Update on COVID-19 visuals for Nigeria

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It is now 567 days since the first COVID-19 case was reported in Nigeria. As at September 17, 2021 the confirmed cases are 202,249 with 2,649 (1.32%) fatalities, however, 189,608 (94.19%) have recovered leaving 9,039 (4.49%) active cases.

Based on equal days forecast, by April 07, 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	1,346,860	1,268,607	17,779	60,474	139
With knots	1,066,555	1,004,589	14,079	47,888	157
Without knots	489,384	460,951	6,460	21,973	373
Linear	288,837	272,055	3,813	12,969	366
Semilog	277,454	261,334	3,662	12,458	139
Essembled based on weight	247,778	233,382	3,271	11,125	387
Essembled with equal weight	175,658	165,453	2,319	7,887	271
Essembled based on weight of fit	152,298	143,449	2,010	6,838	1.6
Growth	3,533	3,328	47	159	163
Essembled based on summed weight	-142,263	-133,998	-1,878	-6,388	380
Quadratic Polynomial	-236,071	-222,355	-3,116	-10,600	200
Lower ARIMA	-945,901	-890,945	-12,486	-42,471	133
Smooth Spline	-1,720,366	-1,620,412	-22,709	-77,244	157

Constrained forecast of COVID-19 for Nigeria

Model	Confirmed cases	Recoveries	Fatalities	Active
ARIMA 95%	1,367,538	1,288,084	18,051.0	61,402
Without knots 95%	1,366,946	1,287,527	18,044.0	61,376
Essembled based on weight 95%	1,304,335	1,228,553	17,217.0	58,565
Essembled based on summed weight 95%	1,131,053	1,065,338	14,930.0	50,784
Essembled with equal weight 95%	860,375	810,387	11,357.0	38,631
Smooth Spline 95%	847,495	798,256	11,187.0	38,053
Essembled based on weight of fit 95%	580,498	546,771	7,663.0	26,064
With knots 95%	539,351	508,014	7,119.0	24,217
Linear	288,837	272,055	3,813.0	12,969
Semilog	277,454	261,334	3,662.0	12,458
Quadratic Polynomial 95%	93,753	88,306	1,238.0	4,210
Essembled based on weight of fit 80%	82,210	77,434	1,085.0	3,691
Essembled with equal weight 80%	77,040	72,564	1,017.0	3,459
Quadratic Polynomial 80%	70,369	66,281	929.0	3,160
Smooth Spline 80%	69,618	65,573	919.0	3,126
Essembled based on summed weight 80%	27,341	25,752	361.0	1,228
Essembled based on weight 80%	16,188	15,247	214.0	727
ARIMA 80%	5,839	5,500	77.0	262
Without knots 80%	4,400	4,144	58.0	198
Growth	3,533	3,328	47.0	159
With knots 80%	3	3	0.0	0

However, the actual forecast made by the various models on the last day i.e. April 07, 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 September 17, 2021

Fig. 3 Cases recorded in percentages Starting from February 29, 2020 to September 17, 2021 (legend as Fig. 2)

Fig. 4 Cumulative cases and Forecast of COVID-19 cases in Nigeria Starting from September 18, 2021 to April 07, 2023

Fig. 4a Components of COVID-19 cases in Nigeria between February 29, 2020 and September 17, 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 September 17, 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 April 07, 2023

