 29 s | 196.8 | 0.99 |

Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 92 s | 8347.51 | 0.912 |

PSO | 1000 | 500 | 53 s | 195,705.52 | 0.918 | |

GWO | 500 | 1000 | 22 s | 12,585.79 | 0.951 | |

China | GA | 300 | 500 | 90 s | 41,544.05 | 0.986 |

PSO | 1000 | 500 | 48 s | 40,195.9 | 0.988 | |

GWO | 500 | 1000 | 23 s | 24,987.34 | 0.895 | |

Iran | GA | 300 | 500 | 99 s | 1,487,501.93 | 0.782 |

PSO | 1000 | 500 | 81 s | 8216.81 | 0.986 | |

GWO | 500 | 1000 | 26 s | 13,635.01 | 0.864 | |

USA | GA | 300 | 500 | 96 s | 655.62 | 0.994 |

PSO | 1000 | 500 | 32 s | 1026.03 | 0.827 | |

GWO | 500 | 1000 | 16 s | 364.87 | 0.988 | |

Germany | GA | 300 | 500 | 98 s | 15,333,537.7 | 0.93 |

PSO | 1000 | 500 | 72 s | 1557.23 | 0.976 | |

GWO | 500 | 1000 | 20 s | 431.97 | 0.998 |

Model | Pop. Size | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 72 s | 7063.4 | 0.983 |

PSO | 1000 | 500 | 40 s | 6150.52 | 0.982 | |

GWO | 500 | 1000 | 13 s | 3450.96 | 0.991 | |

China | GA | 300 | 500 | 65 s | 39,669.92 | 0.976 |

PSO | 1000 | 500 | 39 s | 19,365.58 | 0.987 | |

GWO | 500 | 1000 | 12 s | 4078.99 | 0.989 | |

Iran | GA | 300 | 500 | 83 s | 2,343,032.5 | 0.951 |

PSO | 1000 | 500 | 65 s | 92,755.53 | 0.975 | |

GWO | 500 | 1000 | 15 s | 1031.6 | 0.991 | |

USA | GA | 300 | 500 | 79 s | 1030.01 | 0.779 |

PSO | 1000 | 500 | 24 s | 1005.27 | 0.751 | |

GWO | 500 | 1000 | 11 s | 790.16 | 0.837 | |

Germany | GA | 300 | 500 | 85 s | 1475.39 | 0.871 |

PSO | 1000 | 500 | 69 s | 1387.94 | 0.916 | |

GWO | 500 | 1000 | 14 s | 1341.91 | 0.875 |

Model | POP. SIZE | Iteration | Processing Time | RMSE | Correlation Coefficient | |
---|---|---|---|---|---|---|

Italy | GA | 300 | 500 | 79 s | 8163.1 | 0.995 |

PSO | 1000 | 500 | 48 s | 52,075,925.37 | 0.839 | |

GWO | 500 | 1000 | 18 s | 12,585.79 | 0.951 | |

China | GA | 300 | 500 | 71 s | 68,991.73 | 0.866 |

PSO | 1000 | 500 | 45 s | 80,104.27 | 0.865 | |

GWO | 500 | 1000 | 17 s | 24,987.34 | 0.895 | |

Iran | GA | 300 | 500 | 89 s | 1,436,025.84 | 0.767 |

PSO | 1000 | 500 | 70 s | 3,745,673.26 | 0.744 | |

GWO | 500 | 1000 | 21 s | 13,635.01 | 0.864 | |

USA | GA | 300 | 500 | 84 s | 457,051.4 | 0.974 |

PSO | 1000 | 500 | 30 s | 982.37 | 0.932 | |

GWO | 500 | 1000 | 15 s | 364.87 | 0.988 | |

Germany | GA | 300 | 500 | 87 s | 8176.54 | 0.981 |

PSO | 1000 | 500 | 74 s | 3278.55 | 0.998 | |

GWO | 500 | 1000 | 19 s | 431.97 | 0.998 |

Model Name | Description | RMSE | r-Square |
---|---|---|---|

Linear | $\mathrm{R}=3036.4\times \mathrm{x}-13509.84$ | 5039.48 | 0.964 |

Logarithmic | $\mathrm{R}=-33948.15+27124.70\times \mathrm{log}\left(\mathrm{x}\right)$ | 42,714.93 | 0.718 |

Quadratic | $\mathrm{R}=-5080.88+1455.98\times \mathrm{x}+50.98\times {\mathrm{x}}^{2}$ | 3710.16 | 0.98 |

