+++++++++++++++++++***************************+++++++++++++++++++++++++++

It is now 626 days since the first COVID-19 case was reported in Nigeria. As at November 15, 2021 the confirmed cases are 214,290 with 2,968 (1.39%) fatalities, an average of 5 fatalities per day. However, to date, 205,770 or 96.53% were successfully managed and discharged leaving a balance of 4,437 (2.08%) active cases being managed.

Based on equal days forecast, by August 03, 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
Upper ARIMA 1,324,175 1,278,226 18,406 27,543 136
Semilog 275,763 266,194 3,833 5,736 137
Linear 242,120 233,718 3,365 5,036 353
Without knots 205,779 198,639 2,860 4,280 357
Essembled based on weight of fit 20,673 19,956 287 430 1.5
Growth 3,759 3,629 52 78 162
Essembled with equal weight -10,377 -10,017 -144 -216 261
Essembled based on weight -18,632 -17,985 -259 -388 375
Essembled based on summed weight -215,565 -208,085 -2,996 -4,484 370
Quadratic Polynomial -409,413 -395,206 -5,691 -8,516 194
Lower ARIMA -1,278,834 -1,234,458 -17,776 -26,600 130
Smooth Spline -1,485,356 -1,433,814 -20,646 -30,895 153
With knots -1,577,052 -1,522,328 -21,921 -32,803 153

Constrained forecast of COVID-19 for Nigeria

Model Confirmed cases Recoveries Fatalities Active
ARIMA 95% 1,414,930 1,365,832 19,668.0 29,431.0
Smooth Spline 95% 1,365,452 1,318,070 18,980.0 28,401.0
Essembled based on summed weight 95% 1,195,753 1,154,261 16,621.0 24,872.0
Essembled based on weight 95% 1,079,240 1,041,790 15,001.0 22,448.0
Without knots 95% 919,031 887,141 12,775.0 19,116.0
With knots 95% 778,753 751,730 10,825.0 16,198.0
Essembled with equal weight 95% 352,279 340,055 4,897.0 7,327.0
Essembled based on weight of fit 95% 330,613 319,141 4,596.0 6,877.0
Semilog 275,763 266,194 3,833.0 5,736.0
Linear 242,120 233,718 3,365.0 5,036.0
Essembled based on weight of fit 80% 20,449 19,739 284.0 425.0
Essembled with equal weight 80% 15,938 15,385 222.0 332.0
Smooth Spline 80% 11,444 11,047 159.0 238.0
Quadratic Polynomial 95% 4,971 4,798 69.0 103.0
Quadratic Polynomial 80% 4,189 4,044 58.0 87.0
Growth 3,759 3,629 52.0 78.0
Essembled based on weight 80% 934 902 13.0 19.0
Without knots 80% 839 810 12.0 17.0
Essembled based on summed weight 80% 539 520 7.0 11.0
ARIMA 80% 451 436 6.0 9.0
With knots 80% 7 7 0.0 0.0

However, the actual forecast made by the various models on the last day i.e. August 03, 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.

+++++++++++++++++++***************************+++++++++++++++++++++++++++

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 November 15, 2021

Fig. 3 Cases recorded in percentages Starting from February 29, 2020 to November 15, 2021 (legend as Fig. 2)

Fig. 4 Cumulative cases and Forecast of COVID-19 cases in Nigeria Starting from November 16, 2021 to August 03, 2023

Fig. 4a Components of COVID-19 cases in Nigeria between February 29, 2020 and November 15, 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 November 15, 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 August 03, 2023

