# Models for COVID-19 Daily Confirmed Cases in Different Countries

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## Abstract

**:**

## 1. Introduction

- -
- First category: countries in which coronavirus wave takes low transmission about two-year seasons (about 180 days) to make a complete virus cycle: (case study of Saudi Arabia and Egypt).
- -
- Second category: countries with higher transmission rates with one-year season (about 90 days) to make complete virus cycle. These countries take offline periods with low spreading rate before entering the next wave cycle: (case study of United Kingdom, Germany and Italy).
- -
- The third category: countries with the highest transmission rates with one-year season (about 90 days) to make complete cycle and without offline periods (consecutive waves): (case study of United States of America and Russia).

## 2. Predictive Mathematical Modelling

#### 2.1. Fourier Fitting Models

#### 2.2. Sum of Sine-Waves Fitting Models

## 3. Invasive Weed Optimization Algorithm

- -
- Populations Initialization: populations (seeds) with finite numbers are being scattered over d-dimensional searching space at random positions. The variable d is the number of the optimization process variables.
- -
- Seeds Reproduction: seeds grow to form plants and produce newer number of seeds.
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- Spatial Dispersal: The new seeds are being randomly scattered over the search space using standard normal distribution functions with variable variance. The standard deviation ($\sigma $) of the normal random functions will be produced with initial value (${\sigma}_{initial}$) and final value (${\sigma}_{final}$) in all steps. During simulation, a nonlinear alteration- modulation index ($s$) is selected to reach certain satisfactory performance. Standard deviation (${\sigma}_{iter}$) at each iteration ($iter$) is calculated, where $ite{r}_{\mathrm{max}}$ is the maximum number of iterations.$${\sigma}_{iter}=\frac{{(ite{r}_{\mathrm{max}}-iter)}^{s}}{{(ite{r}_{\mathrm{max}})}^{s}}({\sigma}_{initial}-{\sigma}_{final})+{\sigma}_{final}$$
- -
- Competitive Exclusion: In this process and after maximum number of plants is reached, only the plants with lower fitness can pull out and produce seeds, others are being tossed out. The process continues in each iteration till maximum iterations is reached. Flow chart of the algorithm is as indicated in Figure 1.

- First category countries: these countries have low virus transmission rates and large wave time period, so the next upcoming wave peak will not exceed the first wave peak.
- Second category countries: these countries have medium transmission rates and will have two consecutive waves and with peaks multiples of the first wave peak but not out of control.
- Third category: these countries have the high transmission rates, so the next wave will have increased consecutive peaks and virus spread will be out of control without any limitations.

## 4. Results and Discussion

#### 4.1. First Category Countries

#### 4.2. Second Category Countries

^{2}, SSE, and RMSE indices. As indicated in Figure 3c, the first model describes the best scenario for Germany with reached second wave peak in day 272 (27 November 2020) and the value equals 24,100 persons then daily confirmed cases starts to decrease again. The third wave of the virus will have a peak in day 377 (17 March 2021) but with smaller value than second wave peak where it only equals 4392 cases. Second and third fitting models admitted the same scenario about the second wave peak with same daily confirmed cases and in same day. Both models predict that it will be in day 279 (3 December 2021) with daily confirmed cases equals 26,800 persons. The third wave predicted peak time of action is different when comparing model two and model three. Model two predicts that it will be in day 365 (5 March 2021) with daily confirmed cases equals 22,590 persons.

#### 4.3. Third Category Countries

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Curve fitting models for daily confirmed cases for first category countries: (

**a**) curve fitting models for Egypt data; (

**b**) curve fitting models for Saudi Arabia data.

**Figure 3.**Curve fitting models for daily confirmed cases for second category countries: (

**a**) curve fitting models for United Kingdom data; (

**b**) curve fitting models for Italy data; (

**c**) curve fitting models for Germany data.

**Figure 4.**Curve fitting models for daily confirmed cases for third category countries: (

**a**) Curve fitting models for U.S.A. data; (

**b**) Curve fitting models for Russia data.

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | ||||||
---|---|---|---|---|---|---|---|---|

$\sum _{i=1}^{i=4}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=7}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=8}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | ||||||