Cubic | $\mathrm{R}=3984.73-1790.2\times \mathrm{x}+308.52\times {\mathrm{x}}^{2}-5.53\times {\mathrm{x}}^{3}$ | 2429.45 | 0.99 |

Compound | $\mathrm{R}=1601.03\times {1.16}^{\mathrm{x}}$ | 24,987.34 | 0.801 |

Power | $\mathrm{R}=262.27\times {\mathrm{x}}^{1.69}$ | 4078.99 | 0.98 |

Exponential | $\mathrm{R}=1601.03\times \mathrm{EXP}\left(0.15\times \mathrm{x}\right)$ | 24,987.34 | 0.801 |

Logistic | $\mathrm{R}=85011.297/\left(1+\mathrm{EXP}\left(\left(\left(4\times 4483.304\right)\ast \left(9.423-\mathrm{x}\right)/85011.297\right)+2\right)\right)$ | 2270.58 | 0.992 |

Model Name | Description | RMSE | r-Square |
---|---|---|---|

Linear | $\mathrm{R}=663.71\times \mathrm{x}-5437.25$ | 3642.44 | 0.713 |

Logarithmic | $\mathrm{R}=-7997.93+5162.83\times \mathrm{log}\left(\mathrm{x}\right)$ | 9296.59 | 0.402 |

Quadratic | $\mathrm{R}=2998.21-917.93\times \mathrm{x}+51.02\times {\mathrm{x}}^{2}$ | 1272.1 | 0.965 |

Cubic | $\mathrm{R}=-978.55+506.05\times \mathrm{B}2-61.95\times {\mathrm{x}}^{2}+2.42\times {\mathrm{x}}^{3}$ | 324.33 | 0.997 |

Compound | $\mathrm{R}=2.78\times {1.406}^{\mathrm{x}}$ | 12,585.79 | 0.904 |

Power | $\mathrm{R}=0.096\times {\mathrm{x}}^{3.476}$ | 3450.96 | 0.984 |

Exponential | $\mathrm{R}=2.786\times \mathrm{EXP}\left(0.341\times \mathrm{x}\right)$ | 12,585.79 | 0.904 |

Logistic | $\mathrm{R}=70731.084/\left(1+\mathrm{EXP}\left(\left(\left(4\times 3962.88\right)\times \left(23.88-\mathrm{x}\right)/70731.08\right)+2\right)\right)$ | 187.15 | 0.999 |

Model Name | Description | RMSE | r-Square |
---|---|---|---|

Linear | $\mathrm{R}=656.068\times \mathrm{x}-4527.69$ | 1981.97 | 0.891 |

Logarithmic | $\mathrm{R}=-7921.009+5449.784\times \mathrm{log}\left(\mathrm{x}\right)$ | 8995.52 | 0.574 |

Quadratic | $\mathrm{R}=310.48-251.09\times \mathrm{x}+29.26\times {\mathrm{x}}^{2}$ | 310.027 | 0.997 |

Cubic | $\mathrm{R}=902.33-463.02\times \mathrm{x}+46.07\times {\mathrm{x}}^{2}-0.36\times {\mathrm{x}}^{3}$ | 250.204 | 0.998 |

Compound | $\mathrm{R}=13.26\times {1.33}^{\mathrm{x}}$ | 13,635.014 | 0.748 |

Power | $\mathrm{R}=0.51\times {\mathrm{x}}^{3.09}$ | 1031.607 | 0.982 |

Exponential | $\mathrm{R}=13.26\times \mathrm{EXP}\left(0.28\times \mathrm{x}\right)$ | 13,635.014 | 0.748 |

Logistic | $\mathrm{R}=21936.052/\left(1+\mathrm{EXP}\left(\left(\left(4\ast 1255.36\right)\times \left(14.66-\mathrm{x}\right)/21936.052\right)+2\right)\right)$ | 392.88 | 0.996 |

Model Name | Description | RMSE | r-Square |
---|---|---|---|

Linear | $\mathrm{R}=128.421\times \mathrm{x}-1130.294$ | 951.635 | 0.577 |

Logarithmic | $\mathrm{R}=-1528.684+959.941\times \mathrm{log}\left(\mathrm{x}\right)$ | 1878.672 | 0.3 |

Quadratic | $\mathrm{R}=911.113-254.342\times \mathrm{x}+12.347\times {\mathrm{x}}^{2}$ | 472.624 | 0.895 |

Cubic | $\mathrm{R}=-478.087+243.097\times \mathrm{x}-27.118\times {\mathrm{x}}^{2}+0.848\times {\mathrm{x}}^{3}$ | 196.809 | 0.981 |

