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It is now 650 days since the first COVID-19 case was reported in Nigeria. As at December 09, 2021 the confirmed cases are 217,023 with 2,981 (1.38%) fatalities, an average of 5 fatalities per day. However, to date, 207,670 or 96.18% were successfully managed and discharged leaving a balance of 5,257 (2.44%) active cases being managed.

Based on equal days forecast, by September 20, 2023, Nigeria’s aggregate confirmed COVID-19 cases are forecast to be:

Unconstrained forecast of COVID-19 for Nigeria

Model Confirmed cases Recoveries Fatalities Active RMSE
Smooth Spline 4,854,539 4,669,096 66,993 118,451 153
Upper ARIMA 1,668,661 1,604,918 23,028 40,715 135
With knots 1,528,139 1,469,764 21,088 37,287 153
Essembled based on summed weight 921,586 886,381 12,718 22,487 368
Essembled based on weight 569,933 548,162 7,865 13,906 372
Semilog 252,535 242,888 3,485 6,162 135
Essembled with equal weight 246,610 237,189 3,403 6,017 257
Linear 212,351 204,239 2,930 5,181 348
Essembled based on weight of fit 157,764 151,737 2,177 3,849 1.5
Without knots 101,061 97,201 1,395 2,466 352
Growth 3,742 3,599 52 91 161
Quadratic Polynomial -497,456 -478,454 -6,865 -12,138 192
Lower ARIMA -1,095,243 -1,053,405 -15,114 -26,724 129

Constrained forecast of COVID-19 for Nigeria

Model Confirmed cases Recoveries Fatalities Active
ARIMA 95% 1,538,259.0 1,479,498 21,228.0 37,534.0
Essembled based on weight 95% 1,536,917.0 1,478,206 21,209.0 37,501.0
Essembled based on summed weight 95% 1,395,237.0 1,341,939 19,254.0 34,044.0
Essembled with equal weight 95% 933,308.0 897,656 12,880.0 22,773.0
Without knots 95% 912,344.0 877,493 12,590.0 22,261.0
Smooth Spline 95% 740,812.0 712,513 10,223.0 18,076.0
Essembled based on weight of fit 95% 472,981.0 454,913 6,527.0 11,541.0
Semilog 252,535.0 242,888 3,485.0 6,162.0
Linear 212,351.0 204,239 2,930.0 5,181.0
Without knots 80% 83,465.0 80,277 1,152.0 2,037.0
Essembled based on weight 80% 54,600.0 52,514 753.0 1,332.0
Essembled based on weight of fit 80% 36,251.0 34,866 500.0 885.0
Smooth Spline 80% 33,687.0 32,400 465.0 822.0
Essembled based on summed weight 80% 31,486.0 30,283 435.0 768.0
Essembled with equal weight 80% 29,943.0 28,799 413.0 731.0
Growth 3,742.0 3,599 52.0 91.0
ARIMA 80% 2,764.0 2,658 38.0 67.0
Quadratic Polynomial 95% 1,408.0 1,355 19.0 34.0
Quadratic Polynomial 80% 1,277.0 1,228 18.0 31.0
With knots 80% 3.0 3 0.0 0.0
With knots 95% 4.0 3 0.0 0.0

However, the actual forecast made by the various models on the last day i.e. September 20, 2023 is shown below:

Unconstrained forecasts on the last day

Constrained forecasts on the last day

Refer to Table 2 and Table 3 as well as Fig. 18-20 for more details on how the estimates and forecasts were obtained.

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The visuals below supports this facts, take a look!