${a}_{1}=543.8$ | ${b}_{1}=0.00356$ | ${c}_{1}=0.8723$ | ${a}_{1}=663.1$ | ${b}_{1}=0.00854$ | ${c}_{1}=0.0381$ | ${a}_{1}=673.9$ | ${b}_{1}=0.0101$ | ${c}_{1}=-0.1441$ |

${a}_{2}=306.8$ | ${b}_{2}=0.06305$ | ${c}_{2}=0.8165$ | ${a}_{2}=369.2$ | ${b}_{2}=0.03404$ | ${c}_{2}=3.668$ | ${a}_{2}=288.3$ | ${b}_{2}=0.03923$ | ${c}_{2}=3.149$ |

${a}_{3}=631.8$ | ${b}_{3}=0.03121$ | ${c}_{3}=-1.853$ | ${a}_{3}=385.4$ | ${b}_{3}=0.02492$ | ${c}_{3}=-0.2774$ | ${a}_{3}=431.8$ | ${b}_{3}=0.02371$ | ${c}_{3}=-0.3358$ |

${a}_{4}=106.8$ | ${b}_{4}=0.09438$ | ${c}_{4}=-2.892$ | ${a}_{4}=321.5$ | ${b}_{4}=0.06116$ | ${c}_{4}=1.082$ | ${a}_{4}=293.1$ | ${b}_{4}=0.06203$ | ${c}_{4}=1.015$ |

${a}_{5}=114.4$ | ${b}_{5}=0.09294$ | ${c}_{5}=3.516$ | ${a}_{5}=113.4$ | ${b}_{5}=0.09291$ | ${c}_{5}=3.497$ | |||

${a}_{6}=33.39$ | ${b}_{6}=0.5596$ | ${c}_{6}=0.2357$ | ${a}_{6}=33.35$ | ${b}_{6}=0.5598$ | ${c}_{6}=0.2219$ | |||

${a}_{7}=31.15$ | ${b}_{7}=1.994$ | ${c}_{7}=-2.128$ | ${a}_{7}=32.54$ | ${b}_{7}=1.998$ | ${c}_{7}=-2.509$ | |||

${a}_{8}=30.74$ | ${b}_{8}=1.969$ | ${c}_{8}=0.1529$ | ||||||

SSE = 4.003 × 10^{6}, RMSE = 127.3, R^{2}= 0.9358 | SSE = 3.742 × 10^{6}, RMSE = 125.4, R^{2}= 0.94 | SSE = 3.629 × 10^{6}, RMSE = 124.3, R^{2} = 0.9418 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | |||
---|---|---|---|---|---|

${a}_{0}+{\displaystyle \sum _{i=1}^{i=6}{a}_{i}\mathrm{cos}(iwx)+{b}_{i}\mathrm{sin}(iwx)}$ | ${a}_{0}+{\displaystyle \sum _{i=1}^{i=7}{a}_{i}\mathrm{cos}(iwx)+{b}_{i}\mathrm{sin}(iwx)}$ | ${a}_{0}+{\displaystyle \sum _{i=1}^{i=8}{a}_{i}\mathrm{cos}(iwx)+{b}_{i}\mathrm{sin}(iwx)}$ | |||

${a}_{0}=1305$ | $w=0.02314$ | ${a}_{0}=1395$ | $w=0.02422$ | ${a}_{0}=1497$ | $w=0.02714$ |

${a}_{1}=-1405$ | ${b}_{1}=578.3$ | ${a}_{1}=-1473$ | ${b}_{1}=415$ | ${a}_{1}=-1558$ | ${b}_{1}=-61.53$ |

${a}_{2}=247.7$ | ${b}_{2}=-545.8$ | ${a}_{2}=350.8$ | ${b}_{2}=-440.2$ | ${a}_{2}=430.1$ | ${b}_{2}=-93.8$ |

${a}_{3}=-90.21$ | ${b}_{3}=128.1$ | ${a}_{3}=-140.8$ | ${b}_{3}=72.92$ | ${a}_{3}=-183.3$ | ${b}_{3}=-129$ |

