The proposed COCUDE model is trained, tested, validated, and its evaluation results are summarized in this section.
3.1 Results Analysis of CO model
Table.1 presents the results of the AIC, BIC, and AICc metrics. The COCUDE model has been iterated 10 items on each neuron; among that the lowest AIC iterations are finalized for each neuron. The number neuron 6 has the lowest AIC values. Such that the neuron 6 has the lowest AIC, BIC, and AICc values as 1380.5, 1385.5, and 1380.6 respectively. Its values are the lowest as compared to other neuron’s stationary metrics. Therefore its corresponding neuron 6’s dataset has been taken for the future prediction of CO model.
Table.1 Results of AIC, BIC, and AICc Metrics for CO model
Criterion/Neurons
|
AIC
|
BIC
|
AICc
|
2
|
1469.6
|
1477.6
|
1469.9
|
4
|
1483
|
1490.5
|
1483. 3
|
6
|
1380. 5
|
1385.5
|
1380.6
|
8
|
1423.2
|
1425.7
|
1423.3
|
10
|
1425.5
|
1430.5
|
1425.6
|
12
|
1580.2
|
1585.3
|
1580.4
|
14
|
1539.7
|
1544.7
|
1539.8
|
16
|
1520.2
|
1525.2
|
1520.3
|
18
|
1492.1
|
1497.2
|
1492.3
|
20
|
1450.5
|
1455.5
|
1450.6
|
Table.2 gives the performance error metrics such as MSE, RMSE, and MAE metrics resulted by the CO model. Similar to the stationary (AIC, BIC, and AICc) evaluation results, the neuron 6 has the lowest error values as compared to the results of other neurons. The neuron 6 produces the lowest errors as 1.2054, 1.0979, and 1.0693 for the MSE, RMSE, and MAE metrics respectively for the CO model.
Table.2 Performance Error Metrics resulted by CO model
Metrics/Neurons
|
MSE
|
RMSE
|
MAE
|
2
|
3.0678
|
1.7515
|
1.6886
|
4
|
1.5083
|
1.2281
|
1.0957
|
6
|
1.2054
|
1.0979
|
1.0693
|
8
|
1.6661
|
1.2908
|
1.2377
|
10
|
1.5575
|
2.4259
|
2.4088
|
12
|
3.518
|
1.8756
|
1.8016
|
14
|
2.9307
|
1.7119
|
1.6932
|
16
|
6.4948
|
2.5485
|
2.4928
|
18
|
4.6072
|
2.1464
|
1.9652
|
20
|
2.3903
|
1.546
|
1.4190
|
Figure 2 depicts the results of the proposed CO model for the future 90 days from the date of 10th June 2020. The results indicate the prediction of future infections in the state of Tamilnadu, India. The predicted results are validated with the official dataset and results of the CO model had produced very error values as shown in Table.2
3.2 Results Analysis of CU model
Table.3 presents the stationary metrics results such as AIC, BIC, and AICc for the CU model. The CU model has been iterated 10 items on each neuron; among that the lowest AIC iterations are finalized for each neuron. The number neuron 6 has the lowest AIC values. Such that the neuron 6 has the lowest AIC, BIC, and AICc values as 1479.258, 1486.791, and 1479.534 respectively. Its values are the lowest as compared to other neuron’s stationary metrics. Therefore its corresponding neuron 6’s dataset has been taken for the future prediction of the CU model.
Table.3 Results of AIC, BIC, and AICc Metrics for CU model
Criterion/Neurons
|
AIC
|
BIC
|
AICc
|
2
|
1742.149
|
1749.682
|
1742.425
|
4
|
1527.528
|
1535.061
|
1527.804
|
6
|
1479.258
|
1486.791
|
1479.534
|
8
|
1666.517
|
1674.049
|
1666.793
|
10
|
1801.991
|
1809.524
|
1802.267
|
12
|
1608.141
|
1615.673
|
1608.417
|
14
|
1534.959
|
1542.492
|
1535.235
|
16
|
1841.013
|
1848.546
|
1841.289
|
18
|
1791.097
|
1798.63
|
1791.373
|
20
|
1814.488
|
1822.021
|
1814.764
|
Table.4 Performance Error Metrics resulted by CU model
Metrics/Neurons
|
MSE
|
RMSE
|
MAE
|
2
|
6.7617
|
2.6003
|
2.5389
|
4
|
7.9903
|
2.8267
|
2.7624
|
6
|
1.1093
|
1.0532
|
1.0322
|
8
|
3.6793
|
1.9182
|
1.8653
|
10
|
6.7274
|
2.5937
|
2.639
|
12
|
1.1752
|
1.0841
|
1.0823
|
14
|
4.1006
|
2.0167
|
2.0038
|
16
|
3.3806
|
1.8386
|
1.7888
|
18
|
1.3845
|
1.1767
|
1.1232
|
20
|
3.6452
|
1.9092
|
1.8513
|
Table.4 gives the performance error metrics such as MSE, RMSE, and MAE metrics resulted by the CU model. The neuron 6 has the lowest error values as compared to the results of other neurons, as similar to the neuron 6’s lowest AIC, BIC, and AICc evaluation results. The neuron 6 produces the lowest errors as 1.1093, 1.0532, and 1.0322 for the MSE, RMSE, and MAE metrics respectively for the CU model.