Fig. 1a Daily observed cases of COVID-19 in Nigeria

Fig. 2 Perecentages and previous days differences of COVID-19 in Nigeria Starting from February 29, 2020 to December 09, 2021

Fig. 3 Cases recorded in percentages Starting from February 29, 2020 to December 09, 2021 (legend as Fig. 2)

Fig. 4 Cumulative cases and Forecast of COVID-19 cases in Nigeria Starting from December 10, 2021 to September 20, 2023

Fig. 4a Components of COVID-19 cases in Nigeria between February 29, 2020 and December 09, 2021

Fig. 5 Number of days since average recorded cases exceeded one in each State

Fig. 6 Daily confirmed Coronavirus cases, by number of the days since 1 first daily case recorded

Fig. 7 Number of days from February 29, 2020 to December 09, 2021 that cases were recorded in the States

Fig. 7a Numbers of States that COVID-19 cases were reported on daily basis

Fig. 7b Forecast of Numbers of States that may still be COVID-19 affected by September 20, 2023

Coefficient estimates for number of states reporting COVID-19 daily

LinearSemilogGrowthSpline without knotsLinear splinesSpline with knotsARIMA
(Intercept)0.381 ****12.420 ****2.566 ****6.244 ****2.831 *   -0.716          
(0.078)    (1.375)    (0.048)    (0.838)    (1.564)    (2.437)         
Series-0.001 ****         -0.000 ***                                 
(0.000)             (0.000)                                    
log(Series)         0.163                                              
         (0.248)                                             
bs(Series, knots = NULL)1                           29.012 ****                       
                           (2.421)                           
bs(Series, knots = NULL)2                           -7.783 ****                       
                           (1.536)                           
bs(Series, knots = NULL)3                           7.050 ****                       
                           (1.323)                           
bs(DDPtable$Series, knots = LBREAKS)1                                    -2.753                   
                                    (2.230)                  
bs(DDPtable$Series, knots = LBREAKS)2                                    13.749 ****              
                                    (1.654)                  
bs(DDPtable$Series, knots = LBREAKS)3                                    22.776 ****              
                                    (1.931)                  
bs(DDPtable$Series, knots = LBREAKS)4                                    -0.814                   
                                    (1.714)                  
bs(DDPtable$Series, knots = LBREAKS)5                                    29.094 ****              
                                    (1.766)                  
bs(DDPtable$Series, knots = LBREAKS)6                                    -3.394 *                 
                                    (1.741)                  
bs(DDPtable$Series, knots = LBREAKS)7                                    3.791 **                
                                    (1.771)                  
bs(DDPtable$Series, knots = LBREAKS)8                                    20.041 ****              
                                    (1.952)                  
bs(DDPtable$Series, knots = LBREAKS)9                                    2.549                   
                                    (2.075)                  
bs(DDPtable$Series, knots = LBREAKS)10                                    6.133 ***               
                                    (1.876)                  
bs(Series, knots = QBREAKS)1                                             7.038 **       
                                             (3.002)         
bs(Series, knots = QBREAKS)2                                             22.684 ****     
                                             (2.574)         
bs(Series, knots = QBREAKS)3                                             16.218 ****     
                                             (2.929)         
bs(Series, knots = QBREAKS)4                                             13.937 ****     
                                             (2.615)         
bs(Series, knots = QBREAKS)5                                             6.376 **       
                                             (2.810)         
bs(Series, knots = QBREAKS)6                                             20.539 ****     
                                             (2.851)         
bs(Series, knots = QBREAKS)7                                             3.627          
                                             (2.909)         
ma1                                                      -0.713 
                                                      (0.039)
ma2                                                      -0.061 
                                                      (0.037)
nobs632         632         632         632         632         632         631     
r.squared0.048     0.001     0.014     0.250     0.746     0.329          
adj.r.squared0.047     -0.001     0.012     0.246     0.742     0.322          
sigma0.976     6.106     0.606     5.298     3.099     5.026     3.188 
statistic32.015     0.431     8.707     69.801     182.591     43.805          
p.value0.000     0.512     0.003     0.000     0.000     0.000          
df1.000     1.000     1.000     3.000     10.000     7.000          
logLik-880.605     -2039.232     -578.768     -1948.514     -1606.133     -1913.137     -1626.371 
AIC1767.211     4084.464     1163.536     3907.029     3236.266     3844.274     3258.742 
BIC1780.557     4097.811     1176.883     3929.273     3289.653     3884.314     3272.084 
deviance600.485     23488.775     231.032     17627.176     5965.286     15760.198          
df.residual630.000     630.000     630.000     628.000     621.000     624.000          
nobs.1632.000     632.000     632.000     632.000     632.000     632.000     631.000 
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.

