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Elsevier - PMC COVID-19 Collection logoLink to Elsevier - PMC COVID-19 Collection
. 2020 Jun 9;138:109911. doi: 10.1016/j.chaos.2020.109911

Modeling Nigerian Covid-19 cases: A comparative analysis of models and estimators

Kayode Ayinde a, Adewale F Lukman b,, Rauf I Rauf c, Olusegun O Alabi a, Charles E Okon a, Opeyemi E Ayinde d
PMCID: PMC7282783  PMID: 32536757

Highlights

  • COVID-19 remains a major pandemic currently facing all the countries of the world, Nigeria inclusive.

  • We build some statistical model to the available data.

  • We choose the best model to make some forecast.

Keywords: COVID-19, Curve Estimation Statistical Models, Quartic Linear Regression Model, Estimators, Forecast Values

Abstract

COVID-19 remains a major pandemic currently threatening all the countries of the world. In Nigeria, there were 1, 932 COVID-19 confirmed cases, 319 discharged cases and 58 deaths as of 30th April 2020. This paper, therefore, subjected the daily cumulative reported COVID-19 cases of these three variables to nine (9) curve estimation statistical models in simple, quadratic, cubic, and quartic forms. It further identified the best of the thirty-six (36) models and used the same for prediction and forecasting purposes. The data collected by the Nigeria Centre for Disease Control for sixty-four (64) days, two (2) months and three (3), were daily monitored and eventually analyzed. We identified the best models to be Quartic Linear Regression Model with an autocorrelated error of order 1 (AR(1)); and found the Ordinary Least Squares, Cochrane Orcutt, Hildreth–Lu, and Prais-Winsten and Least Absolute Deviation (LAD) estimators useful to estimate the models’ parameters. Consequently, we recommended the daily cumulative forecast values of the LAD estimator for May and June 2020 with a 99% confidence level. The forecast values are alarming, and so, the Nigerian Government needs to hastily review her activities and interventions towards COVID-19 to provide some tactical and robust structures and measures to avert these challenges.

1. Introduction

Coronavirus Diseases (COVID-19), a respiratory disease characterized by fever, dry cough, and fatigue, and occasional gastrointestinal symptoms, had its initial outbreak in Wuhan city, Hubei, China in late December 2019 [2,9,11,13,21]. Within a month, the disease has escalated in China and further spread to other countries including Thailand, Japan, Republic of Korea, Vietnam, Germany, United States, and Singapore [15,28,31]. On the 30th January 2020, the WHO publicly declared COVID-19 as a disease of international concern [32] and later on 11th March 2020 reported it as a pandemic based on its alarming levels of spread and severity over the world [6].

According to the World Health Organization (WHO) COVID-19 situation report of 29th April 2020, there were 3,018,052 confirmed cases and 207,973 deaths globally. The disease has spread to at least fifteen (15) countries in the Western Pacific Region with 146,720 confirmed cases and 6,037 deaths; fifty-three (53) nations in the European Region with 1,406,899 confirmed cases and 129,311 deaths; ten (10) countries in the South-East Asia Region with 51,351 confirmed cases and 2,001 deaths; twenty-one (21) countries in Eastern Mediterranean Region with 176,928 confirmed cases and 7,304 deaths; thirty-five (35) counties in Region of the Americas with 1,213,088 confirmed cases and 62,404 deaths; and forty-five (45) countries in African Region with 23,254 confirmed cases and 903 deaths of which Nigeria had 1,337 confirmed cases and 40 deaths [29]. Actually, this was the Nigerian situation report of 27th April 2020 [22,30].

The first COVID-19 confirmed case in Nigeria was reported on 27th February 2020, when an Italian citizen in Lagos tested positive for the virus [22,23]. The second case was recorded on the 9th March 2020 in Ewekoro, Ogun State, a Nigerian citizen who had contact with the Italian citizen [30]. Within the first month, the confirmed cases were around 70 but drastically increased to number almost 1,350 cases before the end of the second month. The discharged cases increased from 3 to about 250 in the first two months. The number of recorded deaths increased from 1 to 40. Fig. 1, Fig. 2 presented the situation over the states of the country between the first and second months of occurrence.

Fig. 1.

Fig 1:

Nigerian COVID-19 cases after one month of occurrences.

Fig. 2.