Coefficient estimates for number of states reporting COVID-19 daily

	Linear	Semilog	Growth	Spline without knots	Linear splines	Spline with knots	ARIMA
(Intercept)	15.449 ****	10.521 ****	2.559 ****	4.005 ****	2.806 *	0.011
	(0.532)	(1.485)	(0.054)	(0.893)	(1.576)	(2.302)
Series	-0.007 ****		-0.000 **
	(0.002)		(0.000)
log(Series)		0.589 **
		(0.275)
bs(Series, knots = NULL)1				35.494 ****
				(2.580)
bs(Series, knots = NULL)2				-6.958 ****
				(1.637)
bs(Series, knots = NULL)3				10.092 ****
				(1.410)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))1					-2.678
					(2.248)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))2					13.683 ****
					(1.667)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))3					22.953 ****
					(1.943)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))4					-1.005
					(1.723)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))5					29.444 ****
					(1.762)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))6					-13.311 ****
					(1.849)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))7					13.823 ****
					(1.951)
bs(DDPtable$Series, knots = c(30, 115, 247, 337, 420))8					13.363 ****
					(1.812)
bs(Series, knots = c(30, 247, 420))1						5.023 *
						(2.841)
bs(Series, knots = c(30, 247, 420))2						24.954 ****
						(2.439)
bs(Series, knots = c(30, 247, 420))3						10.542 ****
						(2.812)
bs(Series, knots = c(30, 247, 420))4						19.799 ****
						(2.544)
bs(Series, knots = c(30, 247, 420))5						-3.155
						(2.679)
bs(Series, knots = c(30, 247, 420))6						24.189 ****
						(2.620)
ma1							-0.754
							(0.028)
nobs	549	549	549	549	549	549	548
r.squared	0.027	0.008	0.008	0.307	0.758	0.440
adj.r.squared	0.025	0.007	0.007	0.303	0.754	0.434
sigma	6.227	6.286	0.636	5.266	3.125	4.746	3.192
statistic	15.154	4.604	4.632	80.344	211.497	70.942
p.value	0.000	0.032	0.032	0.000	0.000	0.000
df	1.000	1.000	1.000	3.000	8.000	6.000
logLik	-1782.039	-1787.239	-529.323	-1689.015	-1400.004	-1630.438	-1413.581
AIC	3570.077	3580.479	1064.646	3388.030	2820.009	3276.877	2831.161
BIC	3583.002	3593.403	1077.570	3409.570	2863.090	3311.341	2839.774
deviance	21208.678	21614.317	221.083	15112.550	5273.340	12208.495
df.residual	547.000	547.000	547.000	545.000	540.000	542.000
nobs.1	549.000	549.000	549.000	549.000	549.000	549.000	548.000
**** 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	2800	2900	6200	2100	1300	2400	1100	1300
Absolute Percent Error	440	420	420	230	140	280	120	130
Accuracy	0	0	0	0	0	0	0	0
Adjusted R Square	0.025	0.0065	0.0066	0.43	0.75	0.3	0	0
Akaike’s Information Criterion AIC	3600	3600	1100	3300	2800	3400	0	2800
Allen’s Prediction Sum-Of-Squares (PRESS, P-Square)	0	0	0	0	0	0	0	0
Area under the ROC curve (AUC)	0.87	0.13	0.87	0.033	0.048	0.023	0.015	0.028
Average Precision at k	0	0	0	0	0	0	0	0
Bias	0.00000000000000033	0.00000000000000006	11	-0.00000000000000021	0.000000000000000097	-0.000000000000000033	0.0000000000000008	0.11
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	0.6	0.9	0.9
kappa statistic	0	0	0	0	0	0	0	0
Log Loss	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf
Mallow’s cp	2	2	2	7	9	4	0	0
Matthews Correlation Coefficient	0	0	0	0	0	0	0	0
Mean Log Loss	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf
Mean Absolute Error	5.2	5.3	11	3.9	2.3	4.4	2.1	2.4
Mean Absolute Percent Error	0.8	0.77	0.77	0.42	0.26	0.51	0.21	0.24
Mean Average Precision at k	0	0	0	0	0	0	0.17	0
Mean Absolute Scaled Error	1.8	1.9	4	1.4	0.83	1.5	0.73	0.85
Median Absolute Error	4.9	5.1	12	3.4	1.9	3.9	1.6	2
Mean Squared Error	39	39	160	22	9.6	28	7.8	10
Mean Squared Log Error	0.31	0.31	2	0.15	0.074	0.19	0.053	0.068
Model turning point error	330	297	330	306	304	312	304	405
Negative Predictive Value	0	0	0	0	0	0	0	0
Percent Bias	-0.55	-0.51	0.72	-0.21	-0.1	-0.29	-0.081	-0.068
Positive Predictive Value	0	0	0	0	0	0	0	0
Precision	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
R Square	0.027	0.0083	0.0084	0.44	0.76	0.31	0	0
Relative Absolute Error	0.97	1	2.1	0.73	0.44	0.82	0.39	0.45
Recall	15	12	2.5	3	3.4	5.8	2.7	2.2
Root Mean Squared Error	6.2	6.3	13	4.7	3.1	5.2	2.8	3.2
Root Mean Squared Log Error	0.56	0.56	1.4	0.39	0.27	0.43	0.23	0.26
Root Relative Squared Error	0.99	1	2	0.75	0.49	0.83	0.44	0.51
Relative Squared Error	0.97	0.99	4.2	0.56	0.24	0.69	0.2	0.26
Schwarz’s Bayesian criterion BIC	3600	3600	1100	3300	2900	3400	0	2800
Sensitivity	0	0	0	0	0	0	0	0
specificity	0	0	0	0	0	0	0	0
Squared Error	21000	22000	91000	12000	5300	15000	4300	5600
Squared Log Error	170	170	1100	82	41	100	29	37
Symmetric Mean Absolute Percentage Error	0.42	0.44	1.3	0.33	0.22	0.36	0.18	0.21
Sum of Squared Errors	21000	22000	91000	12000	5300	15000	4300	5600
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 September 17, 2021