Properties of the estimated coefficients

Linear Semilog Growth Spline with knots Linear splines Spline without knots Smooth spline ARIMA
Absolute Error 8400 3300 6900 2600 1500 2800 1300 1500
Absolute Percent Error 630 460 490 300 160 350 140 150
Accuracy 0 0 0 0 0 0 0 0
Adjusted R Square 0.047 -0.0009 0.012 0.32 0.74 0.25 0 0
Akaike’s Information Criterion AIC 1800 4100 1200 3800 3200 3900 0 3300
Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) 0 0 0 0 0 0 0 0
Area under the ROC curve (AUC) 0 0 0 0 0 0 0 0
Average Precision at k 0 0 0 0 0 0 0 0
Bias 13 -0.0000000000000003 11 0.000000000000000017 -0.000000000000000048 -0.00000000000000008 0.00000000000000039 0.056
Brier score 200 40 200 20 9 30 8 10
Classification Error 1 1 1 1 1 1 1 1
F1 Score 0 0 0 0 0 0 0 0
fScore 0 0 0 0 0 0 0 0
GINI Coefficient 0.2 -0.2 0.2 0.6 0.9 0.5 0.9 0.9
kappa statistic 0 0 0 0 0 0 0 0
Log Loss Inf Inf Inf Inf Inf Inf Inf Inf
Matthews Correlation Coefficient 0 0 0 0 0 0 0 0
Mean Log Loss 220 -430 -430 -420 -430 -430 -430 -430
Mean Absolute Error 13 5.2 11 4.2 2.3 4.5 2.1 2.4
Mean Absolute Percent Error 1 0.73 0.77 0.48 0.25 0.55 0.22 0.24
Mean Average Precision at k 0 0 0 0 0 0 0.12 0
Mean Absolute Scaled Error 4.7 1.8 3.8 1.5 0.82 1.6 0.74 0.84
Median Absolute Error 13 4.8 11 4 1.9 4.4 1.7 2
Mean Squared Error 210 37 160 25 9.4 28 7.9 10
Mean Squared Log Error 6.9 0.29 2 0.18 0.072 0.21 0.054 0.069
Model turning point error 378 343 378 357 351 361 353 472
Negative Predictive Value 0 0 0 0 0 0 0 0
Percent Bias 1 -0.48 0.73 -0.25 -0.095 -0.32 -0.082 -0.074
Positive Predictive Value 0 0 0 0 0 0 0 0
Precision 0 1 1 1 1 1 1 1
R Square 0.048 0.00068 0.014 0.33 0.75 0.25 0 0
Relative Absolute Error 2.6 1 2.1 0.81 0.45 0.88 0.41 0.47
Recall 0 1 1 0.71 1 1 1 1
Root Mean Squared Error 15 6.1 12 5 3.1 5.3 2.8 3.2
Root Mean Squared Log Error 2.6 0.54 1.4 0.43 0.27 0.45 0.23 0.26
Root Relative Squared Error 2.4 1 2 0.82 0.5 0.87 0.46 0.52
Relative Squared Error 5.7 1 4.2 0.67 0.25 0.75 0.21 0.27
Schwarz’s Bayesian criterion BIC 1800 4100 1200 3900 3300 3900 0 3300
Sensitivity 0 0 0 0 0 0 0 0
specificity 0 0 0 0 0 0 0 0
Squared Error 140000 23000 98000 16000 6000 18000 5000 6400
Squared Log Error 4400 180 1300 120 46 130 34 44
Symmetric Mean Absolute Percentage Error 2 0.43 1.3 0.36 0.22 0.38 0.19 0.22
Sum of Squared Errors 140000 23000 98000 16000 6000 18000 5000 6400
True negative rate 0 0 0 0 0 0 0 0
True positive rate 0 0 0 0 0 0 0 0

Fig. 8 Number of days the last COVID19 case was recorded as at December 09, 2021

Fig. 9 Diverging Bars of COVID-19 cases in the States (normalised)


