After compiling 36 independent variables, we surveyed their effectiveness on the two dependent variables using Adjusted R-Squared. Adj.R2 suggests that how an independent variable effects a dependent variable. Low Adj. R2 implies that the independent variable can't explain the dependent variable significantly, and the opposite is true for high Adj.R2. The results of this survey are demonstrated in Table 2. Accordingly, the impacts of independent variables on the COVID-19 infection and its mortality are very different. We considered the variables which their Adj.R2 were higher than 0/7 as effective ones. Thus, we found out that 20 variables out of the 36 independent variables could explain COVID-19 infection, and 16 variables could explain the mortality of the COVID-19.
Table 2 shows that the variables including having a large number of men, having a large population, lack of specialist doctors, lack of hospital, having a large urban population, having a large number of people aged 65 or older individuals, and high natural mortality rate had the most prominent impact on the COVID-19 infection increasing rate, respectively. On the other hand, increasing temperature average, increasing unemployment rate, increasing slope average, increasing number of economically active people, increasing altitude average, and increasing rainfall average had the least impact on the COIVID-19 infection increasing rate, respectively. However, the examination of the impact of independent variables on the mortality rate of the COVID-19 revealed some conflicting results; so that lack of ICU beds, low number of insured people, lack of subspecialist physicians, and lack of hospital beds had the most prominent impact on increasing of COVID-19 mortality; and lack of health houses, increasing intra-provincial travels, increasing altitude average, increasing slope average, increasing rainfall average and having high percent of roads had the least impact on the COIVID-19 infection increasing rate, respectively. Figure 3 shows effective and ineffective independent variables on the infection rate (a) and the mortality of COVID-19 (b).
In addition to examining the Adj.R2, we drew the scatter matrix plot to explore the relationship between independent and dependent variables. The results are similar to those obtained by using the Adj.R2 use. Figure 4 illustrates some of the matrix plots of effective and ineffective variables’.
Table 2
Impacts of independent variables on the COVID-19 infection and its mortality
Category
|
Variable Name
|
Infection
|
Death
|
R2
|
Adj. R2
|
R2
|
Adj. R2
|
Demographic
|
(1)Having a large population
|
0.921601
|
0.918898
|
0.837471
|
0.831867
|
(2)Having a large number of men
|
0.921629
|
0.918926
|
0.836103
|
0.830451
|
(3)Having a large urban population
|
0.903996
|
0.900686
|
0.888763
|
0.884927
|
(4)Having a large number of people aged 65 and over
|
0.901503
|
0.898107
|
0.849336
|
0.844140
|
(5)High natural mortality
|
0.900438
|
0.897005
|
0.805765
|
0.799067
|
Economic
|
(1)Percent of family’s annual income
|
0.265130
|
0.239790
|
0.296421
|
0.272160
|
(2)Percent of economic active people
|
0.004084
|
-0.030258
|
0.041465
|
0.008412
|
(3)Unemployment rate
|
0.005708
|
-0.028578
|
0.010323
|
-0.023804
|
Environmental
|
(1)Having high percent of roads
|
0.081739
|
0.050075
|
0.000115
|
-0.034364
|
(2)Increasing rain Average
|
0.000000
|
-0.034483
|
0.000152
|
-0.034326
|
(3)Increasing temperature Average
|
0.005978
|
-0.028298
|
0.014633
|
-0.019346
|
Health infrastructure
|
(1)Lack of doctors
|
0.858574
|
.853698
|
0.689371
|
0.678659
|
(2) Lack of general practitioner
|
0.426534
|
0.406759
|
0.190749
|
0.162843
|
(3) Lack of specialist practitioner
|
0.909654
|
0.906538
|
0.816437
|
0.810107
|
(4) Lack of subspecialist physician
|
0.857349
|
0.852430
|
0.907467
|
0.904276
|
(5) Lack of paramedics
|
0.705673
|
0.695524
|
0.417355
|
0.397264
|
(6) Lack of nurse
|
0.776071
|
0.768349
|