Fig 2:

Nigerian COVID -19 cases after two months of occurrences.

From Figs. 1 and 2, it is not only evident that CIVID-19 cases had increased, but had also spread significantly from eight (8) states to thirty-three (33) (including FCT, Abuja). There were only four states that had no confirmed cases; namely Yobe, Nasarawa, Kogi and Cross River States. At present, only Nasarawa and Yobe States have no record of COVID-19 while Lagos State, Kano State and FCT remained topmost in Nigeria. Fig. 3 presented the cumulative COVID-19 confirmed cases, discharged cases, death cases and yet-to-recover (active) cases. In contrast, Fig. 4 showed the proportion of death cases, the discharged cases and yet-to-recover cases over the cumulative COVID-19 confirmed cases for the periods of the data collection.

Fig. 3.

Fig 3:

Nigerian COVID 19 Reported Cases in the First Sixty Four Days.

Fig. 4.

Fig 4:

Proportions of Nigerian Cumulative COVID 19 Cases in First Sixty Four Days.

The seriousness of this pandemic becomes evident from Figs. 3 and 4. We observed that there was no day within the periods of the data collection that percentage of active / yet-to recover cases is less than 62. Meanwhile, the World Health Organization has listed Nigeria to be among thirteen (13) other African countries with high-risk for the spread of the virus [14].

Apart from the first measure of the Federal Government of Nigeria (FGN) to strengthen surveillance at Enugu, Lagos, Rivers, Kano and FCT International Airports on the 28th January 2020. The FGN on 31st January 2020, set up a group known as Coronavirus Preparedness Group to militate against its should incase it spread to Nigeria [30]. Other measures taken by FGN and various State Governments include the establishment of Presidential Task Force, suspension of all activities and religious gatherings, indefinite closure of public and private schools/institutions, extension of the travel ban to some countries, suspension of the operation of Nigerian Railway Corporation, closing of borders, shops, markets, motor parks, offices, restriction of intra-states and inter-states movements and travelling of the country. However, few states have recently relaxed the lockdown due to difficulties encountered by their citizens [30].

At the beginning of this pandemic, the unavailability of data has made forecasting and predictions a complicated task. A search for numerical models to forecast the epidemic evolution is underway [1,15]. Recent works provided forecasting models for confirmed COVID-19 cases for Germany, Italy, Japan, Canada, Russia, UK, Turkey and France [9,33]. Consequently, this paper attempts to model the daily cumulative reported COVID-19 confirmed cases, discharged cases and death cases using nine (9) statistical models to identify and utilize the best one for prediction.

2. Methodology

NCDC has been monitoring and reporting the cumulative and the new number of confirmed cases, number of discharged cases and recorded death since the first occurrence of COVID-19 in Nigeria. These data were collected daily on NCDC site [22] over a period over sixty-four days (2 months and three days) beginning from 27th February 2020 (first day of occurrence) until 30th April2020. The first discharged case occurred on the 19th March 2020 while the first death case occurred on 23rd March 2020. With the cumulative nature of the data, the number of cases at a time t depends on previous time t-1. We proposed the following curve estimation models with an autoregressive model of order 1 (AR(1)) in their simple, quadratic, cubic and quartic forms to study the pattern of the data so as to use the best one to forecast for the next two months, May and June 2020.

These Statistical Linear Regression Models are:

  • 1
    Classical Linear Regression Model: In the Simple Linear form, the model is defined as:
    yt=β0+β1t+μt (1)

The Quadratic Linear Regression Model is defined as:

yt=β0+β1t+β2t2+μt (2)

The Cubic Linear Regression Model: The model is defined as:

yt=β0+β1t+β2t2+β3t3+μt (3)

The Quartic Linear Regression Model: The model is defined as:

yt=β0+β1t+β2t2+β3t3+β4t4+μt (4)
  • 2
    Logarithm Linear Regression Model: In the Simple form, the model is defined as:
    yt=β0+β1loget+μt (5)

The Logarithm Quadratic Linear Regression Model is defined as:

yt=β0+β1loget+β2loget2+μt (6)

The Logarithm Cubic Linear Regression Model is defined as:

yt=β0+β1loget+β2loget2+β3loget3+μt (7)