${a}_{4}=46.91$ | ${b}_{4}=-243.9$ | ${a}_{4}=175.7$ | ${b}_{4}=-208.7$ | ${a}_{4}=239.6$ | ${b}_{4}=117.2$ |

${a}_{5}=50.73$ | ${b}_{5}=176.5$ | ${a}_{5}=-35.92$ | ${b}_{5}=159.7$ | ${a}_{5}=-140.5$ | ${b}_{5}=-6.673$ |

${a}_{6}=-118.4$ | ${b}_{6}=-37.12$ | ${a}_{6}=-62.3$ | ${b}_{6}=-48.45$ | ${a}_{6}=42.76$ | ${b}_{6}=-82.72$ |

${a}_{7}=80.02$ | ${b}_{7}=578.3$ | ${a}_{7}=-34.32$ | ${b}_{7}=108.2$ | ||

${a}_{8}=-25.43$ | ${b}_{8}=-146.6$ | ||||

SSE = 2.213 × 10^{7}, RMSE = 300.5, R^{2} = 0.9425 | SSE = 2.115 × 10^{7}, RMSE = 295, R^{2} = 0.945 | SSE = 1.903 × 10^{7}, RMSE = 281, R^{2} = 0.9505 |

**Table 3.**Actual vaccinated people in first category countries [14].

Country | Date | Cumulative Cases | Actual Vaccinated | Population | Vaccinated per Cumulative Cases |
---|---|---|---|---|---|

Egypt | 24 February 2021 | 185,334 | 0 | 102,334,403 | 0 |

Saudi Arabia | 5 March 2021 | 379,092 | 1,182,943 | 34,813,867 | 3.120464162 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | ||||||
---|---|---|---|---|---|---|---|---|

$\sum _{i=1}^{i=4}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=5}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=8}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | ||||||

${a}_{1}=12290$ | ${b}_{1}=0.00747$ | ${c}_{1}=-0.542$ | ${a}_{1}=21270$ | ${b}_{1}=0.00953$ | ${c}_{1}=-0.8266$ | ${a}_{1}=22040$ | ${b}_{1}=0.00874$ | ${c}_{1}=-0.7489$ |

${a}_{2}=7628$ | ${b}_{2}=0.02684$ | ${c}_{2}=0.613$ | ${a}_{2}=14400$ | ${b}_{2}=0.02033$ | ${c}_{2}=1.183$ | ${a}_{2}=13930$ | ${b}_{2}=0.01997$ | ${c}_{2}=1.223$ |

${a}_{3}=33830$ | ${b}_{3}=0.0563$ | ${c}_{3}=1.454$ | ${a}_{3}=1385$ | ${b}_{3}=0.05471$ | ${c}_{3}=0.6467$ | ${a}_{3}=1303$ | ${b}_{3}=0.05599$ | ${c}_{3}=0.5582$ |

${a}_{4}=3337$ | ${b}_{4}=0.05711$ | ${c}_{4}=4.554$ | ${a}_{4}=1689$ | ${b}_{4}=0.07899$ | ${c}_{4}=2.187$ | ${a}_{4}=1700$ | ${b}_{4}=0.07788$ | ${c}_{4}=2.315$ |

${a}_{5}=1309$ | ${b}_{5}=0.09304$ | ${c}_{5}=-2.453$ | ${a}_{5}=1261$ | ${b}_{5}=0.09313$ | ${c}_{5}=-2.439$ | |||

${a}_{6}=436.1$ | ${b}_{6}=0.8894$ | ${c}_{6}=1.947$ | ||||||

${a}_{7}=14580$ | ${b}_{7}=0.7912$ | ${c}_{7}=-1.023$ | ||||||

${a}_{8}=14560$ | ${b}_{8}=0.7917$ | ${c}_{8}=2.076$ | ||||||

SSE = 5.684 × 10^{8}, RMSE = 1517, R^{2} = 0.9545 | SSE = 5.194 × 10^{8}, RMSE = 1459, R^{2} = 0.9602 | SSE = 4.368 × 10^{8}, RMSE = 1363, R^{2} = 0.9666 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | ||||||
---|---|---|---|---|---|---|---|---|

$\sum _{i=1}^{i=5}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=6}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=7}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | ||||||