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

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 September 17, 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

	COVID19	PMS	Inflation	Teledensity	Birth rate	Population
(Intercept)	169.543	2975.129	-475.232 ***	-275.360	-36.492 ****	15.452 ****
	(370.172)	(1855.122)	(153.519)	(519.286)	(5.741)	(0.268)
PMSprice	-0.139 ****		0.089 ****	0.217 ****	0.003 **	-0.001 *
	(0.033)		(0.011)	(0.038)	(0.001)	(0.000)
Inflation	1.327 ***	9.179 ****		-1.957 ****	-0.045 ****	0.014 ***
	(0.353)	(1.145)		(0.470)	(0.009)	(0.004)
Teledensity	0.605 ****	3.220 ****	-0.283 ****		-0.008	0.002
	(0.100)	(0.563)	(0.068)		(0.005)	(0.002)
`Birth rate`	12.393	105.864 **	-13.895 ****	-16.411		0.324 ****
	(8.161)	(38.360)	(2.890)	(11.584)		(0.045)
Population	-15.626	-215.033 *	32.716 ***	24.907	2.425 ****
	(23.719)	(116.989)	(9.440)	(33.210)	(0.338)
COVID19		-4.063 ****	0.379 ***	1.197 ****	0.011	-0.002
		(0.956)	(0.101)	(0.197)	(0.008)	(0.003)
nobs	20	20	20	20	20	20
r.squared	0.773	0.895	0.940	0.834	0.860	0.850
adj.r.squared	0.692	0.858	0.918	0.775	0.810	0.796
sigma	1.222	6.612	0.653	1.718	0.037	0.014
statistic	9.552	23.910	43.671	14.102	17.210	15.808
p.value	0.000	0.000	0.000	0.000	0.000	0.000
df	5.000	5.000	5.000	5.000	5.000	5.000
logLik	-28.817	-62.589	-16.280	-35.636	41.086	61.205
AIC	71.633	139.178	46.559	85.273	-68.171	-108.410
BIC	78.603	146.148	53.529	92.243	-61.201	-101.440
deviance	20.895	612.023	5.964	41.326	0.019	0.003
df.residual	14.000	14.000	14.000	14.000	14.000	14.000
nobs.1	20.000	20.000	20.000	20.000	20.000	20.000
**** 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