Coefficient estimates for number of states reporting COVID-19 daily

LinearSemilogGrowthSpline without knotsLinear splinesSpline with knotsARIMA
(Intercept)15.433 ****11.522 ****2.549 ****5.429 ****2.827 *   -0.464          
(0.490)    (1.399)    (0.050)    (0.851)    (1.579)    (2.386)         
Series-0.006 ****         -0.000 **                                  
(0.001)             (0.000)                                    
log(Series)         0.364                                              
         (0.254)                                             
bs(Series, knots = NULL)1                           31.932 ****                       
                           (2.459)                           
bs(Series, knots = NULL)2                           -8.897 ****                       
                           (1.560)                           
bs(Series, knots = NULL)3                           9.238 ****                       
                           (1.344)                           
bs(DDPtable$Series, knots = LBREAKS)1                                    -2.739                   
                                    (2.252)                  
bs(DDPtable$Series, knots = LBREAKS)2                                    13.737 ****              
                                    (1.670)                  
bs(DDPtable$Series, knots = LBREAKS)3                                    22.809 ****              
                                    (1.950)                  
bs(DDPtable$Series, knots = LBREAKS)4                                    -0.850                   
                                    (1.731)                  
bs(DDPtable$Series, knots = LBREAKS)5                                    29.160 ****              
                                    (1.785)                  
bs(DDPtable$Series, knots = LBREAKS)6                                    -3.513 **                
                                    (1.764)                  
bs(DDPtable$Series, knots = LBREAKS)7                                    4.035 **                
                                    (1.812)                  
bs(DDPtable$Series, knots = LBREAKS)8                                    17.615 ****              
                                    (1.984)                  
bs(DDPtable$Series, knots = LBREAKS)9                                    8.503 ****              
                                    (2.115)                  
bs(DDPtable$Series, knots = LBREAKS)10                                    4.679 **                
                                    (1.963)                  
bs(Series, knots = QBREAKS)1                                             6.339 **       
                                             (2.941)         
bs(Series, knots = QBREAKS)2                                             23.469 ****     
                                             (2.523)         
bs(Series, knots = QBREAKS)3                                             14.264 ****     
                                             (2.882)         
bs(Series, knots = QBREAKS)4                                             15.827 ****     
                                             (2.575)         
bs(Series, knots = QBREAKS)5                                             2.673          
                                             (2.756)         
bs(Series, knots = QBREAKS)6                                             24.755 ****     
                                             (2.792)         
bs(Series, knots = QBREAKS)7                                             2.175          
                                             (2.948)         
ma1                                                      -0.708 
                                                      (0.040)
ma2                                                      -0.062 
                                                      (0.038)
nobs608         608         608         608         608         608         607     
r.squared0.033     0.003     0.008     0.264     0.744     0.365          
adj.r.squared0.032     0.002     0.006     0.260     0.740     0.357          
sigma6.038     6.131     0.614     5.279     3.129     4.920     3.214 
statistic20.882     2.046     4.786     72.035     173.691     49.170          
p.value0.000     0.153     0.029     0.000     0.000     0.000          
df1.000     1.000     1.000     3.000     10.000     7.000          
logLik-1954.961     -1964.235     -565.164     -1872.279     -1550.791     -1827.425     -1569.421 
AIC3915.921     3934.469     1136.328     3754.558     3125.582     3672.851     3144.843 
BIC3929.152     3947.700     1149.559     3776.609     3178.504     3712.543     3158.069 
deviance22094.619     22779.045     228.467     16833.231     5846.412     14524.118          
df.residual606.000     606.000     606.000     604.000     597.000     600.000          
