# Evaluation of the COVID-19 Era by Using Machine Learning and Interpretation of Confidential Dataset

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Regression Models and Performance Comparison

## 4. Concavity and Points of Inflection

## 5. Proposed Cloud Framework

Algorithm 1. Modified Levenberg–Marquardt Algorithm |

Requirements: |

$\mathrm{x}$: Input sequence of days from first reported case |

$\mathrm{y}$: Input number of cases corresponding to each day in x |

$\mathrm{t}$: Threshold parameter (the earliest time a failure may occur) |

Process: |

${\mathrm{w}}_{0}\leftarrow 1\ast \mathrm{x}$ |

for iteration n from 0, step 1 do |

$\mathrm{f}\leftarrow \mathrm{Levenberg}\text{}\mathrm{Marquardt}\text{}\left(\mathrm{input}:\mathrm{x},\mathrm{y},{\mathrm{w}}^{\mathrm{n}}\right)$ |

${\mathrm{d}}_{\mathrm{i}}\leftarrow \left|\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)-{\mathrm{y}}_{\mathrm{i}}\right|,\text{}\forall \mathrm{i}\in \mathbb{N}$ |

Apply one of the following: |

${\mathrm{w}}_{\mathrm{i}}^{\mathrm{n}+1}\leftarrow \left(7\right)$ |

${\mathrm{w}}_{\mathrm{i}}^{\mathrm{n}+1}\leftarrow \left(8\right)$ |

${\mathrm{w}}_{\mathrm{i}}^{\mathrm{n}+1}\leftarrow \left(9\right)$ |

if ${\sum}_{i}\left|{\mathrm{w}}_{\mathrm{i}}^{\mathrm{n}}-{\mathrm{w}}_{\mathrm{i}}^{\mathrm{n}+1}\right|<\mathrm{t}$ then |

break |

end for |

end procedure |

## 6. Distribution Fitting

_{B}, Gen. Extreme Value, Person 6 and Degum as the best performance of goodness of fit for Italy, Czech Republic, France and Denmark, respectively, and they were evaluated by Kolmogorov Smirnov and Anderson Darling tests. Johnson S

_{B}distribution shows the best fitting performance compared to the other distributions in two countries, Italy (Figure 5) and Spain (Figure 8) [36]. From the iteratively weighted approach in section zero, the distributions fit the curve better than without weight.

## 7. Personal and Health Information Protection

_{0}represents the NIDN, and the coefficients a

_{1}= (1,2,5,6,4) and a

_{2}= (7,3,2,1,9) are randomly selected. Moreover, the secret values of ${\mathrm{x}}_{\mathrm{i}},\text{}\mathrm{i}=1,2,3$ are randomly selected and correspond to each DSP, respectively; let ${\mathrm{x}}_{1}=1,\text{}{\mathrm{x}}_{2}=2,\text{}{\mathrm{x}}_{3}=4$. Table 5 presents the computational results of substitution to each polynomial of the coefficients and the secret values.

_{0}[41]. Finaly, we retrieve the reconstructed Table 10.

## 8. Mortality Rate

## 9. Cumulative Cases vs. Daily Case Rate

^{2}= 0.9885.

^{2}= 0.866 is decreasing within the interval [273,289] in contrast to the previous Figure 10 where the rapid increment in the interval [235, ∞) is presented.