Fig. 10 Monthly summary of COVID19 cases in the States

Fig. 11 Daily recorded cases of COVID19 in the States

Fig. 12 Number of days since average recorded cases exceeded one in each geo-political zone

Fig. 13 Number of days from February 29, 2020 to December 09, 2021 that cases were recorded in the Zones

Fig. 14 Monthly summary of COVID19 cases in the Zones

Table 1 Regression estimates of factors that might have stressed Nigeria’s economy within the period of the COVID-19 pandemic

COVID19PMSInflationTeledensityBirth ratePopulation
(Intercept)-334.791     -1329.054     -66.147     503.936     -34.481 ****16.027 ****
(244.516)    (1425.368)    (162.838)    (335.082)    (7.975)    (0.322)    
PMSprice-0.136 ****         0.100 ****0.209 ****0.001     0.000     
(0.027)             (0.012)    (0.031)    (0.002)    (0.001)    
Inflation1.170 ****7.941 ****         -1.678 ****-0.031 *   0.004     
(0.256)    (0.991)             (0.337)    (0.015)    (0.006)    
Teledensity0.619 ****3.509 ****-0.353 ****         -0.000     -0.003     
(0.090)    (0.513)    (0.071)             (0.008)    (0.003)    
`Birth rate`1.901     18.438     -6.247 *   -0.074              0.258 ****
(5.388)    (30.343)    (3.082)    (7.486)             (0.053)    
Population16.610     58.933     7.047     -25.055     2.269 ****         
(15.506)    (89.739)    (10.030)    (21.330)    (0.462)             
COVID19         -4.367 ****0.472 ****1.186 ****0.004     0.004     
         (0.878)    (0.103)    (0.173)    (0.011)    (0.004)    
nobs23         23         23         23         23         23         
r.squared0.784     0.901     0.920     0.844     0.710     0.745     
adj.r.squared0.721     0.872     0.896     0.798     0.625     0.671     
sigma1.093     6.200     0.694     1.513     0.049     0.017     
statistic12.374     30.865     38.907     18.392     8.344     9.957     
p.value0.000     0.000     0.000     0.000     0.000     0.000     
df5.000     5.000     5.000     5.000     5.000     5.000     
logLik-31.205     -71.122     -20.763     -38.685     40.196     65.177     
AIC76.410     156.244     55.526     91.371     -66.391     -116.353     
BIC84.358     164.193     63.474     99.319     -58.443     -108.405     
deviance20.309     653.381     8.191     38.922     0.041     0.005     
df.residual17.000     17.000     17.000     17.000     17.000     17.000     
nobs.123.000     23.000     23.000     23.000     23.000     23.000     
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.

Fig. 15 COVID-19, inflation, PMS price, Teledensity and birth rate in Nigeria

Fig. 15 Relationship between COVID-19, inflation, PMS price, Teledensity and birth rate in Nigeria

Table 2 The coefficient estimates of the various models for forecasting of COVID-19 for Nigeria1