0.487775
|
0.470112
|
(7) Lack of doctor assistant
|
0.295785
|
0.271502
|
0.155724
|
0.126611
|
(8) Lack of hospital
|
0.904625
|
0.901336
|
0.801735
|
0.794898
|
(9) Lack of hospital’s bed
|
0.892623
|
0.888921
|
0.891791
|
0.888060
|
(10) Lack of ICU’s bed
|
0.860957
|
0.856163
|
0.924012
|
0.921392
|
(11) Lack of medical laboratory
|
0.868171
|
0.863625
|
0.805765
|
0.799067
|
(12) Lack of emergency center
|
0.235739
|
0.209358
|
0.041465
|
0.008412
|
(13) Lack of health care center
|
0.791024
|
0.783817
|
0.516292
|
0.499612
|
(14) Lack of health house
|
0.092374
|
0.061077
|
0.006111
|
-0.028161
|
Social
|
(1)Low number of insured people
|
0.888764
|
0.884928
|
0.913515
|
0.910533
|
(2)High number of doctor consultation
|
0.877923
|
0.873714
|
0.856553
|
0.851606
|
(3)High incoming immigrants rate
|
0.859000
|
0.854138
|
0.852076
|
0.846976
|
(4)High number of annual hospitalization
|
0.835445
|
0.829771
|
0.752567
|
0.744035
|
(5) High number of incoming passengers from the other province
|
0.824903
|
0.818865
|
0.825182
|
0.819152
|
(6) High number of intra-provincial passengers
|
0.132030
|
0.102100
|
0.002833
|
-0.031552
|
(7) High number of supported people by charity organizations
|
0.238306
|
0.212041
|
0.118999
|
0.088620
|
(8)High literacy rate
|
0.123405
|
0.093178
|
0.115002
|
0.084485
|
(9)High age average
|
0.049790
|
0.017024
|
0.056263
|
0.023720
|
Topographic
|
(1)Increasing altitude average
|
0.003649
|
-0.030708
|
0.00083
|
-0.033624
|
(2) Increasing slope average
|
0.004623
|
-0.029700
|
0.000728
|
-0.033730
|
Bold cells are significantly effective on infection and death of COVID-19 |
After investigating the effectiveness of 36 independent variables and detecting the effective ones, we eliminated non-significant variables. In the next step, we aimed to predict the COIVD-19 incidence and mortality in Iran. For this purpose, we needed to solve multiple collinearity problems between independent variables, so we used variance inflation factor (VIF) to examine multiple collinearities between 20 variables for infection and 16 variables for mortality due to COVID-19. We eliminated variables with high VIF one by one until the VIF dropped to 7/5. Finally, only two variables for infection and two variables for mortality of COVID-19 were chosen to be included in the spatial analysis and prediction. Table 3 demonstrates the multiple collinearity analysis results. Accordingly, the value of VIF index is lower than 7/5. The infection variables are high incoming immigrants rate and lack of nurses and for mortality of COVID-19 were high number of doctor consultation and high incoming immigrants rate. Then we found some other important statistical parameters in spatial analysis and prediction by the OLS and GWR models that we that merit mentioning. The coefficient was one of the important parameters representing the strength and type of the relationship between independent and dependent variables. The higher coefficient value, the better the model and the actual fitting effect; and when the coefficient was negative, the relationship is negative and when it is positive, the relationship is positive (Yu et al., 2020); So according to Table 3, the coefficient is a strong significant of both infection rate and the mortality OLS analysis. The second important parameter was the probability or p-value, which must be lower than 0.01 (p < 0.01) to be statistically significant (Mollalo et al., 2020); so, regarding Table 3, all of the variables’ were statistically significant (p < 0.01). However, if the koenker test is statistically significant, we should use the robust probabilities to assess explanatory variable statistical significance; so in our OLS result the koenker test is statistically significant and the robust pr is also statistically significant (p < 0.01). Eventually, according to the results of the OLS, which are shown in Table 3, the statistical parameters were significant.