Compound | $\mathrm{R}=3.821\times {1.263}^{\mathrm{x}}$ | 431.975 | 0.996 |

Power | $\mathrm{R}=0.937{\mathrm{x}}^{2.021}$ | 1341.911 | 0.766 |

Exponential | $\mathrm{R}=3.821\times \mathrm{EXP}\left(0.233\times \mathrm{x}\right)$ | 431.975 | 0.996 |

Logistic | $\mathrm{R}=55179.669/\left(1+\mathrm{EXP}\left(\left(\left(4\times 3740.457\right)\times \left(30.49-\mathrm{x}\right)/55179.669\right)+2\right)\right)$ | 55.546 | 0.998 |

Model Name | Description | RMSE | r-Square |
---|---|---|---|

Linear | $\mathrm{R}=76.833\times \mathrm{x}-666.79$ | 592.486 | 0.557 |

Logarithmic | $\mathrm{R}=-902.637+573.32\times \mathrm{log}\left(\mathrm{x}\right)$ | 1135.124 | 0.289 |

Quadratic | $\mathrm{R}=584.76-157.831\times \mathrm{x}+7.569\times {\mathrm{x}}^{2}$ | 307.585 | 0.88 |

Cubic | $\mathrm{R}=-333.235+170.881\times \mathrm{x}-18.509\times {\mathrm{x}}^{2}+0.56\times {\mathrm{x}}^{3}$ | 118.247 | 0.982 |

Compound | $\mathrm{R}=6.296\times {1.214}^{\mathrm{x}}$ | 364.875 | 0.977 |

Power | $\mathrm{R}=1.707\times {\mathrm{x}}^{1.735}$ | 790.163 | 0.702 |

Exponential | $\mathrm{R}=6.296\times \mathrm{EXP}\left(0.194\times \mathrm{x}\right)$ | 364.875 | 0.977 |

Logistic | $\mathrm{R}=32604.552/\left(1+\mathrm{EXP}\left(\left(\left(4\times 2288.932\right)\times \left(30.303-\mathrm{x}\right)/32604.552\right)+2\right)\right)$ | 22.354 | 0.999 |

Scenario 1 | Scenario 2 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MLP | ANFIS | MLP | ANFIS | |||||||||

No. of Neurons | r | RMSE | MF Type | r | RMSE | No. of Neurons | r | RMSE | MF Type | r | RMSE | |

Italy | 8 | 0.999 | 190.81 | Tri. | 0.999 | 189.76 | 8 | 0.999 | 199.52 | Tri. | 0.999 | 188.55 |

12 | 0.999 | 194.84 | Trap. | 0.841 | 3743.63 | 12 | 0.999 | 195.79 | Trap. | 0.876 | 3276 | |

16 | 0.999 | 188.18 | Gauss | 0.998 | 320.93 | 16 | 0.999 | 195.2 | Gauss | 0.999 | 206.66 | |

Average | 0.999 | 191.27 | 0.946 | 1418.1 | Average | 0.999 | 196.83 | 0.958 | 1223.73 | |||

China | 8 | 0.995 | 2287.55 | Tri. | 0.996 | 2293.09 | 8 | 0.996 | 2265.95 | Tri. | 0.996 | 2272.13 |

12 | 0.996 | 2259.95 | Trap. | 0.987 | 4231.05 | 12 | 0.996 | 2285.73 | Trap. | 0.989 | 3835.34 | |

16 | 0.995 | 2407.16 | Gauss | 0.996 | 2358.3 | 16 | 0.996 | 2260.05 | Gauss | 0.996 | 2272.58 | |

Average | 0.995 | 2318.22 | 0.993 | 2960.81 | Average | 0.996 | 2270.57 | 0.993 | 2793.35 | |||

Iran | 8 | 0.998 | 392.17 | Tri. | 0.998 | 395.33 | 8 | 0.998 | 404.21 | Tri. | 0.998 | 394.04 |

12 | 0.998 | 391.04 | Trap. | 0.977 | 1282.33 | 12 | 0.998 | 392.77 | Trap. | 0.986 | 994 | |

16 | 0.998 | 392.19 | Gauss | 0.998 | 396.51 | 16 | 0.998 | 395.43 | Gauss | 0.998 | 391.96 | |

Average | 0.998 | 391.8 | 0.991 | 391.39 | Average | 0.998 | 397.47 | 0.994 | 593.33 | |||

Germany | 8 | 0.999 | 55.6 | Tri. | 0.999 | 56.25 | 8 | 0.999 | 55.58 | Tri. | 0.999 | 55.63 |

12 | 0.999 | 55.38 | Trap. | 0.12 | 1658.7 | 12 | 0.999 | 55.56 | Trap. | 0.13 | 1537.26 | |

