# Pandemic Analytics by Advanced Machine Learning for Improved Decision Making of COVID-19 Crisis

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## Abstract

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## 1. Introduction

- Integrated and interoperable data representation.
- Intelligent data management methods (time-series analysis, anomaly detection, dimensional reduction, parameter selection, etc.).
- Real-time analysis mechanisms.
- Ability to securely exchange data between distributed systems.

## 2. Related Work

## 3. Mathematical Modeling and Pandemic Analytics

#### 3.1. Real-Time Statistics

#### 3.2. Near Real-Time Analytics

#### 3.2.1. Basic Reproduction Number (R_{0})

_{0}can be thought of as the expected number of outbreaks at the beginning of an epidemic that results directly from an outbreak in a population where all individuals are susceptible to infection when there is no immunity in the population (natural or vaccinated) and no restrictive measures have begun to be implemented [27,28,32].

_{0}= 3, each case can infect another three people on average, and these, in turn, another three each, and so on. As a result, the number of cases gradually increases, and there is an extensive dispersion. If R

_{0}< 1, then there is no risk of epidemic. This is because, in this case, one case can infect another person, and therefore, the transmission gradually declines. In general, the higher the value of R

_{0}, the more difficult it is to control the epidemic. For simple models, the percentage of the population to be immunized to prevent the prolonged spread of the infectious disease must be greater than 1 − $\frac{1}{{R}_{0}}$. On the other hand, the percentage of the population that remains prone to infection during the endemic equilibrium is $\frac{1}{{R}_{0}}$.

_{0}is not a biological constant for a pathogen, as it is also influenced by other factors, such as environmental conditions and the behavior of the infected population. In addition, R

_{0}does not in itself assess how quickly an infection is spreading in the population but should be considered in a broader research horizon. In addition, the estimated values of R

_{0}depend on the model used and the values of other parameters, which suggests that the estimated values only make sense in the given space-time frame, and it is recommended not to use outdated values or to compare values based on different models [32].

#### 3.2.2. Effective Reproduction Number (R_{t})

_{0}to R

_{t}. This indicator expresses the number of people who can infect a case based on the restrictions imposed by the implementation of these restrictive measures [6,27,32].

_{t}< 1, as this indicates that control of the epidemic has been achieved.

_{t}is extremely important, and its assessment should be updated at regular intervals based on the data collected from epidemiological surveillance (diagnosed cases per day) with the application of an appropriate methodology. In this way, the course of the epidemic and the effectiveness of the measures in real time can be approximated, since there is inevitably a delay from the moment a person becomes infected until he is diagnosed. Consequently, a possible increase in infections today could be reflected in the diagnosed cases of the coming days.

_{t}reduced to low levels, the stopping of the measures may lead to an increase of cases, which is a typical example we have seen in Greece. Therefore, in the phase of gradual phasing out of the measures, the monitoring of R

_{t}is very important as it will allow decisions to be taken for corrective actions if R

_{t}is approaching or exceeding the value of 1.

_{t}index is the input process of the recorded cases. A popular option for distributing these arrivals is to use the Poisson distribution, which is a distinct distribution function that expresses the probability of a given number of events occurring over a fixed period if these events occur by a known means rhythm and are independent of the time from the last case, as in the case under investigation. The Poisson distribution has the parameter λ that indicates the average percentage of infections per day, which are independent of the last time of occurrence of the event, which is interpreted as the probability of occurrence of new cases every day and is given by the following function [26,28]:

_{s}. The distribution of λ on k is called the probability function. The representation of the probability function by determining the number of new cases observed k is calculated from the probability function in a range of values λ.

_{t}|k

_{t}), which parameterizes the relation between the Poisson distribution and the index R

_{t}and is expressed by the following relation [33,34]:

_{t}

_{−1}is the number of new cases observed in time t − 1.