The Logarithm Quartic Linear Regression Model is defined as:

yt=β0+β1loget+β2loget2+β3loget3+β4loget4+μt (8)
  • 3
    Inverse Linear Regression Model: The Simple form of the model is defined as:
    yt=β0+β11t+μt (9)

Similarly, the Quadratic, Cubic and Quartic forms are respectively defined as:

yt=β0+β11t+β21t2+μt (10)
yt=β0+β11t+β21t2+β31t3+μt (11)
yt=β0+β11t+β21t2+β31t3++β41t4μt (12)
  • 4
    Power Linear Regression Model: The Simple form of the model is defined as:
    yt=β0tβ1μtLogeyt=Logeβ0+β1Loget+Logeμt (13)

Similarly, the Quadratic, Cubic and Quartic forms are respectively defined as:

Logeyt=Logeβ0+β1Loget+β2Loget2+Logeμt (14)
Logeyt=Logeβ0+β1Loget+β2Loget2+β3Loget3+Logeμt (15)
Logeyt=Logeβ0+β1Loget+β2Loget2+β3Loget3+β4Loget4+Logeμt (16)
  • 5
    Compound Linear Regression Model: In the Simple form, the model is defined as:
    yt=β0β1tμtLogeyt=Logeβ0+tLogeβ1+Logeμt (17)

In the same way, the Quadratic, Cubic and Quartic forms are respectively defined as:

Logeyt=Logeβ0+tLogeβ1+t2Logeβ2+Logeμt (18)
Logeyt=Logeβ0+tLogeβ1+t2Logeβ2+t3Logeβ3+Logeμt (19)
Logeyt=Logeβ0+tLogeβ1+t2Logeβ2+t3Logeβ3+t4Logeβ4+Logeμt (20)
  • 6
    S– Curve Linear Regression Model: The simple form of the model is defined as:
    yt=eβ0+β11tμtLogeyt=β0+β11t+Logeμt (21)

In the same way, the Quadratic, Cubic and Quartic forms are respectively defined as:

Logeyt=β0+β11t+β21t2+Logeμt (22)
Logeyt=β0+β11t+β21t2+β31t3+Logeμt (23)
Logeyt=β0+β11t+β21t2+β31t3+β31t4+Logeμt (24)
  • 7
    Growth Linear Regression Model: The Simple form of the model is defined as:
    yt=eβ0+β1tμtLogeyt=β0+β1t+Logeμt (25)

Similarly, the Quadratic, Cubic, and Quartic forms are respectively defined as:

Logeyt=β0+β1t+β2t2+Logeμt (26)
Logeyt=β0+β1t+β2t2+β3t3+Logeμt (27)
Logeyt=β0+β1t+β2t2+β3t3+β4t4+Logeμt (28)
  • 8
    Exponential Linear Regression Model: The simple form of the model is defined as:
    yt=β0eβ1tμtLogeyt=Logeβ0+β1t+Logeμt (29)

In the same way, the forms of Quadratic, Cubic and Quartic are respectively defined as:

Logeyt=Logeβ0+β1t+β2t2+Logeμt (30)
Logeyt=Logeβ0+β1t+β2t2+β3t3+Logeμt (31)
Logeyt=Logeβ0+β1t+β2t2+β3t3+β4t4+Logeμt (32)
  • 9
    Logistic Linear Regression Model: The Simple form of the model is defined as:
    yt=1(1u+β0β1tμt)yt(1u+β0β1tμt)=11yt1u=β0β1tμtLoge(1yt1u)=Loge(β0)+Logeβ1t+Logeμt (33)

Similarly, the forms of Quadratic, Cubic and Quartic are respectively defined as:

Loge(1yt1u)=Loge(β0)+Logeβ1t+Logeβ2t2+Logeμt (34)
Loge(1yt1u)=Loge(β0)+Logeβ1t+Logeβ2t2+Logeβ3t3+Logeμt (35)
Loge(1yt1u)=Loge(β0)+Logeβ1t+Logeβ2t2+Logeβ3t3+Logeβ4t4+Logeμt (36)

where u is the upper boundary value, which must be a positive number greater than the largest value of y, the dependent variable.

It should be noted that model (5) to (36) are intrinsically linear regression model in that they are all linear in parameters; and that in all the models, the error terms μt=ρμt1+εt,εtN(0,σ2).