nobs.1608.000     608.000     608.000     608.000     608.000     608.000     607.000 
**** 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 3000 3100 6700 2500 1400 2700 1300 1500
Absolute Percent Error 460 450 470 280 150 330 130 150
Accuracy 0 0 0 0 0 0 0 0
Adjusted R Square 0.032 0.0017 0.0062 0.36 0.74 0.26 0 0
Akaike’s Information Criterion AIC 3900 3900 1100 3700 3100 3800 0 3100
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 -0.000000000000000016 -0.00000000000000054 11 0.0000000000000001 0.00000000000000006 0.000000000000000094 -0.0000000000000035 0.044
Brier score 40 40 200 20 10 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 -430 -430 -430 -430 -430 -430 -430 -430
Mean Absolute Error 5 5.2 11 4 2.4 4.5 2.1 2.4
Mean Absolute Percent Error 0.75 0.74 0.77 0.45 0.25 0.54 0.22 0.24
Mean Average Precision at k 0 0 0 0 0 0 0.17 0
Mean Absolute Scaled Error 1.7 1.8 3.9 1.4 0.83 1.6 0.74 0.85
Median Absolute Error 4.5 4.8 12 3.7 1.9 4.2 1.7 2
Mean Squared Error 36 37 160 24 9.6 28 8 10
Mean Squared Log Error 0.29 0.29 2 0.17 0.073 0.2 0.054 0.069
Model turning point error 365 331 365 345 340 346 340 452
Negative Predictive Value 0 0 0 0 0 0 0 0
Percent Bias -0.51 -0.48 0.73 -0.23 -0.097 -0.31 -0.082 -0.075
Positive Predictive Value 0 0 0 0 0 0 0 0
Precision 1 1 1 1 1 1 1 1
R Square 0.033 0.0034 0.0078 0.36 0.74 0.26 0 0
Relative Absolute Error 0.97 1 2.2 0.78 0.46 0.87 0.41 0.47
Recall 1 1 1 0.71 1 1 1 1
Root Mean Squared Error 6 6.1 13 4.9 3.1 5.3 2.8 3.2
Root Mean Squared Log Error 0.54 0.54 1.4 0.41 0.27 0.44 0.23 0.26
Root Relative Squared Error 0.98 1 2.1 0.8 0.51 0.86 0.46 0.52
Relative Squared Error 0.97 1 4.2 0.64 0.26 0.74 0.21 0.27
Schwarz’s Bayesian criterion BIC 3900 3900 1100 3700 3200 3800 0 3200
Sensitivity 0 0 0 0 0 0 0 0
specificity 0 0 0 0 0 0 0 0
Squared Error 22000 23000 97000 15000 5800 17000 4900 6200
Squared Log Error 180 180 1200 100 44 120 33 42
Symmetric Mean Absolute Percentage Error 0.41 0.42 1.3 0.35 0.22 0.38 0.19 0.21
Sum of Squared Errors 22000 23000 97000 15000 5800 17000 4900 6200
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 November 15, 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 November 15, 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)-313.029     -1227.625     -75.073     478.665     -34.025 ****16.005 ****
(253.264)    (1466.303)    (165.653)    (347.045)    (8.180)    (0.336)    
PMSprice-0.136 ****         0.099 ****0.210 ****0.001     0.000     
(0.028)             (0.013)    (0.032)    (0.002)    (0.001)    
Inflation1.186 ****7.995 ****         -1.698 ****-0.032 *   0.004     
(0.265)    (1.026)             (0.350)    (0.016)    (0.006)    
Teledensity0.618 ****3.493 ****-0.350 ****         -0.001     -0.003     
(0.094)    (0.528)    (0.072)             (0.008)    (0.003)    
`Birth rate`2.502     21.035     -6.471 *   -0.759              0.260 ****
(5.580)    (31.296)    (3.139)    (7.774)             (0.055)    
Population15.192     52.413     7.612     -23.401     2.245 ****         
(16.061)    (92.345)    (10.204)    (22.094)    (0.474)             
COVID19         -4.348 ****0.469 ****1.184 ****0.005     0.003     
         (0.903)    (0.105)    (0.179)    (0.011)    (0.004)    
nobs22         22         22         22         22         22         
r.squared0.783     0.901     0.920     0.842     0.712     0.743     
adj.r.squared0.715     0.869     0.896     0.793     0.622     0.662     
sigma1.132     6.398     0.712     1.568     0.050     0.017     
statistic11.551     28.973     37.013     17.099     7.911     9.236     
p.value0.000     0.000     0.000     0.000     0.001     0.000     
df5.000     5.000     5.000     5.000     5.000     5.000     
logLik-30.443     -68.545     -20.241     -37.606     38.016     61.734     
AIC74.886     151.090     54.481     89.213     -62.033     -109.469     
BIC82.524     158.728     62.118     96.850     -54.395     -101.831     
deviance20.506     654.944     8.111     39.328     0.041     0.005     
df.residual16.000     16.000     16.000     16.000     16.000     16.000     
nobs.122.000     22.000     22.000     22.000     22.000     22.000     
**** 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)320.052 ****-15.504     4.653 ****-79.457     -2.923          57.979     -12.972  -0.249     
(30.097)    (83.766)    (0.120)    (56.256)    (62.314)         (43.031)    (83.319) (16.843)    
Day0.071              0.001 ****                       2.575 ****               
(0.083)             (0.000)                           (0.317)                   
log(Day)         65.704 ****                                                        
         (15.139)                                                            
bs(Day, knots = NULL)1                           1097.050 ****                                      
                           (162.526)                                          