LinearSemilogGrowthSpline without knotsSpline with knotsARIMAQuardratic polynomialEssembled based on weightEssembled based on summed weight
(Intercept)337.481 ****34.214     4.736 ****-66.099     -2.728          62.582     31.583    -2.233     
(29.277)    (82.301)    (0.118)    (54.443)    (62.082)         (41.586)    (74.699)   (15.450)    
Day-0.011              0.001 ****                       2.519 ****                 
(0.078)             (0.000)                           (0.295)                     
log(Day)         54.650 ****                                                          
         (14.775)                                                              
bs(Day, knots = NULL)1                           1070.007 ****                                        
                           (157.283)                                            
bs(Day, knots = NULL)2                           276.382 ***                                         
                           (99.761)                                            
bs(Day, knots = NULL)3                           255.215 ***                                         
                           (85.982)                                            
bs(Day, knots = BREAKS)1                                    2.871                                    
                                    (120.017)                                   
bs(Day, knots = BREAKS)2                                    15.242                                    
                                    (77.745)                                   
bs(Day, knots = BREAKS)3                                    840.005 ****                               
                                    (89.121)                                   
bs(Day, knots = BREAKS)4                                    175.388 **                                 
                                    (75.711)                                   
bs(Day, knots = BREAKS)5                                    190.409 **                                 
                                    (82.897)                                   
bs(Day, knots = BREAKS)6                                    -62.942                                    
                                    (77.929)                                   
bs(Day, knots = BREAKS)7                                    2000.928 ****                               
                                    (77.280)                                   
bs(Day, knots = BREAKS)8                                    -205.714 ***                                
                                    (76.814)                                   
bs(Day, knots = BREAKS)9                                    -125.964                                    
                                    (78.242)                                   
bs(Day, knots = BREAKS)10                                    916.743 ****                               
                                    (85.128)                                   
bs(Day, knots = BREAKS)11                                    -92.649                                    
                                    (87.716)                                   
bs(Day, knots = BREAKS)12                                    161.845 **                                 
                                    (80.010)                                   
ar1                                             1.026                           
                                             (0.057)                          
ar2                                             -0.200                           
                                             (0.050)                          
ma1                                             -1.746                           
                                             (0.041)                          
ma2                                             0.818                           
                                             (0.033)                          
I(Day^2)                                                  -0.004 ****                 
                                                  (0.000)                     
fitf                                                           -4.680    -0.107     
                                                           (5.391)   (0.069)    
fit0f                                                           0.882    -0.017     
                                                           (0.700)   (0.108)    
fit1f                                                           -3.008    1.299 ****
                                                           (5.870)   (0.114)    
fitpif                                                           -0.175    0.017     
                                                           (0.704)   (0.115)    
fitaf                                                           4.535    -0.187 **  
                                                           (4.370)   (0.087)    
fitf:fit0f                                                           0.026             
                                                           (0.025)            
fitf:fit1f                                                           0.033 **          
                                                           (0.014)            
fit0f:fit1f                                                           0.002             