Table 3
VIF and important statistical parameters
|
Variable
|
Coefficient
|
t-Statistic
|
Probability
|
Robust_Pr
|
VIF
|
Infection
|
Incoming immigrants
|
2618.149701
|
6.292509
|
0.000001*
|
0.000000*
|
2.939438
|
Nurse
|
2172.058404
|
3.816076
|
0.000685*
|
0.001207*
|
2.939438
|
Death
|
Incoming immigrants
|
104.535586
|
2.991613
|
0.005737*
|
0.002231*
|
6.291144
|
Annual doctor’s visit
|
114.499893
|
3.178478
|
0.003596*
|
0.002231*
|
6.291144
|
*An asterisk next to a number indicates a statistically significant |
After examining the statistical accuracy of the selected variables, we performed OLS and GWR models to predict the COVID-19 infection and mortality rates; then we used adjusted-R2 and AICc to compare the performance of both models. The higher adjusted R2 value is, the better the model and the actual fitting effect and the smaller the ACIc value is, the better is the model fitting degree. For more details about adjusted R2 and AIC see Zhang et al., 2020 and Yu et al., 2020. Regarding Table 4, Adj.R2 for infection and death is around 0.9, but for GWR is slightly better than the OLS; also, AICc’s values, for death are lesser than infection; for death analysis, it’s fitter than infection analysis in both models. But the results show that AICc’s values are the same in the OLS and GWR; just for death it is a bit better than in GWR and the opposite for infection. If the difference between AICs is less than around 3, the performance of models is the same (Fotheringham et al., 2002).
Table 4
Comparing OLS and GWR results
Criterion
|
OLS
|
GWR
|
Infection
|
death
|
Infection
|
death
|
Adj. R2
|
0.900617
|
0.883533
|
0.902149
|
0.894194
|
AICC
|
618.817728
|
441.645874
|
620.2046
|
441.28969
|
After examining the models' propriety for predicting COVID-19, we performed GWR and OLS models on the spatial data. As seen in Fig. 5, the dark red areas depict areas where the actual values are higher than where the model predicted. On the contrary, the light blue to dark blue values indicate where the actual values are lower than the model predicted. Figure 5(a) and (b) are respectively the OLS and GWR models’ results in COVID-19 infection that have mostly the same results in different provinces excluding Tehran and Ilam. Regarding Fig. 5 and Table 5, COVID-19 infection will increase in Kerman, Kermanshah, Alborz, Hamedan, Khorasan Jonubi, Khorasan Razavi, Esfahan, and Semnan; On the contrary, it will decrease in Lorestan, Khuzestan, Azarbayjan Shargi, Fars, Golestan, Hormozgan, Kordestan, Mazandaran and Sistan va Baluchestan. However, the degree of fluctuations varies in different provinces. There was not any change in the other provinces, and they will continue the previous process. These results are common to both models. But according to the GWR result, infection in Tehran and Ilam will decrease, while in the OLS result, their infection process won’t change. As seen in Fig. 6 and Table 5, Tehran, Esfahan, Khorasan Razavi, and Fars will have the largest infection contribution, and Khorasan Shomali, Ilam, Golestan, and ChaharmahaloBakhtiari will have the lowest infection contribution.
Mortality due to COVID-19 prediction results is shown in Fig. 7 and Table 5. According to these, mortality will increase in Fars, Khorasan Razavi, Alborz, and Esfahan, and it will decrease in Tehran, Zanjan, Lorestan, Khuzestan, Hormozgan, Golestan, Gilan, Bushehr, and Ardebil. But the intensity of the increase or decrease varies in the different provinces. In some of the provinces, the models’ results are different. But the main difference is in Azarbayjan Gharbi, the OLS predicts it will decrease and GWR predicts it will increase. According to Fig. 8 and Table 5, Tehran, Esfahan, Fars, Khuzestan, Khorasan Shomali, Alborz, and Azarbayjan Shargi will have the largest mortality contribution and Ilam, ChaharmahaloBakhtiari, Kohgiluye va Boyerahmad, and Semnan, will have the lowest COVID-19 mortality contribution.