_{t}and specifically as follows (Figure 14):

_{t}. To combine the actual information from the previous days with the current day, Bayes’ theorem is used to inform the hypotheses about the true value of R

_{t}based on the number of new cases reported daily. By this logic, Bayes’ theorem is used as follows:

_{0}), this is reduced to:

_{t}index and the HDI fluctuation over time can be plotted (Figure 16) [35].

_{t}, while expressing the certainty expressed over time, where the interval of the highest density decreases as the daily recorded cases increase. Below is captured each day (row) of the rear distribution that is designed simultaneously. The rear distributions start without much confidence (wide) and gradually become more confident (narrower) for the true value of R

_{t}(Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21).

_{t}for the examined countries and the probabilities related to the mentioned index (Figure 23 and Figure 24) [6,11,33].

#### 3.2.3. Case Fatality Rate (CFR)

#### 3.2.4. Mortality Rate (MR)

#### 3.2.5. Recovery Rate (RR) or Discharge Rate (DR)

#### 3.2.6. Infection Rate (IR)

_{1}is the time of the first measurement, t

_{2}is the time of the second measurement, x

_{1}is the proportion of infection measured at time t

_{1}, and x

_{2}is the proportion of infection measured at time t

_{2}. The values for the maximum infection rate of the study countries are presented in the Table 6 below [6,28,32,33].

#### 3.2.7. Prevalence

## 4. Prediction Model

- $g\left(t\right)$, trend models non-periodic changes (i.e., growth over time)
- $s\left(t\right)$, seasonality presents periodic changes (i.e., weekly, monthly, yearly)
- $h\left(t\right)$, ties in effects of holidays (on potentially irregular schedules ≥1 day(s))
- $e\left(t\right)$, covers idiosyncratic changes not accommodated by the model

## 5. Data and Results

## 6. Discussion and Conclusions

- Prophet makes it much more straightforward to create a reasonable, accurate forecast. The forecast package includes many different forecasting techniques (ARIMA, exponential smoothing, etc.), each with its own strengths, weaknesses, and tuning parameters. We have found that choosing the wrong model or parameters can often yield poor results, and it is unlikely that even experienced analysts can choose the correct model and parameters efficiently given this array of choices.
- Prophet forecasts are customizable in ways that are intuitive to non-experts. There are smoothing parameters for seasonality that allow us to adjust how close to fit historical cycles, as well as smoothing parameters for trends that allow us to adjust how aggressively to follow historical trend changes. For growth curves, we can manually specify “capacities” or the upper limit of the growth curve, allowing us to inject our own prior information about how the forecast will grow (or decline). Finally, we can specify irregular holidays to model such as the dates of the local holidays, etc.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Total Cases | New Cases | Total Deaths | Reproduction Rate | Weekly ICU Admissions | |
---|---|---|---|---|---|

mean | 109,424.8912 | 872.9142259 | 3475.760776 | 1.074684096 | 112.8019394 |

std | 131,362.2468 | 1008.649671 | 4084.12127 | 0.21673656 | 119.1627889 |

min | 1 | 0 | 1 | 0.69 | 1.945 |

max | 417,253 | 4322 | 12,488 | 1.58 | 382.165 |

New Tests | Total Tests | Total Tests/1000 | New Tests/1000 | Positive Rate | Tests Per Case | |
---|---|---|---|---|---|---|

mean | 23,151.10644 | 3,056,182.995 | 293.2137222 | 2.221138614 | 0.034083871 | 84.47204301 |

std | 21,782.07213 | 3,037,565.947 | 291.4275674 | 2.089800416 | 0.025939906 | 122.2038529 |

min | 45,335 | 570 | 0.055 | −4.349 | 0.001 | 9.5 |

max | 130,207 | 10,207,626 | 979.331 | 12.492 | 0.105 | 768.2 |

Total Vaccinations | People Vaccinated | People Fully Vaccinated | New Vaccinations | Total Vaccinations/1000 | |
---|---|---|---|---|---|

mean | 220,830,6.81 | 1,455,548.608 | 887,829.8134 | 47,651.25564 | 21.18607843 |