                                                           (0.031)            
fitf:fitpif                                                           0.002             
                                                           (0.010)            
fit0f:fitpif                                                           -0.002             
                                                           (0.002)            
fit1f:fitpif                                                           0.013             
                                                           (0.014)            
fitf:fitaf                                                           -0.009             
                                                           (0.022)            
fit0f:fitaf                                                           -0.029             
                                                           (0.020)            
fit1f:fitaf                                                           0.018             
                                                           (0.020)            
fitpif:fitaf                                                           -0.007             
                                                           (0.013)            
fitf:fit0f:fit1f                                                           -0.000 **          
                                                           (0.000)            
fitf:fit0f:fitpif                                                           -0.000             
                                                           (0.000)            
fitf:fit1f:fitpif                                                           -0.000             
                                                           (0.000)            
fit0f:fit1f:fitpif                                                           -0.000             
                                                           (0.000)            
fitf:fit0f:fitaf                                                           -0.000             
                                                           (0.000)            
fitf:fit1f:fitaf                                                           -0.000 **          
                                                           (0.000)            
fit0f:fit1f:fitaf                                                           0.000             
                                                           (0.000)            
fitf:fitpif:fitaf                                                           0.000             
                                                           (0.000)            
fit0f:fitpif:fitaf                                                           0.000             
                                                           (0.000)            
fit1f:fitpif:fitaf                                                           -0.000 **          
                                                           (0.000)            
fitf:fit0f:fit1f:fitpif                                                           0.000 *           
                                                           (0.000)            
fitf:fit0f:fit1f:fitaf                                                           0.000 *           
                                                           (0.000)            
fitf:fit0f:fitpif:fitaf                                                           -0.000             
                                                           (0.000)            
fitf:fit1f:fitpif:fitaf                                                           0.000 ***         
                                                           (0.000)            
fit0f:fit1f:fitpif:fitaf                                                           0.000             
                                                           (0.000)            
fitf:fit0f:fit1f:fitpif:fitaf                                                           -0.000 **          
                                                           (0.000)            
nobs650         650         650         650         650         649     650         650        650         
r.squared0.000     0.021     0.017     0.126     0.813          0.108     0.880    0.869     
adj.r.squared-0.002     0.019     0.015     0.122     0.809          0.105     0.874    0.868     
sigma372.780     368.911     1.500     349.008     162.733     153.382 352.328     132.047    135.258     
statistic0.020     13.681     11.131     31.100     230.292          39.218     146.665    855.652     
p.value0.887     0.000     0.001     0.000     0.000          0.000     0.000    0.000     
df1.000     1.000     1.000     3.000     12.000          2.000     31.000    5.000     
logLik-4769.950     -4763.170     -1184.788     -4726.116     -4225.615     -4185.883 -4732.772     -4079.954    -4108.968     
AIC9545.901     9532.341     2375.576     9462.233     8479.230     8381.766 9473.544     8225.909    8231.935     
BIC9559.332     9545.772     2389.007     9484.617     8541.908     8404.143 9491.452     8373.649    8263.274     
deviance90049085.445     88190001.207     1457.674     78687240.492     16868988.854          80315309.853     10775667.111    11781869.198     
df.residual648.000     648.000     648.000     646.000     637.000          647.000     618.000    644.000     
nobs.1650.000     650.000     650.000     650.000     650.000     649.000 650.000     650.000    650.000     
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.