16 | 0.999 | 55.58 | Gauss | 0.998 | 154.99 | 16 | 0.999 | 55.56 | Gauss | 0.999 | 62.91 | |

Average | 0.999 | 55.52 | 0.705 | 623.31 | Average | 0.999 | 55.56 | 0.709 | 551.93 | |||

USA | 8 | 0.999 | 21.65 | Tri. | 0.999 | 21.75 | 8 | 0.999 | 22.31 | Tri. | 0.999 | 22.52 |

12 | 0.999 | 22.36 | Trap. | 0.22 | 861.08 | 12 | 0.999 | 22.3 | Trap. | 0.2 | 935.41 | |

16 | 0.999 | 22.31 | Gauss | 0.998 | 86.32 | 16 | 0.999 | 22.4 | Gauss | 0.999 | 25.03 | |

Average | 0.999 | 22.1 | 0.739 | 323.05 | Average | 0.999 | 22.33 | 0.739 | 327.65 |

Logistic by GWO | Linear by GWO | Logarithmic by GWO | Quadratic by GWO | Power by GWO | MLP | ANFIS | |
---|---|---|---|---|---|---|---|

Day 20th | 3794.045 | 7837.054 | −1280.93 | 5047.906 | 3225.523 | 3792.734 | 3796.738 |

Day 40th | 58,966.55 | 21,111.37 | 273.235 | 47,914.4 | 35,898.08 | 58,966.74 | 58,964.96 |

Day 60th | 70,571.86 | 34,385.68 | 1182.365 | 13,1597.7 | 14,6966.2 | 70,571.66 | 70,572.12 |

Day 80th | 70,729.28 | 47,659.99 | 1827.402 | 256,097.8 | 399,523.4 | 70,729.27 | 70,729.15 |

Day 100th | 70,731.06 | 60,934.31 | 2327.733 | 421,414.7 | 867,822 | 70,731.09 | 70,730.93 |

Day 120th | 70,731.08 | 74,208.62 | 2736.532 | 627,548.4 | 1,635,643 | 70,731.14 | 70,730.87 |

Day 140th | 70,731.08 | 87,482.94 | 3082.167 | 874,498.9 | 2,795,218 | 70,731.19 | 70,730.79 |

Day 150th | 70,731.08 | 94,120.09 | 3236.862 | 1,013,280 | 3,552,851 | 70,731.21 | 70,730.75 |

Logistic by GWO | Linear by GWO | Logarithmic by GWO | Quadratic by GWO | Power by GWO | MLP | ANFIS | |
---|---|---|---|---|---|---|---|

Day 20th | 47,397.6 | 47,218.47 | 1341.899 | 44,431.48 | 41,916.55 | 47,397.6 | 47,360.98 |

Day 40th | 84,030.16 | 107,946.8 | 9507.249 | 134,729.1 | 135,599.1 | 84,030.17 | 84,030.39 |

Day 60th | 84,996.7 | 168,675.1 | 14,283.67 | 265,812 | 269,471.3 | 84,996.7 | 84,996.67 |

Day 80th | 85,011.08 | 229,403.4 | 17,672.6 | 437,680.2 | 438,660.2 | 85,011.08 | 85,011.05 |

Day 100th | 85,011.29 | 290,131.7 | 20,301.26 | 650,333.6 | 640,132.8 | 85,011.3 | 85,011.22 |

Day 120th | 85,011.3 | 350,860 | 22,449.02 | 903,772.3 | 871,733.6 | 85,011.34 | 85,011.13 |

Day 140th | 85,011.3 | 411,588.3 | 24,264.94 | 1,197,996 | 1,131,815 | 85,011.38 | 85,011.05 |

Day 150th | 85,011.3 | 441,952.5 | 25,077.68 | 1,360,403 | 1,272,113 | 85,011.41 | 85,011.01 |

Logistic by GWO | Linear by GWO | Logarithmic by GWO | Quadratic by GWO | Power by GWO | MLP | ANFIS | |
---|---|---|---|---|---|---|---|

Day 20th | 6898.344 | 8593.676 | −830.677 | 6993.955 | 5494.377 | 6902.315 | 6875.585 |

Day 40th | 21,455.58 | 21,715.05 | 809.8719 | 37,087.98 | 47,060.48 | 21,457.4 | 21,456.65 |

Day 60th | 21,931.01 | 34,836.43 | 1769.531 | 90,592.56 | 165,300.1 | 21,932.24 | 21,930.68 |

Day 80th | 21,936 | 47,957.8 | 2450.42 | 167,507.7 | 403,082.8 | 21,935.1 | 21,935.54 |