std | 212,368,4.319 | 1,346,725.121 | 826,843.6484 | 36,188.52581 | 20.37470194 |

min | 447 | 447 | 2 | 147 | 0 |

max | 7,244,517 | 4,381,177 | 3,045,889 | 114,676 | 69.5 |

People Vaccinated/1000 | People Fully Vaccinated/1000 | Stringency Index | Hospital Beds/1000 | % Death/Cases | |
---|---|---|---|---|---|

mean | 13.96457516 | 8.518432836 | 68.39331197 | 4.21 | 3.385838864 |

std | 12.92053129 | 7.932278859 | 16.53239424 | 2.49 × 10^{−14} | 1.412956795 |

min | 0 | 0 | 11.11 | 4.21 | 0 |

max | 42.03 | 29.22 | 88.89 | 4.21 | 6.134338588 |

ID | Country | Most Likely | Low R_{t} | Max R_{t} |
---|---|---|---|---|

1 | Albania | 0.83 | 0.65 | 1.61 |

2 | Bulgaria | 0.89 | 0.61 | 1.16 |

3 | Greece | 0.74 | 0.62 | 0.84 |

4 | North Macedonia | 0.97 | 0.28 | 1.68 |

5 | Turkey | 0.98 | 0.68 | 1.94 |

ID | Country | Max IR |
---|---|---|

1 | Albania | 1239.0 |

2 | Bulgaria | 4828.0 |

3 | Greece | 3316.0 |

4 | North Macedonia | 1402.0 |

5 | Turkey | 82,325.0 |

Prophet | R^{2} | RMSE | MAE | MAPE |

99,998 | 2.259 | 1.357 | 0.179 |

Date | Forecasted | Trend | |||||
---|---|---|---|---|---|---|---|

Value | High | Low | Yearly | Quarterly | Monthly | Weekly | |

1/6/2021 | 404,185 | 405,914 | 405,495 | 0.15301 | 0.03672 | 0.00013 | −0.00131 |

2/6/2021 | 405,563 | 406,259 | 406,069 | 0.15132 | 0.03662 | −0.00017 | 0.0003 |

3/6/2021 | 406,241 | 408,937 | 407,573 | 0.14958 | 0.03626 | −0.00057 | 0.00174 |

4/6/2021 | 407,386 | 409,059 | 407,990 | 0.14776 | 0.03572 | −0.00083 | 0.0022 |

5/6/2021 | 408,414 | 410,570 | 408,029 | 0.14586 | 0.03505 | −0.00073 | 0.00216 |

6/6/2021 | 409,442 | 411,155 | 409,148 | 0.14387 | 0.0343 | −0.00029 | −0.0013 |

7/6/2021 | 410,470 | 412,972 | 410,067 | 0.14178 | 0.03347 | 0.00031 | −0.00379 |

8/6/2021 | 411,498 | 413,968 | 411,286 | 0.13959 | 0.03254 | 0.00076 | −0.00131 |

9/6/2021 | 412,526 | 415,169 | 412,305 | 0.13729 | 0.03145 | 0.00093 | 0.0003 |

10/6/2021 | 413,554 | 416,370 | 413,124 | 0.1349 | 0.03016 | 0.0009 | 0.00174 |

11/6/2021 | 414,582 | 417,570 | 413,943 | 0.13241 | 0.02866 | 0.00082 | 0.0022 |

12/6/2021 | 415,610 | 418,771 | 414,762 | 0.12982 | 0.02697 | 0.00071 | 0.00216 |

13/6/2021 | 416,638 | 419,972 | 415,581 | 0.12714 | 0.02517 | 0.00052 | −0.0013 |

14/6/2021 | 417,666 | 421,173 | 416,400 | 0.12438 | 0.02337 | 0.00029 | −0.00379 |

15/6/2021 | 418,694 | 422,374 | 417,219 | 0.12155 | 0.0217 | 0.00021 | −0.00131 |