Table 3 Various selection criteria for the estimated models2

Linears Semilogs Growths Spline with knots Spline without knots Smooth spline ARIMA Quardratic polynomial Essembled equal weight Essembled on weight Essembled summed weight Essembled weight of fit
Absolute Error 180000 170000 210000 69000 170000 50000 58000 170000 220000 49000 50000 220000
Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Accuracy 0 0 0 0 0 0 0 0 0.028 0 0 0.028
Adjusted R Square -0.0015 0.019 0.015 0.81 0.12 0 0 0.11 0 0.87 0.87 0
Akaike’s Information Criterion AIC 9500 9500 2400 8500 9500 0 8400 9500 0 8200 8200 0
Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) 0 0 0 0 0 0 0 0 0 0 0 0
Area under the ROC curve (AUC) 0 0 0 0 0 0 0 0 0 0 0 0
Average Precision at k 0 0 0 0 0 0 0 0 0.5 0 0 0.5
Bias -0.000000000000034 0.0000000000000081 330 0.0000000000000058 -0.0000000000000054 -0.000000000000041 1.6 -0.0000000000000083 330 -0.00000000000000052 -0.0000000000000033 330
Brier score 100000 100000 200000 30000 100000 20000 20000 100000 4000000 20000 20000 200000
Classification Error 1 1 1 1 1 1 1 1 1 1 1 1
F1 Score 0 0 0 0 0 0 0 0 0 0 0 0
fScore 0 0 0 0 0 0 0 0 0 0 0 0
GINI Coefficient 0.007 -0.007 -0.007 0.9 0.4 1 0.9 0.5 0.9 1 1 0.9
kappa statistic 0 0 0 0 0 0 0 0 0 0 0 0
Log Loss Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Matthews Correlation Coefficient 0 0 0 0 0 0 0 0 NaN 0 0 NaN
Mean Log Loss -11000 -11000 -11000 -11000 -11000 -11000 -11000 -11000 NaN -11000 -11000 NaN
Mean Absolute Error 270 270 330 110 250 77 89 260 520 76 78 330
Mean Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Mean Average Precision at k 0 0 0 0 0 0.5 0 0 0 0 0 0
Mean Absolute Scaled Error 2.6 2.6 3.2 1 2.5 0.75 0.86 2.5 3.2 0.74 0.75 3.2
Median Absolute Error 230 220 190 72 220 36 44 220 100 41 38 140
Mean Squared Error 140000 140000 250000 26000 120000 18000 23000 120000 4400000 17000 18000 250000
Mean Squared Log Error 2.8 2.5 13 NaN NaN NaN 0.27 2.2 28 NaN NaN 28
Model turning point error 338 329 329 312 328 310 434 320 390 299 272 390
Negative Predictive Value 0 0 0 0 0 0 0 0 0 0 0 0
Percent Bias -Inf -Inf -Inf NaN NaN NaN -Inf -Inf -Inf NaN NaN -Inf
Positive Predictive Value 0 0 0 0 0 0 0 0 0 0 0 0
Precision 0.1 0.1 0.1 0 0 0.1 0.33 0.1 0 0.071 0.1 0
R Square 0.000031 0.021 0.017 0.81 0.13 0 0 0.11 0 0.88 0.87 0
Relative Absolute Error 1 0.99 1.2 0.39 0.93 0.28 0.33 0.95 0.48 0.28 0.28 0.63
Recall 1 1 1 0 0 0.5 0.5 1 0 0.5 0.5 0
Root Mean Squared Error 370 370 500 160 350 140 150 350 2100 130 130 500
Root Mean Squared Log Error 1.7 1.6 3.6 NaN NaN NaN 0.52 1.5 5.3 NaN NaN 5.3
Root Relative Squared Error 1 0.99 1.3 0.43 0.93 0.36 0.41 0.94 1.3 0.35 0.36 1.3
Relative Squared Error 1 0.98 1.8 0.19 0.87 0.13 0.17 0.89 1.8 0.12 0.13 1.8
Schwarz’s Bayesian criterion BIC 9600 9500 2400 8500 9500 0 8400 9500 0 8400 8300 0
Sensitivity 0 0 0 0 0 0 0 0 0.5 0 0 0.5
specificity 0 0 0 0 0 0 0 0 0 0 0 0
Squared Error 90000000 88000000 160000000 17000000 79000000 12000000 15000000 80000000 160000000 11000000 12000000 160000000
Squared Log Error 1800 1600 8400 NaN NaN NaN 180 1400 18000 NaN NaN 18000
Symmetric Mean Absolute Percentage Error 0.88 0.89 1.8 0.58 0.86 0.35 0.4 0.85 0.59 0.38 0.36 0.68
Sum of Squared Errors 90000000 88000000 160000000 17000000 79000000 12000000 15000000 80000000 160000000 11000000 12000000 160000000
True negative rate 0 0 0 0 0 0 0 0 0 0 0 0
True positive rate 0 0 0 0 0 0 0 0 0 0 0 0