## 10. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Regression Models | R-Square |
---|---|

Linear | R^{2} = 0.8609 |

Exponential | R^{2} = 0.922 |

6th-degree Polynomial | R^{2} = 0.999336 |

x | x_{1} | x_{2} | ||
---|---|---|---|---|

${\mathrm{F}}^{\u2033}\left(\mathrm{x}\right)$ | + | - | + | |

$\mathrm{F}\left(\mathrm{x}\right)$ |

SSE | R-Square | Adjusted R-Square | RMSE |
---|---|---|---|

3.836 × 10^{11} | 0.9979 | 0.9979 | 3.306 × 10^{4} |

NIDN | Name | DoB | MN | PC | PoI |
---|---|---|---|---|---|

880,618 | Andrew | 26/03/1984 | 96,536,499 | 4529 | 80% |

526,548 | Nicolas | 12/05/1968 | 99,652,342 | 2324 | 95% |

616,636 | Jane | 13/07/1975 | 96,521,548 | 2528 | 3% |

844,131 | David | 25/04/1983 | 99,215,482 | 4528 | 0% |

321,131 | Mathew | 01/09/1950 | 99,992,272 | 5232 | 75% |

NIDN | Polynomial | x = 1 | x = 2 | x = 4 |
---|---|---|---|---|

P(x) | DSP_{1} | DSP_{2} | DSP_{3} | |

880,618 | 1x^{2} + 7x + 880,618 | 880,626 | 880,636 | 880,662 |

526,548 | 2x^{2} + 3x + 526,548 | 526,553 | 526,562 | 526,592 |

616,636 | 5x^{2} + 2x + 616,636 | 616,643 | 616,660 | 616,724 |

844,131 | 6x^{2} + 1x + 844,131 | 844,138 | 844,157 | 844,231 |

321,131 | 4x^{2} + 9x + 321,131 | 321,144 | 321,165 | 321,231 |

NIDN | Name |
---|---|

880,626 | Andrew |

526,553 | Nicolas |

616,643 | Jane |

844,138 | David |

321,144 | Mathew |

NIDN | DoB | MN |
---|---|---|

880,636 | 26/03/1984 | 96,536,499 |

526,562 | 12/05/1968 | 99,652,342 |

616,660 | 13/07/1975 | 96,521,548 |

844,157 | 25/04/1983 | 99,215,482 |

321,165 | 01/09/1950 | 99,992,272 |

NIDN | PC | PoI |
---|---|---|

880,662 | 4529 | 80% |

526,592 | 2324 | 95% |

616,724 | 2528 | 3% |

844,231 | 4528 | 0% |

321,231 | 5232 | 75% |

$\mathbf{i}$ | ${\mathbf{x}}_{\mathbf{i}}$ | $\mathbf{P}\left({\mathbf{x}}_{\mathbf{i}}\right)$ | ${\mathbf{\Delta}}_{\mathbf{P}\left({\mathbf{x}}_{\mathbf{i}}\right)}$ | ${\mathbf{\Delta}}_{\mathbf{\Delta}\mathbf{P}\left({\mathbf{x}}_{\mathbf{i}}\right)}^{2}$ |
---|---|---|---|---|

1 | 1 | 880,626 | ||

${\Delta}_{\mathrm{P}\left({\mathrm{x}}_{1}\right)}=\frac{\mathrm{P}\left({\mathrm{x}}_{2}\right)-\mathrm{P}\left({\mathrm{x}}_{1}\right)}{{\mathrm{x}}_{2}-{\mathrm{x}}_{1}}=10$ | ||||

2 | 2 | 880,636 | $\frac{{\Delta}_{\mathrm{P}\left({\mathrm{x}}_{2}\right)}-{\Delta}_{\mathrm{P}\left({\mathrm{x}}_{1}\right)}}{{\mathrm{x}}_{3}-{\mathrm{x}}_{1}}=1$ | |

${\Delta}_{\mathrm{P}\left({\mathrm{x}}_{2}\right)}=\frac{\mathrm{P}\left({\mathrm{x}}_{3}\right)-\mathrm{P}\left({\mathrm{x}}_{2}\right)}{{\mathrm{x}}_{3}-{\mathrm{x}}_{2}}=13$ | ||||

3 | 4 | 880,662 |

NIDN | Name | DoB | MN | PC | PoI |
---|---|---|---|---|---|

880,618 | Andrew | 26/03/1984 | 96,536,499 | 4529 | 80% |

$\mathbf{f}$ | $\mathbf{x}$ | $\mathbf{y}$ | $\mathbf{m}$% | $\mathbf{x}\mathbf{y}$ | ${\mathbf{x}}^{\mathbf{2}}$ | ${\mathbf{y}}^{\mathbf{2}}$ | ${\left(\mathbf{m}-\overline{\mathbf{m}}\right)}^{2}$ |
---|---|---|---|---|---|---|---|