16/6/2021 | 419,722 | 423,575 | 418,038 | 0.11864 | 0.02028 | 0.00037 | 0.0003 |

17/6/2021 | 420,750 | 424,776 | 418,857 | 0.11566 | 0.01915 | 0.00061 | 0.00174 |

18/6/2021 | 421,778 | 425,977 | 419,676 | 0.11262 | 0.0183 | 0.0006 | 0.0022 |

19/6/2021 | 422,806 | 427,178 | 420,495 | 0.10951 | 0.01763 | 0.00024 | 0.00216 |

20/6/2021 | 423,834 | 428,379 | 421,314 | 0.10634 | 0.017 | −0.00018 | −0.0013 |

21/6/2021 | 424,862 | 429,580 | 422,133 | 0.10309 | 0.01624 | −0.00024 | −0.00379 |

22/6/2021 | 425,890 | 430,781 | 422,952 | 0.09975 | 0.01521 | 0.00012 | −0.00131 |

23/6/2021 | 426,918 | 431,982 | 423,771 | 0.09632 | 0.01383 | 0.00046 | 0.0003 |

24/6/2021 | 427,946 | 433,183 | 424,591 | 0.09277 | 0.01213 | 0.00029 | 0.00174 |

25/6/2021 | 428,974 | 434,384 | 425,410 | 0.08909 | 0.01021 | −0.00046 | 0.0022 |

26/6/2021 | 430,002 | 435,584 | 426,229 | 0.08525 | 0.00828 | −0.00129 | 0.00216 |

27/6/2021 | 431,030 | 436,785 | 427,048 | 0.08122 | 0.00652 | −0.00163 | −0.0013 |

28/6/2021 | 432,058 | 437,986 | 427,867 | 0.07697 | 0.00513 | −0.00131 | −0.00379 |

29/6/2021 | 433,086 | 439,187 | 428,686 | 0.07247 | 0.00418 | −0.00062 | −0.00131 |

30/6/2021 | 434,114 | 440,388 | 429,505 | 0.06767 | 0.00367 | −0.00003 | 0.0003 |

1/7/2021 | 435,142 | 441,589 | 430,324 | 0.06255 | 0.00345 | 0.00017 | 0.00174 |

2/7/2021 | 436,170 | 442,790 | 431,143 | 0.05707 | 0.00328 | −0.00001 | 0.0022 |

3/7/2021 | 437,198 | 443,991 | 431,962 | 0.05118 | 0.00291 | −0.0004 | 0.00216 |

4/7/2021 | 438,226 | 445,192 | 432,781 | 0.04485 | 0.00208 | −0.00075 | −0.0013 |

5/7/2021 | 439,254 | 446,393 | 433,600 | 0.03806 | 0.00062 | −0.00082 | −0.00379 |

6/7/2021 | 440,282 | 447,594 | 434,419 | 0.03076 | −0.00152 | −0.00052 | −0.00131 |

7/7/2021 | 441,310 | 448,795 | 435,238 | 0.02293 | −0.00428 | 0.00005 | 0.0003 |

8/7/2021 | 442,338 | 449,996 | 436,057 | 0.01455 | −0.00747 | 0.0006 | 0.00174 |

9/7/2021 | 443,366 | 451,197 | 436,876 | 0.00562 | −0.01084 | 0.00089 | 0.0022 |

10/7/2021 | 444,394 | 452,397 | 437,695 | −0.00388 | −0.01417 | 0.00093 | 0.00216 |

11/7/2021 | 445,422 | 453,598 | 438,514 | −0.01395 | −0.01725 | 0.00086 | −0.0013 |

12/7/2021 | 446,450 | 454,799 | 439,333 | −0.02458 | −0.01999 | 0.00077 | −0.00379 |

13/7/2021 | 447,478 | 456,000 | 440,152 | −0.03574 | −0.0224 | 0.00062 | −0.00131 |