bs(Day, knots = NULL)2                           267.308 ***                                       
                           (103.098)                                          
bs(Day, knots = NULL)3                           324.399 ****                                      
                           (88.842)                                          
bs(Day, knots = BREAKS)1                                    3.587                                  
                                    (120.465)                                 
bs(Day, knots = BREAKS)2                                    14.547                                  
                                    (78.035)                                 
bs(Day, knots = BREAKS)3                                    841.225 ****                             
                                    (89.455)                                 
bs(Day, knots = BREAKS)4                                    173.812 **                               
                                    (75.997)                                 
bs(Day, knots = BREAKS)5                                    194.076 **                               
                                    (83.221)                                 
bs(Day, knots = BREAKS)6                                    -68.908                                  
                                    (78.260)                                 
bs(Day, knots = BREAKS)7                                    2012.295 ****                             
                                    (77.715)                                 
bs(Day, knots = BREAKS)8                                    -227.092 ***                              
                                    (77.620)                                 
bs(Day, knots = BREAKS)9                                    -85.004                                  
                                    (80.406)                                 
bs(Day, knots = BREAKS)10                                    751.354 ****                             
                                    (86.192)                                 
bs(Day, knots = BREAKS)11                                    243.937 ***                              
                                    (88.530)                                 
bs(Day, knots = BREAKS)12                                    13.010                                  
                                    (83.537)                                 
ar1                                             1.023                         
                                             (0.057)                        
ar2                                             -0.196                         
                                             (0.050)                        
ma1                                             -1.748                         
                                             (0.041)                        
ma2                                             0.819                         
                                             (0.033)                        
I(Day^2)                                                  -0.004 ****               
                                                  (0.000)                   
fitf                                                           -4.448  -0.112     
                                                           (5.644) (0.072)    
fit0f                                                           0.245  -0.002     
                                                           (0.543) (0.104)    
fit1f                                                           2.638  1.276 ****
                                                           (6.170) (0.119)    
fitpif                                                           0.218  -0.003     
                                                           (0.826) (0.112)    
fitaf                                                           2.664  -0.159 *   
                                                           (5.373) (0.089)    
fitf:fit0f                                                           0.019           
                                                           (0.025)          
fitf:fit1f                                                           0.022 *         
                                                           (0.013)          
fit0f:fit1f                                                           0.001           
                                                           (0.031)          
fitf:fitpif                                                           0.004           
                                                           (0.011)          
fit0f:fitpif                                                           -0.001           
                                                           (0.002)          