1 | 2 | 0 | 0 | 0 | 4 | 0 | 81.29 |

2 | 1128 | 29 | 2.57 | 32712 | 1,272,384 | 841 | 41.54 |

3 | 105,792 | 12,428 | 11.75 | 1,314,782,976 | $1.12\times {10}^{10}$ | $1.54\times {10}^{8}$ | 7.46 |

4 | 205,463 | 27,967 | 13.61 | 5,746,183,721 | $4.22\times {10}^{10}$ | $7.28\times {10}^{8}$ | 21.12 |

5 | 232,997 | 33,415 | 14.34 | 7,785,594,755 | $5.43\times {10}^{10}$ | $1.12\times {10}^{9}$ | 28.36 |

6 | 240,136 | 34,767 | 14.48 | 8,348,808,312 | $5.77\times {10}^{10}$ | $1.21\times {10}^{9}$ | 29.83 |

7 | 247,537 | 35,141 | 14.20 | 8,698,697,717 | $6.13\times {10}^{10}$ | $1.23\times {10}^{9}$ | 26.83 |

8 | 269,214 | 35,483 | 13.18 | 9,552,520,362 | $7.25\times {10}^{10}$ | $1.26\times {10}^{9}$ | 17.34 |

9 | 314,861 | 35,894 | 11.40 | $1.1302\times {10}^{10}$ | $9.91\times {10}^{10}$ | $1.29\times {10}^{9}$ | 5.68 |

10 | 679,430 | 38,618 | 5.68 | $2.6238\times {10}^{10}$ | $4.62\times {10}^{11}$ | $1.49\times {10}^{9}$ | 11.10 |

11 | 1,601,554 | 55,576 | 3.47 | $8.9008\times {10}^{10}$ | $2.56\times {10}^{12}$ | $3.09\times {10}^{9}$ | 30.76 |

12 | 2,047,696 | 71,925 | 3.51 | $1.4728\times {10}^{11}$ | $4.19\times {10}^{12}$ | $5.17\times {10}^{9}$ | 30.29 |

n | $\sum \mathrm{x}$ | $\sum \mathrm{y}$ | $\sum \mathrm{m}$ | $\sum \mathrm{x}\mathrm{y}$ | $\sum {\mathrm{x}}^{2}$ | $\sum {\mathrm{y}}^{2}$ | $\sum {\left(\mathrm{m}-\overline{\mathrm{m}}\right)}^{2}$ |

12 | 5,945,808 | 381,243 | 108.19 | $3.1527\times {10}^{11}$ | $7.62\times {10}^{12}$ | $1.68\times {10}^{10}$ | 331.6104 |

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**MDPI and ACS Style**

Andreou, A.; Mavromoustakis, C.X.; Mastorakis, G.; Batalla, J.M.; Pallis, E.
Evaluation of the COVID-19 Era by Using Machine Learning and Interpretation of Confidential Dataset. *Electronics* **2021**, *10*, 2910.
https://doi.org/10.3390/electronics10232910

**AMA Style**

Andreou A, Mavromoustakis CX, Mastorakis G, Batalla JM, Pallis E.
Evaluation of the COVID-19 Era by Using Machine Learning and Interpretation of Confidential Dataset. *Electronics*. 2021; 10(23):2910.
https://doi.org/10.3390/electronics10232910

**Chicago/Turabian Style**

Andreou, Andreas, Constandinos X. Mavromoustakis, George Mastorakis, Jordi Mongay Batalla, and Evangelos Pallis.
2021. "Evaluation of the COVID-19 Era by Using Machine Learning and Interpretation of Confidential Dataset" *Electronics* 10, no. 23: 2910.
https://doi.org/10.3390/electronics10232910