	Linear	Semilog	Growth	Spline without knots	Spline with knots	ARIMA	Quardratic polynomial	Essembled based on weight	Essembled based on summed weight
(Intercept)	280.209 ****	-118.017	4.541 ****	-132.578 **	-3.333		46.925	38.847	-1.736
	(32.601)	(88.858)	(0.131)	(61.329)	(62.794)		(47.255)	(146.654)	(19.438)
Day	0.269 ***		0.002 ****				2.729 ****
	(0.099)		(0.000)				(0.384)
log(Day)		88.772 ****
		(16.346)
bs(Day, knots = NULL)1				1245.435 ****
				(177.199)
bs(Day, knots = NULL)2				196.414 *
				(112.441)
bs(Day, knots = NULL)3				516.899 ****
				(96.842)
bs(Day, knots = BREAKS)1					5.086
					(121.394)
bs(Day, knots = BREAKS)2					13.093
					(78.637)
bs(Day, knots = BREAKS)3					843.779 ****
					(90.146)
bs(Day, knots = BREAKS)4					170.515 **
					(76.586)
bs(Day, knots = BREAKS)5					201.752 **
					(83.882)
bs(Day, knots = BREAKS)6					-81.410
					(78.919)
bs(Day, knots = BREAKS)7					2036.208 ****
					(78.519)
bs(Day, knots = BREAKS)8					-273.019 ****
					(78.962)
bs(Day, knots = BREAKS)9					45.325
					(91.864)
bs(Day, knots = BREAKS)10					478.647 ****
					(89.701)
bs(Day, knots = BREAKS)11					634.786 ****
					(81.532)
ar1						1.012
						(0.061)
ar2						-0.196
						(0.053)
ma1						-1.739
						(0.046)
ma2						0.814
						(0.036)
I(Day^2)							-0.004 ****
							(0.001)
fitf								1.098	-0.120
								(7.519)	(0.079)
fit0f								0.029	-0.008
								(0.986)	(0.086)
fit1f								-0.497	1.291 ****
								(6.444)	(0.125)
fitpif								-0.380	0.007
								(1.230)	(0.099)
fitaf								0.383	-0.166 *
								(5.700)	(0.093)
fitf:fit0f								-0.007
								(0.023)
fitf:fit1f								0.021
								(0.020)
fit0f:fit1f								0.013
								(0.026)
fitf:fitpif								-0.003
								(0.017)
fit0f:fitpif								0.001
								(0.002)
fit1f:fitpif								-0.009
								(0.020)
fitf:fitaf								-0.059
								(0.036)
fit0f:fitaf								-0.007
								(0.020)
fit1f:fitaf								0.038
								(0.034)
fitpif:fitaf								0.013
								(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)
nobs	567	567	567	567	567	566	567	567	567
r.squared	0.013	0.050	0.042	0.116	0.825		0.084	0.884	0.873
adj.r.squared	0.011	0.048	0.040	0.111	0.822		0.081	0.877	0.872
sigma	387.626	380.333	1.555	367.508	164.599	157.540	373.756	136.730	139.330
statistic	7.334	29.494	24.762	24.571	238.101		25.801	131.125	773.763
p.value	0.007	0.000	0.000	0.000	0.000		0.000	0.000	0.000
df	1.000	1.000	1.000	3.000	11.000		2.000	31.000	5.000
logLik	-4182.880	-4172.110	-1053.747	-4151.655	-3692.165	-3665.518	-4161.717	-3576.581	-3600.714
AIC	8371.760	8350.221	2113.494	8313.310	7410.330	7341.035	8331.434	7219.162	7215.428
BIC	8384.781	8363.242	2126.515	8335.012	7466.755	7362.728	8348.796	7362.394	7245.811
deviance	84893620.260	81729086.991	1365.673	76039856.291	15036516.318		78787166.131	10001930.986	10890631.588
df.residual	565.000	565.000	565.000	563.000	555.000		564.000	535.000	561.000
nobs.1	567.000	567.000	567.000	567.000	567.000	566.000	567.000	567.000	567.000
**** 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	160000	160000	200000	61000	150000	44000	51000	160000	200000	44000	45000	200000
Absolute Percent Error	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf
Accuracy	0	0	0	0	0	0	0	0	0.032	0	0	0.032
Adjusted R Square	0.011	0.048	0.04	0.82	0.11	0	0	0.081	0	0.88	0.87	0
Akaike’s Information Criterion AIC	8400	8400	2100	7400	8300	0	7300	8300	0	7200	7200	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)	0.008	0.008	0.008	0.088	0.008	0.008	0.016	0.008	0.008	0.032	0.008	0.008
Average Precision at k	0	0	0	0	0	0	0	0	0.5	0	0	0.5
Bias	-0.0000000000000064	-0.000000000000032	350	0.0000000000000082	-0.000000000000011	0.00000000000026	1.5	0.000000000000023	360	0.00000000000000042	-0.0000000000000016	360
Brier score	100000	100000	300000	30000	100000	20000	20000	100000	NaN	20000	20000	10000000
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	0.1	0.1	0.1	0.9	0.3	1	0.9	0.4	0.9	1	1	0.9
kappa statistic	0	0	0	0	0	0	0	0	NaN	0	0	NaN
Log Loss	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf
Mallow’s cp	2	2	2	8.9	4	0	0	3	0	0	6	0
Matthews Correlation Coefficient	0	0	0	0	0	0	0	0	NaN	0	0	NaN
Mean Log Loss	Inf	Inf	Inf	Inf	Inf	Inf	Inf	Inf	NaN	Inf	Inf	NaN
Mean Absolute Error	290	280	350	110	270	78	90	290	NaN	77	79	800
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	3.3	1	2.5	0.74	0.86	2.7	3.4	0.73	0.75	3.4
Median Absolute Error	250	220	210	75	250	35	43	270	110	41	38	150
Mean Squared Error	NA	NA	NA	NA	NA	NA	NA	NA	NaN	NA	NA	12000000
Mean Squared Log Error	3	NaN	13	NaN	NaN	NaN	0.26	2.4	29	NaN	NaN	29
Model turning point error	288	288	288	279	290	275	380	281	348	257	236	344
Negative Predictive Value	0	0	0	0	0	0	0	0	0	0	0	0
Percent Bias	-Inf	NaN	-Inf	NaN	NaN	NaN	-Inf	-Inf	NaN	NaN	NaN	NaN
Positive Predictive Value	0	0	0	0	0	0	0	0	0	0	0	0
Precision	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0	NaN	NaN	0
R Square	0.013	0.05	0.042	0.83	0.12	0	0	0.084	0	0.88	0.87	0
Relative Absolute Error	0.99	0.96	1.2	0.37	0.92	0.27	0.31	0.98	0.47	0.27	0.27	0.63
Recall	280	-12	4.6	-2	-100	-0.19	0.5	63	0	4.3	-0.59	0
Root Mean Squared Error	NA	NA	NA	NA	NA	NA	NA	NA	NaN	NA	NA	3400
Root Mean Squared Log Error	1.7	NaN	3.7	NaN	NaN	NaN	0.51	1.6	5.3	NaN	NaN	5.3
Root Relative Squared Error	0.99	0.97	1.3	0.42	0.94	0.36	0.4	0.96	1.4	0.34	0.36	1.4
Relative Squared Error	0.99	0.95	1.8	0.17	0.88	0.13	0.16	0.92	1.8	0.12	0.13	1.8
Schwarz’s Bayesian criterion BIC	8400	8400	2100	7500	8300	0	7400	8300	0	7400	7200	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	85000000	82000000	160000000	15000000	76000000	11000000	14000000	79000000	160000000	10000000	11000000	160000000
Squared Log Error	1700	NaN	7600	NaN	NaN	NaN	150	1400	16000	NaN	NaN	16000
Symmetric Mean Absolute Percentage Error	0.89	0.88	1.8	0.59	0.85	0.34	0.4	0.91	0.6	0.37	0.36	0.7
Sum of Squared Errors	85000000	82000000	160000000	15000000	76000000	11000000	14000000	79000000	160000000	10000000	11000000	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 September 18, 2021 to April 07, 2023 using a more advaced plotting method