14/7/2021 | 448,506 | 457,201 | 440,971 | −0.04741 | −0.02457 | 0.00039 | 0.0003 |

15/7/2021 | 449,534 | 458,402 | 441,790 | −0.05955 | −0.02664 | 0.00022 | 0.00174 |

16/7/2021 | 450,562 | 459,603 | 442,609 | −0.07211 | −0.02873 | 0.00027 | 0.0022 |

17/7/2021 | 451,590 | 460,804 | 443,428 | −0.08505 | −0.03094 | 0.00051 | 0.00216 |

18/7/2021 | 452,618 | 462,005 | 444,247 | −0.09829 | −0.03325 | 0.00065 | −0.0013 |

19/7/2021 | 453,646 | 463,206 | 445,066 | −0.11176 | −0.03558 | 0.00043 | −0.00379 |

20/7/2021 | 454,674 | 464,407 | 445,885 | −0.12538 | −0.03778 | −0.00002 | −0.00131 |

21/7/2021 | 455,702 | 465,608 | 446,704 | −0.13907 | −0.03968 | −0.00027 | 0.0003 |

22/7/2021 | 456,730 | 466,809 | 447,523 | −0.15275 | −0.04115 | −0.00007 | 0.00174 |

23/7/2021 | 457,758 | 468,010 | 448,342 | −0.16631 | −0.04211 | 0.00035 | 0.0022 |

24/7/2021 | 458,786 | 469,211 | 449,161 | −0.17967 | −0.04256 | 0.00044 | 0.00216 |

25/7/2021 | 459,814 | 470,411 | 449,980 | −0.19274 | −0.04263 | −0.00008 | −0.0013 |

26/7/2021 | 460,842 | 471,612 | 450,799 | −0.20541 | −0.04247 | −0.00095 | −0.00379 |

27/7/2021 | 461,870 | 472,813 | 451,618 | −0.21761 | −0.04226 | −0.00157 | −0.00131 |

28/7/2021 | 462,898 | 474,014 | 452,437 | −0.22924 | −0.04212 | −0.00152 | 0.0003 |

29/7/2021 | 463,926 | 475,215 | 453,256 | −0.24023 | −0.04212 | −0.00094 | 0.00174 |

30/7/2021 | 464,954 | 476,416 | 454,075 | −0.25052 | −0.0422 | −0.00026 | 0.0022 |

31/7/2021 | 465,982 | 477,617 | 454,894 | −0.26003 | −0.04222 | 0.00014 | 0.00216 |

1/8/2021 | 467,010 | 478,818 | 455,713 | −0.26872 | −0.04198 | 0.00011 | −0.0013 |

2/8/2021 | 468,039 | 480,019 | 456,532 | −0.27655 | −0.04124 | −0.00022 | −0.00379 |

3/8/2021 | 469,067 | 481,220 | 457,351 | −0.2835 | −0.03981 | −0.00062 | −0.00131 |

4/8/2021 | 470,095 | 482,421 | 458,171 | −0.28955 | −0.03757 | −0.00084 | 0.0003 |

5/8/2021 | 471,123 | 483,622 | 458,990 | −0.29469 | −0.03452 | −0.00069 | 0.00174 |

6/8/2021 | 472,151 | 484,823 | 459,809 | −0.29894 | −0.03074 | −0.00021 | 0.0022 |

7/8/2021 | 473,179 | 486,024 | 460,628 | −0.30233 | −0.0264 | 0.00038 | 0.00216 |

8/8/2021 | 474,207 | 487,224 | 461,447 | −0.30489 | −0.02173 | 0.0008 | −0.0013 |

9/8/2021 | 475,235 | 488,425 | 462,266 | −0.30667 | −0.01694 | 0.00094 | −0.00379 |

10/8/2021 | 476,263 | 489,626 | 463,085 | −0.30773 | −0.01222 | 0.00089 | −0.00131 |

11/8/2021 | 477,291 | 490,827 | 463,904 | −0.30814 | −0.00768 | 0.00081 | 0.0003 |