${a}_{1}=20000$ | ${b}_{1}=0.01263$ | ${c}_{1}=-1.266$ | ${a}_{1}=24710$ | ${b}_{1}=0.00923$ | ${c}_{1}=-0.9455$ | ${a}_{1}=27960$ | ${b}_{1}=0.011$ | ${c}_{1}=-1.127$ |

${a}_{2}=16420$ | ${b}_{2}=0.02194$ | ${c}_{2}=0.851$ | ${a}_{2}=16920$ | ${b}_{2}=0.02204$ | ${c}_{2}=0.7784$ | ${a}_{2}=21440$ | ${b}_{2}=0.02024$ | ${c}_{2}=0.9949$ |

${a}_{3}=10400$ | ${b}_{3}=0.0635$ | ${c}_{3}=-1.005$ | ${a}_{3}=4569$ | ${b}_{3}=0.04886$ | ${c}_{3}=0.6835$ | ${a}_{3}=4201$ | ${b}_{3}=0.05069$ | ${c}_{3}=0.4756$ |

${a}_{4}=38770$ | ${b}_{4}=0.07715$ | ${c}_{4}=0.6183$ | ${a}_{4}=2740$ | ${b}_{4}=0.08085$ | ${c}_{4}=0.1128$ | ${a}_{4}=3070$ | ${b}_{4}=0.08125$ | ${c}_{4}=0.09188$ |

${a}_{5}=30890$ | ${b}_{5}=0.07975$ | ${c}_{5}=3.489$ | ${a}_{5}=3000$ | ${b}_{5}=0.09997$ | ${c}_{5}=1.318$ | ${a}_{5}=4634$ | ${b}_{5}=0.1009$ | ${c}_{5}=1.257$ |

${a}_{6}=1660$ | ${b}_{6}=0.1117$ | ${c}_{6}=3.37$ | ${a}_{6}=3061$ | ${b}_{6}=0.108$ | ${c}_{6}=3.757$ | |||

${a}_{7}=632.2$ | ${b}_{7}=0.9004$ | ${c}_{7}=0.8979$ | ||||||

SSE = 4.577 × 10^{8}, RMSE = 1370, R^{2} = 0.9737 | SSE = 4.166 × 10^{8}, RMSE = 1315, R^{2} = 0.976 | SSE = 3.617 × 10^{8}, RMSE = 1233, R^{2} = 0.9792 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | |||||
---|---|---|---|---|---|---|---|

${a}_{0}+{\displaystyle \sum _{i=1}^{i=4}{a}_{i}\mathrm{cos}(iwx)+{b}_{i}\mathrm{sin}(iwx)}$ | $\sum _{i=1}^{i=7}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=8}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | |||||

${a}_{0}=4948$ | $w=0.01832$ | ${a}_{1}=18920$ | ${b}_{1}=0.01002$ | ${c}_{1}=-0.9919$ | ${a}_{1}=14690$ | ${b}_{1}=0.008242$ | ${c}_{1}=-0.7996$ |

${a}_{1}=1713$ | ${b}_{1}=-6890$ | ${a}_{2}=13300$ | ${b}_{2}=0.01918$ | ${c}_{2}=1.135$ | ${a}_{2}=8897$ | ${b}_{2}=0.02222$ | ${c}_{2}=0.7905$ |

${a}_{2}=-5237$ | ${b}_{2}=-1578$ | ${a}_{3}=3520$ | ${b}_{3}=0.05628$ | ${c}_{3}=-0.3835$ | ${a}_{3}=3278$ | ${b}_{3}=0.05336$ | ${c}_{3}=0.01089$ |

${a}_{3}=-3071$ | ${b}_{3}=3513$ | ${a}_{4}=2297$ | ${b}_{4}=0.07041$ | ${c}_{4}=1.044$ | ${a}_{4}=1750$ | ${b}_{4}=0.07153$ | ${c}_{4}=0.9566$ |

${a}_{4}=403.9$ | ${b}_{4}=2153$ | ${a}_{5}=21500$ | ${b}_{5}=0.8897$ | ${c}_{5}=3.178$ | ${a}_{5}=36350$ | ${b}_{5}=0.8895$ | ${c}_{5}=3.185$ |