Day 100th | 21,936.05 | 61,079.18 | 2978.559 | 267,833.4 | 804,764.4 | 21,935.11 | 21,935.6 |

Day 120th | 21,936.05 | 74,200.55 | 3410.08 | 391,569.6 | 1,415,829 | 21,935.12 | 21,935.63 |

Day 140th | 21,936.05 | 87,321.93 | 3774.925 | 538,716.4 | 2,282,679 | 21,935.13 | 21,935.65 |

Day 150th | 21,936.05 | 93,882.61 | 3938.219 | 621,068.7 | 2,826,737 | 21,935.13 | 21,935.67 |

Logistic by GWO | Linear by GWO | Logarithmic by GWO | Quadratic by GWO | Power by GWO | MLP | ANFIS | |
---|---|---|---|---|---|---|---|

Day 20th | 431.027 | 1438.128 | −279.772 | 763.1467 | 400.0548 | 432.8991 | 431.8119 |

Day 40th | 35,356.27 | 4006.551 | 9.199328 | 10,492.96 | 1624.405 | 35,355.14 | 35,355.72 |

Day 60th | 55,043.44 | 6574.974 | 178.2366 | 30,100.56 | 3687.126 | 55,036.14 | 55,044.03 |

Day 80th | 55,179.07 | 9143.397 | 298.1705 | 59,585.93 | 6595.829 | 55,179.05 | 55,178.88 |

Day 100th | 55,179.67 | 11,711.82 | 391.1984 | 98,949.09 | 10,355.87 | 55,179.9 | 55,179.47 |

Day 120th | 55,179.67 | 14,280.24 | 467.2078 | 148,190 | 14,971.42 | 55,179.92 | 55,179.42 |

Day 140th | 55,179.67 | 16,848.66 | 531.4728 | 207,308.7 | 20,445.86 | 55,179.94 | 55,179.37 |

Day 150th | 55,179.67 | 18,132.88 | 560.2357 | 240,572.3 | 23,506.09 | 55,179.96 | 55,179.35 |

Logistic by GWO | Linear by GWO | Logarithmic by GWO | Quadratic by GWO | Power by GWO | MLP | ANFIS | |
---|---|---|---|---|---|---|---|

Day 20th | 242.6091 | 869.8855 | −156.73 | 456.0663 | 309.616 | 244.0038 | 243.6504 |

Day 40th | 21,951.15 | 2406.562 | 15.85698 | 6383.264 | 1031.324 | 21,942.25 | 21,948.25 |

Day 60th | 32,547.08 | 3943.238 | 116.8138 | 18,366.35 | 2084.876 | 32,552.6 | 32,548.47 |

Day 80th | 32,604.34 | 5479.914 | 188.4437 | 36,405.33 | 3435.319 | 32,606.19 | 32,604.47 |

Day 100th | 32,604.55 | 7016.591 | 244.0043 | 60,500.21 | 5060.548 | 32,606.63 | 32,604.72 |

Day 120th | 32,604.55 | 8553.267 | 289.4005 | 90,650.97 | 6944.676 | 32,606.7 | 32,604.76 |

Day 140th | 32,604.55 | 10,089.94 | 327.7825 | 126,857.6 | 9075.446 | 32,606.78 | 32,604.8 |

Day 150th | 32,604.55 | 10,858.28 | 344.9611 | 147,231.9 | 10,230.16 | 32,606.81 | 32,604.82 |

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**MDPI and ACS Style**

Ardabili, S.F.; Mosavi, A.; Ghamisi, P.; Ferdinand, F.; Varkonyi-Koczy, A.R.; Reuter, U.; Rabczuk, T.; Atkinson, P.M. COVID-19 Outbreak Prediction with Machine Learning. *Algorithms* **2020**, *13*, 249.
https://doi.org/10.3390/a13100249

**AMA Style**

Ardabili SF, Mosavi A, Ghamisi P, Ferdinand F, Varkonyi-Koczy AR, Reuter U, Rabczuk T, Atkinson PM. COVID-19 Outbreak Prediction with Machine Learning. *Algorithms*. 2020; 13(10):249.
https://doi.org/10.3390/a13100249

**Chicago/Turabian Style**

Ardabili, Sina F., Amir Mosavi, Pedram Ghamisi, Filip Ferdinand, Annamaria R. Varkonyi-Koczy, Uwe Reuter, Timon Rabczuk, and Peter M. Atkinson. 2020. "COVID-19 Outbreak Prediction with Machine Learning" *Algorithms* 13, no. 10: 249.
https://doi.org/10.3390/a13100249