12/8/2021 | 478,319 | 492,028 | 464,723 | −0.30798 | −0.0034 | 0.00069 | 0.00174 |

13/8/2021 | 479,347 | 493,229 | 465,542 | −0.30734 | 0.00061 | 0.00049 | 0.0022 |

14/8/2021 | 480,375 | 494,430 | 466,361 | −0.30629 | 0.00437 | 0.00027 | 0.00216 |

15/8/2021 | 481,403 | 495,631 | 467,180 | −0.30494 | 0.00792 | 0.00021 | −0.0013 |

16/8/2021 | 482,431 | 496,832 | 467,999 | −0.30337 | 0.01126 | 0.0004 | −0.00379 |

17/8/2021 | 483,459 | 498,033 | 468,818 | −0.30169 | 0.0144 | 0.00063 | −0.00131 |

18/8/2021 | 484,487 | 499,234 | 469,637 | −0.29997 | 0.01731 | 0.00057 | 0.0003 |

19/8/2021 | 485,515 | 500,435 | 470,456 | −0.29831 | 0.01997 | 0.00018 | 0.00174 |

20/8/2021 | 486,543 | 501,636 | 471,275 | −0.29679 | 0.02236 | −0.00021 | 0.0022 |

21/8/2021 | 487,571 | 502,837 | 472,094 | −0.29549 | 0.02449 | −0.00021 | 0.00216 |

22/8/2021 | 488,599 | 504,037 | 472,913 | −0.29445 | 0.02639 | 0.00017 | −0.0013 |

23/8/2021 | 489,627 | 505,238 | 473,732 | −0.29374 | 0.0281 | 0.00047 | −0.00379 |

24/8/2021 | 490,655 | 506,439 | 474,551 | −0.2934 | 0.02967 | 0.00022 | −0.00131 |

25/8/2021 | 491,683 | 507,640 | 475,370 | −0.29346 | 0.03115 | −0.00057 | 0.0003 |

26/8/2021 | 492,711 | 508,841 | 476,189 | −0.29394 | 0.03253 | −0.00137 | 0.00174 |

27/8/2021 | 493,739 | 510,042 | 477,008 | −0.29484 | 0.0338 | −0.00163 | 0.0022 |

28/8/2021 | 494,767 | 511,243 | 477,827 | −0.29616 | 0.03491 | −0.00124 | 0.00216 |

29/8/2021 | 495,795 | 512,444 | 478,646 | −0.29788 | 0.03579 | −0.00054 | −0.0013 |

30/8/2021 | 496,823 | 513,645 | 479,465 | −0.29996 | 0.0364 | 0.00002 | −0.00379 |

31/8/2021 | 497,851 | 514,846 | 480,284 | −0.30237 | 0.03669 | 0.00017 | −0.00131 |

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## Share and Cite

**MDPI and ACS Style**

Demertzis, K.; Taketzis, D.; Tsiotas, D.; Magafas, L.; Iliadis, L.; Kikiras, P. Pandemic Analytics by Advanced Machine Learning for Improved Decision Making of COVID-19 Crisis. *Processes* **2021**, *9*, 1267.
https://doi.org/10.3390/pr9081267

**AMA Style**

Demertzis K, Taketzis D, Tsiotas D, Magafas L, Iliadis L, Kikiras P. Pandemic Analytics by Advanced Machine Learning for Improved Decision Making of COVID-19 Crisis. *Processes*. 2021; 9(8):1267.
https://doi.org/10.3390/pr9081267

**Chicago/Turabian Style**

Demertzis, Konstantinos, Dimitrios Taketzis, Dimitrios Tsiotas, Lykourgos Magafas, Lazaros Iliadis, and Panayotis Kikiras. 2021. "Pandemic Analytics by Advanced Machine Learning for Improved Decision Making of COVID-19 Crisis" *Processes* 9, no. 8: 1267.
https://doi.org/10.3390/pr9081267