${a}_{6}=368.3$ | ${b}_{6}=0.9251$ | ${c}_{6}=1.678$ | ${a}_{6}=366.9$ | ${b}_{6}=0.9252$ | ${c}_{6}=1.678$ | ||

${a}_{7}=20950$ | ${b}_{7}=0.8892$ | ${c}_{7}=0.07616$ | ${a}_{7}=36150$ | ${b}_{7}=0.8892$ | ${c}_{7}=0.06693$ | ||

${a}_{8}=483.2$ | ${b}_{8}=0.1485$ | ${c}_{8}=2.758$ | |||||

SSE = 3.535 × 10^{8}, RMSE = 1192, R^{2} = 0.9394 | SSE = 2.321 × 10^{8}, RMSE = 987.4, R^{2} = 0.9602 | SSE = 2.013 × 10^{8}, RMSE = 925.5, R^{2} = 0.9655 |

**Table 7.**Actual vaccinated people in second category countries [14].

Country | Date | Cumulative Cases | Actual Vaccinated | Population | Vaccinated per Cumulative Cases |
---|---|---|---|---|---|

United Kingdom | 4 March 2021 | 4,213,764 | 21,358,815 | 67,886,004 | 5.068820893 |

Italy | 5 March 2021 | 3,023,129 | 3,564,698 | 60,461,828 | 1.179141876 |

Germany | 4 March 2021 | 2,484,306 | 4,736,174 | 83,783,945 | 1.906437452 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | ||||||
---|---|---|---|---|---|---|---|---|

$\sum _{i=1}^{i=5}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=6}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=7}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | ||||||

${a}_{1}=400600$ | ${b}_{1}=0.00321$ | ${c}_{1}=-0.2983$ | ${a}_{1}=452100$ | ${b}_{1}=0.00403$ | ${c}_{1}=-0.4072$ | ${a}_{1}=498600$ | ${b}_{1}=0.00941$ | ${c}_{1}=-1.017$ |

${a}_{2}=96230$ | ${b}_{2}=0.02034$ | ${c}_{2}=0.6373$ | ${a}_{2}=141900$ | ${b}_{2}=0.0178$ | ${c}_{2}=0.9664$ | ${a}_{2}=40820$ | ${b}_{2}=0.01767$ | ${c}_{2}=1.073$ |

${a}_{3}=37820$ | ${b}_{3}=0.04033$ | ${c}_{3}=1.48$ | ${a}_{3}=92600$ | ${b}_{3}=0.03939$ | ${c}_{3}=1.604$ | ${a}_{3}=107900$ | ${b}_{3}=0.03055$ | ${c}_{3}=2.696$ |

${a}_{4}=7571$ | ${b}_{4}=0.08621$ | ${c}_{4}=2.28$ | ${a}_{4}=8093$ | ${b}_{4}=0.08655$ | ${c}_{4}=2.23$ | ${a}_{4}=8886$ | ${b}_{4}=0.08118$ | ${c}_{4}=2.858$ |

${a}_{5}=5684$ | ${b}_{5}=0.9012$ | ${c}_{5}=0.4016$ | ${a}_{5}=5648$ | ${b}_{5}=0.9011$ | ${c}_{5}=0.4179$ | ${a}_{5}=5637$ | ${b}_{5}=0.901$ | ${c}_{5}=0.4269$ |

${a}_{6}=3327$ | ${b}_{6}=0.1378$ | ${c}_{6}=2.088$ | ${a}_{6}=2297$ | ${b}_{6}=0.1451$ | ${c}_{6}=1.196$ | |||

${a}_{7}=2168$ | ${b}_{7}=0.1231$ | ${c}_{7}=2.613$ | ||||||

SSE = 1.022 × 10^{10}, RMSE = 6473, R^{2} = 0.9457 | SSE = 8.741 × 10^{9}, RMSE = 6023, R^{2} = 0.9536 | SSE = 8.248 × 10^{9}, RMSE = 5887, R^{2} = 0.9562 |

Fitting Model 1 | Fitting Model 2 | Fitting Model 3 | ||||||
---|---|---|---|---|---|---|---|---|