fit1f:fitpif                                                           -0.015           
                                                           (0.018)          
fitf:fitaf                                                           0.005           
                                                           (0.025)          
fit0f:fitaf                                                           -0.024           
                                                           (0.020)          
fit1f:fitaf                                                           -0.003           
                                                           (0.024)          
fitpif:fitaf                                                           0.005           
                                                           (0.016)          
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)          
nobs626         626         626         626         626         625     626         626      626         
r.squared0.001     0.029     0.029     0.118     0.815          0.098     0.880  0.869     
adj.r.squared-0.000     0.028     0.028     0.114     0.811          0.095     0.874  0.868     
sigma376.057     370.723     1.505     353.989     163.340     154.028 357.736     133.439  136.653     
statistic0.729     18.836     18.704     27.684     224.868          33.679     140.894  822.218     
p.value0.394     0.000     0.000     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-4599.272     -4590.329     -1143.142     -4560.409     -4071.679     -4033.672 -4567.504     -3935.256  -3963.562     
AIC9204.544     9186.658     2292.285     9130.818     8171.359     8077.343 9143.007     7936.512  7941.123     
BIC9217.862     9199.976     2305.603     9153.014     8233.510     8099.532 9160.765     8083.010  7972.199     
deviance88245470.980     85759781.041     1413.304     77941540.044     16354829.228          79728435.038     10576823.191  11577909.914     
df.residual624.000     624.000     624.000     622.000     613.000          623.000     594.000  620.000     
nobs.1626.000     626.000     626.000     626.000     626.000     625.000 626.000     626.000  626.000     
**** 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 170000 170000 210000 67000 160000 49000 56000 170000 210000 48000 49000 210000
Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Accuracy 0 0 0 0 0 0 0 0 0.029 0 0 0.029
Adjusted R Square -0.00043 0.028 0.028 0.81 0.11 0 0 0.095 0 0.87 0.87 0
Akaike’s Information Criterion AIC 9200 9200 2300 8200 9100 0 8100 9100 0 7900 7900 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 -0.000000000000043 -0.00000000000005 340 0.0000000000000015 -0.000000000000032 0.00000000000048 0.14 -0.000000000000018 340 -0.0000000000000028 0.00000000000000024 340
Brier score 100000 100000 300000 30000 100000 20000 20000 100000 20000000 20000 20000 300000
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 0.04 0.04 0.04 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 -12000 -12000 -12000 -11000 -12000 -12000 -12000 -12000 NaN -12000 -12000 NaN
Mean Absolute Error 280 270 340 110 260 78 90 270 1300 77 78 340
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 2.7 2.6 3.2 1 2.5 0.75 0.86 2.6 3.3 0.74 0.75 3.3
Median Absolute Error 230 220 200 76 230 36 45 240 110 40 39 140
Mean Squared Error 140000 140000 250000 26000 120000 19000 24000 130000 24000000 17000 18000 260000
Mean Squared Log Error 2.8 NaN 13 NaN NaN NaN 0.26 2.3 28 NaN NaN 28
Model turning point error 318 318 318 303 318 304 417 305 378 294 264 377
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 NaN -Inf NaN NaN
Positive Predictive Value 0 0 0 0 0 0 0 0 0 0 0 0
Precision 0.1 0.053 0.1 0 0 0.1 0.33 0.1 0 0.1 0.1 0
R Square 0.0012 0.029 0.029 0.81 0.12 0 0 0.098 0 0.88 0.87 0
Relative Absolute Error 1 0.98 1.2 0.39 0.94 0.28 0.33 0.97 0.48 0.28 0.28 0.64
Recall 1 0.5 1 0 0 0.5 0.5 1 0 1 0.5 0
Root Mean Squared Error 380 370 500 160 350 140 150 360 4900 130 140 510
Root Mean Squared Log Error 1.7 NaN 3.6 NaN NaN NaN 0.51 1.5 5.3 NaN NaN 5.3
Root Relative Squared Error 1 0.99 1.3 0.43 0.94 0.36 0.41 0.95 1.4 0.35 0.36 1.4
Relative Squared Error 1 0.97 1.8 0.19 0.88 0.13 0.17 0.9 1.8 0.12 0.13 1.8
Schwarz’s Bayesian criterion BIC 9200 9200 2300 8200 9200 0 8100 9200 0 8100 8000 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 88000000 86000000 160000000 16000000 78000000 12000000 15000000 80000000 160000000 11000000 12000000 160000000
Squared Log Error 1800 NaN 8200 NaN NaN NaN 160 1400 18000 NaN NaN 18000
Symmetric Mean Absolute Percentage Error 0.87 0.88 1.8 0.58 0.85 0.34 0.4 0.86 0.59 0.38 0.36 0.68
Sum of Squared Errors 88000000 86000000 160000000 16000000 78000000 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 November 16, 2021 to August 03, 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 November 16, 2021 to August 03, 2023 using a more advaced plotting method