Table 5
Prediction of COVID-19 infection and mortality due to it at the provincial level
Province Name
|
Infection
|
Death
|
Type Of Change
|
Prediction
|
Type Of Change
|
Prediction
|
OLS
|
GWR
|
OLS
|
GWR
|
OLS
|
GWR
|
OLS
|
GWR
|
Alborz
|
+ 1
|
+ 1
|
19615
|
19015
|
+ 1
|
+ 1
|
1084
|
1126
|
Ardebil
|
0
|
0
|
6564
|
6593
|
-1
|
-1
|
298
|
321
|
Azarbayjan Gharbi
|
0
|
0
|
14640
|
15166
|
-1
|
+ 1
|
687
|
734
|
Azarbayjan Shargi
|
-2
|
-2
|
18905
|
19761
|
0
|
0
|
1314
|
1375
|
Bushehr
|
0
|
0
|
6555
|
6442
|
-1
|
-1
|
245
|
223
|
ChaharmahaloBakhtiari
|
0
|
0
|
5156
|
4945
|
0
|
0
|
194
|
178
|
Esfahan
|
+ 1
|
+ 2
|
33305
|
33418
|
+ 1
|
+ 1
|
1295
|
1282
|
Fars
|
-1
|
-1
|
32428
|
32766
|
+ 2
|
+ 2
|
1304
|
1260
|
Gazvin
|
0
|
0
|
8027
|
7720
|
0
|
0
|
254
|
263
|
Gilan
|
0
|
0
|
16321
|
16460
|
-1
|
-1
|
554
|
584
|
Golestan
|
-1
|
-1
|
4384
|
4367
|
-1
|
-1
|
422
|
401
|
Hamedan
|
+ 1
|
+ 1
|
8560
|
8601
|
0
|
0
|
413
|
441
|
Hormozgan
|
-1
|
-1
|
9548
|
9666
|
-1
|
-1
|
464
|
432
|
Ilam
|
0
|
-1
|
2470
|
2220
|
0
|
0
|
104
|
117
|
Kerman
|
+ 2
|
+ 2
|
13755
|
12824
|
+ 1
|
0
|
712
|
643
|
Kermanshah
|
+ 2
|
+ 2
|
11923
|
12504
|
0
|
0
|
538
|
475
|
Khorasan Jonubi
|
+ 1
|
+ 1
|
5516
|
5124
|
+ 1
|
0
|
306
|
235
|
Khorasan Razavi
|
+ 1
|
+ 1
|
37115
|
33821
|
+ 2
|
+ 2
|
1506
|
1403
|
Khorasan Shomali
|
0
|
0
|
4689
|
4022
|
0
|
0
|
318
|
285
|
Khuzestan
|
-2
|
-2
|
18588
|
19389
|
-1
|
-1
|
1015
|
1094
|
Kohgiluye va Boyerahmad
|
0
|
0
|
5156
|
5094
|
0
|
0
|
141
|
104
|
Kordestan
|
-1
|
-1
|
10235
|
10080
|
0
|
+ 1
|
538
|
578
|
Lorestan
|
-2
|
-2
|
8442
|
8890
|
-1
|
-1
|
282
|
301
|
Markazi
|
0
|
0
|
7161
|
6944
|
0
|
+ 1
|
461
|
489
|
Mazandaran
|
-1
|
-1
|
16618
|
16648
|
0
|
0
|
710
|
747
|
Qom
|
0
|
0
|
6705
|
6405
|
0
|
0
|
321
|
322
|
Semnan
|
+ 1
|
+ 1
|
6463
|
5921
|
+ 1
|
0
|
237
|
170
|
Sistan va Baluchestan
|
-1
|
-1
|
9158
|
8717
|
0
|
-1
|
461
|
404
|
Tehran
|
0
|
-2
|
74614
|
74418
|
-2
|
-2
|
4136
|
4344
|
Yaz
|
0
|
0
|
7526
|
7032
|
0
|
-1
|
398
|
335
|
Zanjan
|
0
|
0
|
5338
|
5174
|
-1
|
-1
|
252
|
272
|
Meaning of type of change’s sign: +2: will increase a lot, + 1: will increase, 0: no change, -1: will decrease, and − 2: will decrease a lot.