Fig. 18 Models of COVID-19 Cases using ensemble technology

Fig. 19 Equal duration forecast of COVID-19 Cases from the ensemble models using a native plotting method

Fig. 20 Unconstrained forecast of COVID-19 cases in Nigeria Starting from December 10, 2021 to September 20, 2023 using a more advaced plotting method

Fig. 20a Lagged unconstrained forecasts (1-14 days) of COVID-19 cases in Nigeria

Fig. 20b Constrained forecast of COVID-19 cases in Nigeria Starting from December 10, 2021 to September 20, 2023 using a more advaced plotting method

Fig. 20c Constrained forecast of COVID-19 cases in Nigeria Starting from December 10, 2021 to September 20, 2023 using a more advaced plotting method

Fig. 20c Lagged constrained forecasts (1-14 days) of COVID-19 cases in Nigeria

Table 4 Summary of the unconstrained dynamic COVID-19 forecasts
Model Nov 26, 21 - Aug 23, 23 Dec 03, 21 - Sep 06, 23 Dec 06, 21 - Sep 12, 23 Dec 07, 21 - Sep 14, 23 Dec 08, 21 - Sep 16, 23 Dec 09, 21 - Sep 18, 23
Linear 226353 215195 211317 210491 209248 209135
Semilog 272266 269704 251299 251299 268578 251257
Growth 3734 3712 3712 3717 3719 3727
Without knots 116767 61703 49553 50735 47474 56424
Smooth Spline -667898 -95547 248840 426542 532676 798908
With knots -96093 37267 375274 779343 816149 1603264
Quadratic Polynomial -460842 -495668 -506757 -508616 -512052 -511152
Lower ARIMA -1271423 -1294861 -1284740 -1262949 -1265261 -1225385
Upper ARIMA 1368616 1374162 1398026 1424458 1426867 1477453
Essembled with equal weight 44765 41351 68229 73227 95695 119511
Essembled based on weight 392211 344439 317695 189968 278042 221102
Essembled based on summed weight 193754 208355 213571 213119 216448 214618
Essembled based on weight of fit 45900 39491 54064 56538 69601 83337
Table 4a Summary of the dynamic COVID-19 constrained forecasts
Model Nov 26, 21 - Aug 23, 23 Dec 03, 21 - Sep 06, 23 Dec 06, 21 - Sep 12, 23 Dec 07, 21 - Sep 14, 23 Dec 08, 21 - Sep 16, 23 Dec 09, 21 - Sep 18, 23
Linear 226353 215195 211317 210491 209248 209135
Semilog 272266 269704 251299 251299 268578 251257
Growth 3734 3712 3712 3717 3719 3727
Without knots 80% 285 325 502 5143 4080 1075
Without knots 95% NaN NaN NaN 1304577 1389804 NaN
Smooth Spline 80% 12 4 5 4 6 5
Smooth Spline 95% 817533 1219896 1259052 1333144 1249743 1356229
With knots 80% 74822 51481 76915 62835 65259 64600
With knots 95% 310397 406479 206925 279792 258103 271379
Quadratic Polynomial 80% 2248 1295 1052 1014 946 966
Quadratic Polynomial 95% 2519 1414 1141 1098 1023 1044
ARIMA 80% 1147 908 1271 1051 1607 1621
ARIMA 95% 1482122 1487940 1496368 1502803 1521416 1522303
Essembled with equal weight 80% 871 916 705 13299 15369 21638
Essembled with equal weight 95% NaN 1508052 1549122 631716 715629 594287
Essembled based on weight 80% 21506 11051 10348 9372 26413 8751
Essembled based on weight 95% 1515135 1543206 1544402 1502790 1438327 1525857
Essembled based on summed weight 80% 143229 152477 158349 161039 163562 168018
Essembled based on summed weight 95% 304501 331621 333329 323618 328781 309614
Essembled based on weight of fit 80% 25034 7452 20772 21554 20460 25176
Essembled based on weight of fit 95% 244735 888330 276221 273291 380359 328384
Table 3 RMSE of the models in the dynamic forecasts
Model Nov 26, 21 - Aug 23, 23 Dec 03, 21 - Sep 06, 23 Dec 06, 21 - Sep 12, 23 Dec 07, 21 - Sep 14, 23 Dec 08, 21 - Sep 16, 23 Dec 09, 21 - Sep 18, 23
Linear 374.23 373.34 372.83 372.6 372.42 372.14
Semilog 369.59 369.22 368.92 368.74 368.62 368.36
Growth 500.94 498.26 497.17 496.82 496.46 496.18
Without knots 350.64 349.02 348.28 348.01 347.75 347.5
Smooth Spline 160.6 159.8 159.54 159.48 159.36 159.4
With knots 135.5 134.79 134.62 134.6 134.48 134.42
Quadratic Polynomial 354.1 352.19 351.41 351.17 350.9 350.74
Lower ARIMA 152.31 151.52 151.27 151.2 151.08 151.11
Upper ARIMA 152.31 151.52 151.27 151.2 151.08 151.11
Essembled with equal weight 192.84 191.88 191.53 191.42 191.27 191.21
Essembled based on weight 400.95 403.87 404.38 403.74 404.04 402.79
Essembled based on summed weight 372.84 374.15 374.48 374.41 374.52 374.25
Essembled based on weight of fit 237.75 244.09 246.46 247.08 247.83 248.17

Fig. 21 Percentage of COVID19 cases that resulted into casualty per State as at December 09, 2021

Fig. 22 Percentage of COVID19 cases that recovered per State as at December 09, 2021

Fig. 23 Percentage of recoveries and deaths from COVID19 cases per Zone as at December 09, 2021

Fig. 24 Distribution of COVID19 in the States as at December 09, 2021

  1. Note that Smooth spline does not estimate coefficients and other model-characteristic statistics↩︎

  2. Multiclass Area Under the Curve (MAUC) is the mean of the various AUC estimated from the same data↩︎