Role of children in the Bulgarian COVID-19 epidemic: A mathematical model study

Table 1 Correlations between the variables for Model I – factors contributing to the spread among children

Variables	Variants	Vaccines	Schools L1	Schools L2
Variants	1	0.7877448	-0.4553950	-0.4553950
Vaccines	0.7877448	1	-0.4089070	-0.4502049
Schools L1	0.4553950	-0.4089070	1	-0.4089070
Schools L2	0.4553950	0.4502049	0.8506835	1

Table 2 Regression models with ARIMA (0,1,1) errors - Model I – factors contributing to spread among children

Model summary
Coefficient	Estimate	Standard error
MA1	0.4995	0.1272
Variantsa	71.0883	98.4872
Vaccines L2	191.2172	114.5689
Schools L1	-103.5798	57.1372
Schools L2	-37.4081	56.7021
R2	0.926
RMSE	154.84
Bias	8.79
MAPE	43.35

^aThis variable is not so well estimated because the newest variant has not enough data.

Table 3 Correlations between the variables for Model II

Variables	Variants	Vaccines	0-19 L1	0-19 L2	0-19 L3
Variants	1	0.00	-0.08	0	0.00
Vaccines	0	1	-0.19	-0.13	0.34
0-19 L1	-0.08	-0.19	1	-0.40	-0.04
0-19 L2	0	-0.13	-0.40	1	-0.28
0-19 L3	0.00	0.34	-0.04	-0.28	1

Table 4 Regression models with ARIMA (0,2,1) errors - Model II

Model summary
Coefficient	Estimate	Standard error
MA1	-0.4661	0.1438
Variantsa	147.7111	385.2214
Vaccines	548.6656	412.7460
0-19 L1	1.2614	0.5521
0-19 L2	1.4164	0.5521
0-19 L3	1.1012	0.6543
R2	0.962
RMSE	620.16
Bias	-16.44
MAPE	23.38

^aThis variable is not so well estimated because the newest variant has not enough data.

Table 5 Regression models with ARIMA (0,2,1) errors – Model III

Model summary
Coefficient	Estimate	Standard error
MA1	-0.9502	0.1272
Variantsa	724.0295	641.8759
Vaccines	1095.1284	691.3952
0-19 L1	5.7357	0.0519
0-19 L3	1.9966	0.8769
R2	0.953
RMSE	897.5266
Bias	-72.74389
MAPE	31.96102

^aThis variable is not so well estimated because the newest variant has not enough data.

Table 6 Regression models with ARIMA (0,1,0) errors

Model summary
Coefficient	Estimate	Standard error
NC L21	0.0016	0.0008
NC L22	-0.0011	0.0007
NC L23	1e-04	7e-04
R2	N/A
RMSE	0.8425338
Bias	N/A
MASE	0.4601526

N/A: Not applicable.