Fig. 20a

Fig. 20b Constrained forecast of COVID-19 cases in Nigeria Starting from September 18, 2021 to April 07, 2023 using a more advaced plotting method

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

Table 4 Summary of the dynamic COVID-19 forecasts

Model	Sep 05, 21 - Mar 11, 23	Sep 12, 21 - Mar 25, 23	Sep 15, 21 - Mar 31, 23	Sep 16, 21 - Apr 02, 23	Sep 17, 21 - Apr 04, 23	Sep 18, 21 - Apr 06, 23
Without knots	244613	413515	446360	463311	463540	486447
Smooth Spline	3462771	2544669	1827374	1689162	1371793	1327628
With knots	-1050368	-373943	-1489237	-1316597	-1983981	-1304816
Quadratic Polynomial	-305855	-255514	-247231	-242266	-243256	-236121
Lower ARIMA	-839128	-798187	-879781	-879412	-942191	-902238
Upper ARIMA	1363682	1428825	1373444	1381459	1342851	1377018
Essembled with equal weight	257423	326777	219645	197036	179852	158637
Essembled based on weight	261975	544769	436140	394743	473424	353491
Essembled based on summed weight	-35515	-80576	-52924	-61714	-29933	-65088
Essembled based on weight of fit	183708	234242	175520	163216	153972	141763

Table 3 RMSE of the models in the dynamic forecasts

Model	Sep 05, 21 - Mar 11, 23	Sep 12, 21 - Mar 25, 23	Sep 15, 21 - Mar 31, 23	Sep 16, 21 - Apr 02, 23	Sep 17, 21 - Apr 04, 23	Sep 18, 21 - Apr 06, 23
Without knots	368.79	368.21	367.32	367.04	366.73	366.53
Smooth Spline	158.68	160.72	161.93	161.96	162.6	162.48
With knots	138.57	139.5	139.43	139.33	139.22	139.35
Quadratic Polynomial	372.75	373.91	373.39	373.3	373	373.05
Lower ARIMA	156.13	156.95	156.84	156.7	156.84	156.84
Upper ARIMA	156.13	156.95	156.84	156.7	156.84	156.84
Essembled with equal weight	199.49	200.19	200.06	199.95	199.94	199.92
Essembled based on weight	412.36	410.59	409.56	409.12	408.88	408.5
Essembled based on summed weight	387.21	385.44	384.38	384.03	383.71	383.38
Essembled based on weight of fit	203.41	199.58	199.14	198.79	198.98	198.49

Fig. 21 Percentage of COVID19 cases that resulted into casualty per State as at September 17, 2021

Fig. 22 Percentage of COVID19 cases that recovered per State as at September 17, 2021

Fig. 23 Percentage of recoveries and deaths from COVID19 cases per Zone as at September 17, 2021

Fig. 24 Distribution of COVID19 in the States as at September 17, 2021

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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↩︎