Figure 3 depicts the results of the proposed CU model for the future 90 days from the date of 10th June 2020. The results indicate the prediction of future infections in the state of Tamilnadu, India. The predicted results are validated with the official dataset and results of the CO model had produced very error values as shown in Table.4
3.3 Results Analysis of the DE model
Table.5 presents the stationary metrics results such as AIC, BIC, and AICc for the DE model. The DE model has been iterated 10 items on each neuron; among that the lowest AIC iterations are finalized for each neuron. The number neuron 12 has the lowest AIC values. Such that the neuron 12 has the lowest AIC, BIC, and AICc values as 585.7667, 593.2993, and 586.0426 respectively. Its values are the lowest as compared to other neuron’s stationary metrics. Therefore its corresponding neuron 12’s dataset has been taken for the future prediction of the DE model.
Table.5 Results of AIC, BIC, and AICc Metrics for DE model
Criterion/Neurons
|
AIC
|
BIC
|
AICc
|
2
|
595.592
|
599.1246
|
594.8678
|
4
|
707.7984
|
712.8201
|
707.9347
|
6
|
743.8817
|
751.4143
|
744.1576
|
8
|
635.7356
|
643.2682
|
636.0114
|
10
|
727.1973
|
734.7299
|
727.4732
|
12
|
585.7667
|
593.2993
|
586.0426
|
14
|
714.9297
|
722.4622
|
715.2055
|
16
|
661.058
|
668.5906
|
661.3338
|
18
|
696.2258
|
703.7584
|
696.5016
|
20
|
687.5292
|
692.5509
|
687.6655
|
Table.6 gives the performance error metrics such as MSE, RMSE, and MAE metrics resulted by the DE model. The neuron 12 has the lowest error values as compared to the results of other neurons, as similar to the neuron 12’s lowest AIC, BIC, and AICc evaluation results. The neuron 12 produces lowest errors as 3.4151, 1.8480, and 1.7925 for the MSE, RMSE, and MAE metrics respectively for the DE model.
Table.6 Performance Error Metrics resulted by DE model
Metrics/Neurons
|
MSE
|
RMSE
|
MAE
|
2
|
4.0340
|
2.0085
|
1.9684
|
4
|
4.1325
|
2.0328
|
2.9889
|
6
|
4.286
|
2.0702
|
2.147
|
8
|
4.7965
|
2.1901
|
2.0969
|
10
|
4.8489
|
2.2020
|
2.1658
|
12
|
3.4151
|
1.8480
|
1.7925
|
14
|
7.1387
|
2.6718
|
2.5672
|
16
|
5.6801
|
2.3833
|
2.3125
|
18
|
4.1346
|
2.0337
|
1.9865
|
20
|
9.4947
|
3.0813
|
3.0175
|
Figure 4 depicts the results of the proposed DE model for the future 90 days from the date of 10th June 2020. The results indicate the prediction of future infections in the state of Tamilnadu, India. The predicted results are validated with the official dataset and results of the CO model had produced very error values as shown in Table.2
3.4 Comparative Analysis of COCUDE model
The future prediction results of the COVID–19 using the COCUDE model is analyzed by using Table.7 and Table.8. Table.7 summarizes the AIC, BIC, and AICc metrics for COCUDE model. In Table.7, the neuron 6 had given the lowest AIC, BIC, and AICc metrics as 1380. 5, 1385.5, and 1380.6 respectively for the CO model; for the CU model its values are 1479.258, 1486.791, and 1479.534 respectively for the neuron 6. Similarly, the neuron 12 had given the lowest AIC, BIC, and AICc metrics as 585.7667, 593.2993, and 586.0426 respectively for the DE model using artificial neural network algorithm.
Table.7 AIC, BIC, and AICc Metrics for COCUDE model
Model
|
Criterion/Neurons
|
AIC
|
BIC
|
AICc
|
CO
|
6
|
1380. 5
|
1385.5
|
1380.6
|
CU
|
6
|
1479.258
|
1486.791
|
1479.534
|
DE
|
12
|
585.7667
|
593.2993
|
586.0426
|
Table.8 summarizes the MSE, RMSE, and MAE metrics for COCUDE model. In Table.7, the neuron 6 had given the lowest MSE, RMSE, and MAE metrics as 1.2054, 1.0979, and 1.0693 respectively for the CO model; for the CU model its values are 1.1093, 1.0532, and 1.0322 respectively for the neuron 6. Similarly, the neuron 12 had given the lowest MSE, RMSE, and MAE metrics as 3.4151, 1.8480, and 1.7925 respectively for the DE model using artificial neural network algorithm.
Table.8 Performance Error Metrics resulted by COCUDE model
Model
|
Metrics/Neurons
|
MSE
|
RMSE
|
MAE
|
CO
|
6
|
1.2054
|
1.0979
|
1.0693
|
CU
|
6
|
1.1093
|
1.0532
|
1.0322
|
DE
|
12
|
3.4151
|
1.8480
|
1.7925
|