$\sum _{i=1}^{i=5}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=7}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | $\sum _{i=1}^{i=8}{a}_{i}\mathrm{sin}({b}_{i}x+{c}_{i})$ | ||||||

${a}_{1}=83530$ | ${b}_{1}=0.00223$ | ${c}_{1}=-0.1837$ | ${a}_{1}=91990$ | ${b}_{1}=0.00264$ | ${c}_{1}=0.2512$ | ${a}_{1}=35880$ | ${b}_{1}=0.00313$ | ${c}_{1}=-0.1839$ |

${a}_{2}=14410$ | ${b}_{2}=0.01383$ | ${c}_{2}=1.518$ | ${a}_{2}=20040$ | ${b}_{2}=0.01428$ | ${c}_{2}=1.382$ | ${a}_{2}=7460$ | ${b}_{2}=0.01973$ | ${c}_{2}=0.7906$ |

${a}_{3}=2341$ | ${b}_{3}=0.03704$ | ${c}_{3}=4.395$ | ${a}_{3}=1405$ | ${b}_{3}=0.04701$ | ${c}_{3}=3.023$ | ${a}_{3}=2006$ | ${b}_{3}=0.04475$ | ${c}_{3}=3.259$ |

${a}_{4}=1536$ | ${b}_{4}=0.08227$ | ${c}_{4}=1.251$ | ${a}_{4}=1874$ | ${b}_{4}=0.08093$ | ${c}_{4}=1.425$ | ${a}_{4}=1455$ | ${b}_{4}=0.07198$ | ${c}_{4}=2.66$ |

${a}_{5}=939.5$ | ${b}_{5}=0.09879$ | ${c}_{5}=1.871$ | ${a}_{5}=1085$ | ${b}_{5}=0.09618$ | ${c}_{5}=2.279$ | ${a}_{5}=549.9$ | ${b}_{5}=0.1076$ | ${c}_{5}=0.3223$ |

${a}_{6}=362.7$ | ${b}_{6}=0.1633$ | ${c}_{6}=3.053$ | ${a}_{6}=320.4$ | ${b}_{6}=0.1634$ | ${c}_{6}=2.919$ | |||

${a}_{7}=308.7$ | ${b}_{7}=0.1987$ | ${c}_{7}=0.3792$ | ${a}_{7}=329.4$ | ${b}_{7}=0.199$ | ${c}_{7}=0.2491$ | |||

${a}_{8}=377.6$ | ${b}_{8}=0.123$ | ${c}_{8}=0.3394$ | ||||||

SSE = 8.804 × 10^{7}, RMSE = 600.7, R^{2} = 0.9872 | SSE = 5.083 × 10^{7}, RMSE = 462.2, R^{2} = 0.9926 | SSE = 4.492 × 10^{7}, RMSE = 437.2, R^{2} = 0.9935 |

**Table 10.**Actual vaccinated people in third category countries [14].

Country | Date | Cumulative Cases | Actual Vaccinated | Population | Vaccinated per Cumulative Cases |
---|---|---|---|---|---|

U.S.A | 5 March 2021 | 28,894,541 | 55,547,697 | 331,002,647 | 1.922428773 |

Russia | 5 March 2021 | 4,252,876 | 4,908,178 | 145,934,460 | 1.154084436 |

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**MDPI and ACS Style**

Ahmed, H.M.; Elbarkouky, R.A.; Omar, O.A.M.; Ragusa, M.A.
Models for COVID-19 Daily Confirmed Cases in Different Countries. *Mathematics* **2021**, *9*, 659.
https://doi.org/10.3390/math9060659

**AMA Style**

Ahmed HM, Elbarkouky RA, Omar OAM, Ragusa MA.
Models for COVID-19 Daily Confirmed Cases in Different Countries. *Mathematics*. 2021; 9(6):659.
https://doi.org/10.3390/math9060659

**Chicago/Turabian Style**

Ahmed, Hamdy M., Reda A. Elbarkouky, Othman A. M. Omar, and Maria Alessandra Ragusa.
2021. "Models for COVID-19 Daily Confirmed Cases in Different Countries" *Mathematics* 9, no. 6: 659.
https://doi.org/10.3390/math9060659