Fig. 20c Constrained forecast of COVID-19 cases in Nigeria Starting from November 16, 2021 to August 03, 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 02, 21 - Jul 06, 23 Nov 09, 21 - Jul 20, 23 Nov 12, 21 - Jul 26, 23 Nov 13, 21 - Jul 28, 23 Nov 14, 21 - Jul 30, 23 Nov 15, 21 - Aug 01, 23
Linear 263847 254081 248966 247750 245993 244025
Semilog 280322 257063 256588 277116 276710 276226
Growth 3784 3788 3779 3781 3778 3767
Without knots 354582 287841 251762 245356 233257 219078
Smooth Spline -2320261 -1871444 -1776518 -1630730 -1596931 -1597959
With knots -1170699 -1511298 -1630954 -1278869 -1309285 -1442456
Quadratic Polynomial -333652 -368056 -385922 -389934 -396001 -402845
Lower ARIMA -1218309 -1269775 -1275008 -1255479 -1263143 -1273276
Upper ARIMA 1315675 1305061 1308982 1330262 1330005 1325392
Essembled with equal weight -9598 -39360 -30060 -15225 5227 -853
Essembled based on weight 274839 140293 272659 276179 384162 453310
Essembled based on summed weight 151051 157039 162765 162913 166760 169610
Essembled based on weight of fit 30297 8109 11894 19953 31382 26995
Table 4a Summary of the dynamic COVID-19 constrained forecasts
Model Nov 02, 21 - Jul 06, 23 Nov 09, 21 - Jul 20, 23 Nov 12, 21 - Jul 26, 23 Nov 13, 21 - Jul 28, 23 Nov 14, 21 - Jul 30, 23 Nov 15, 21 - Aug 01, 23
Linear 263847 254081 248966 247750 245993 244025
Semilog 280322 257063 256588 277116 276710 276226
Growth 3784 3788 3779 3781 3778 3767
Without knots 80% 683 322 529 228 188 645
Without knots 95% NaN NaN 1373670 NaN NaN 1237395
Smooth Spline 80% 4 6 5 4 3 4
Smooth Spline 95% 681168 699492 819909 973297 1070605 1031822
With knots 80% 13483 3553 89684 105652 74058 2437
With knots 95% 1365039 1483113 403690 312383 493033 1505601
Quadratic Polynomial 80% 8406 6292 5325 5126 4826 4497
Quadratic Polynomial 95% 11034 7822 6469 6189 5787 5352
ARIMA 80% 2152 789 527 536 767 642
ARIMA 95% 1443951 1417408 1413164 1395175 1431097 1421363
Essembled with equal weight 80% 26237 13128 16715 16763 17791 2199
Essembled with equal weight 95% 580609 670082 362929 384313 393252 1340650
Essembled based on weight 80% 9276 98785 96375 82428 25126 131014
Essembled based on weight 95% 1455275 658336 858059 956115 1482448 1003381
Essembled based on summed weight 80% 96989 113136 117165 119475 121909 123239
Essembled based on summed weight 95% 290040 258018 267438 260418 267546 274483
Essembled based on weight of fit 80% 34657 34225 1937 2455 4658 19721
Essembled based on weight of fit 95% 413072 268796 1427850 1397274 1293537 408750
Table 3 RMSE of the models in the dynamic forecasts
Model Nov 02, 21 - Jul 06, 23 Nov 09, 21 - Jul 20, 23 Nov 12, 21 - Jul 26, 23 Nov 13, 21 - Jul 28, 23 Nov 14, 21 - Jul 30, 23 Nov 15, 21 - Aug 01, 23
Linear 377.05 376.09 375.82 375.64 375.56 375.51
Semilog 370.91 370.31 370.22 370.1 370.08 370.11
Growth 510.34 507.6 506.4 506.02 505.62 505.21
Without knots 355.61 354.17 353.62 353.37 353.19 353.03
Smooth Spline 163.2 162.47 162.09 162.02 161.89 161.76
With knots 138 137.27 136.86 136.81 136.7 136.65
Quadratic Polynomial 360.83 358.82 357.98 357.7 357.42 357.15
Lower ARIMA 155.03 154.24 153.86 153.77 153.65 153.53
Upper ARIMA 155.03 154.24 153.86 153.77 153.65 153.53
Essembled with equal weight 196.02 195.1 194.68 194.56 194.43 194.32
Essembled based on weight 400.21 399.14 398.9 398.47 398.57 398.88
Essembled based on summed weight 371.24 370.99 371.23 371.14 371.26 371.46
Essembled based on weight of fit 216.75 222.22 225.01 225.77 226.72 227.76

Fig. 21 Percentage of COVID19 cases that resulted into casualty per State as at November 15, 2021

Fig. 22 Percentage of COVID19 cases that recovered per State as at November 15, 2021

Fig. 23 Percentage of recoveries and deaths from COVID19 cases per Zone as at November 15, 2021

Fig. 24 Distribution of COVID19 in the States as at November 15, 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↩︎