Also, the three variables: Cumulative COVID-19 Confirmed Cases (CCCOC), Cumulative COVID-19 Discharged Cases (CCDIC), and Cumulative COVID-19 Death Cases (CCDEC) were each considered as dependent variable in this study. The independent variable is time, t, and it takes values 1,2,…,64 for CCCOC; 1, 2,…,43 for CCDIC; and 1,2,…,39 for CCDEC. The model regression parameters are; β 0,β 1,β 2,β 3,β 4, and the auto-correlated parameter, ρ. The Ordinary Least Square (OLS) Estimator is the most common estimator to estimate the parameters of the Classical Linear Regression Model. The estimator is best linear unbiased estimator (BLUE) provided none of the assumptions of the model is violated [5,18,20]. In model (1) to (36), the assumption of independent error terms is not satisfied, leading to the problem of autocorrelated error terms. Using the OLS estimator in this kind of situation produces unbiased but inefficient estimates [3,4]. Researchers had developed estimators to handle linear regression Model with AR(1). These include the Cochrane Orcutt (CORC) estimator developed by Cochrane and Orcutt [7], Prais-Winsten (PW) developed by Prais and Winsten [25], and Hildreth-LU (HILU) estimator developed by Hildreth and Lu [12]. Reports show that the efficiency of these estimators depends on the structure of the explanatory variables [3,16]. Durbin [8] developed the Durbin Watson test statistic to test for the presence of AR(1) in a regression model after OLS estimation. Also in modeling (1) to (36), it is expected that the error terms are normally distributed. This may not always be true and as a result, hypothesis testing is affected. Saphiro-Wilk (SW) test developed by Shapiro and Wilk [26] and recently recommended by Kuranga et al. [17] is often being used to test for the assumption of normality of error terms; and the Least Absolute Deviation (LAD) estimator, a robust estimation method originated by KF Gauss and PS Laplace as mentioned by Taylor [27], is often recommended for handling parameter estimation of models with non-normal error terms or outliers [19,24]. These test statistics and estimators were also found useful in this study. Consequently in this study, we adopted these five (5) estimators and utilized proportion of variation explained by each estimator through their Adjusted coefficient of determination (Adj. R2) as a major criterion for a model to be used prediction and forecast purpose. For each of the four (4) forms in a particular model, a form was preferred if it has the highest Adj. R2 among the four (4) forms; and most preferred if it has the highest Adj. R2 among the preferred forms and hence called the best model. An estimator was considered best, among the estimators considered, if it gives highest Adj. R2 when applied to the best model. The best one and the competing ones were employed to produce forecast values. We adopted the [10], to achieve all these in this study.

3. Results and discussion

Results obtained from the analysis carried out on COVID-19 confirmed cases, discharged cases and death cases are presented as follows:

3.1. COVID-19 Confirmed Cases

We presented the form of the model that gave the highest value of adjusted coefficient of determination in Table 1 with some other relevant results.

Table 1.

Preferred form of the Nine Curve Estimation models with OLS estimator: COVID-19 Confirmed Cases.

Models Form Adj. R2 DW-test
SW-test
Value P-value Value P-value
Linear Quartic 0.9949 0.3204 4.783e-013*** 0.9695 0.1137
Logarithm Simple+ 0.3448 0.0312 1.798e-018*** 0.7721 1.37e-008***
Inverse Quartic 0.4137 0.112 1.798e-018*** 0.8302 4.32e-007***
Power Simple+ 0.7876 0.0848 1.798e-018*** 0.9156 0.0003***
Compound Quartic 0.9891 0.3768 5.459e-013*** 0.9087 0.0002***
S-Curve Quartic 0.9318 0.526 1.798e-010*** 0.9271 0.001***
Growth Quartic 0.9891 0.3768 5.459e-013*** 0.9087 0.0002***
Exponential Quartic 0.9891 0.3768 5.459e-013*** 0.9087 0.0002***
Logistic (u=2000) Quartic 0.9901 0.5327 1.798e-010*** 0.9097 0.0002***

NOTE: (i) Bold implies most preferred of the nine models.

(ii) + implies exact multicollinearity made other forms of the variable to be omitted.

(iii) The maximum COVID-19 confirmed cases for the period of study was1932.

From Table 1, we preferred the quartic form for all the models except under Logarithm and Inverse model. At these exceptions, the simple form is most preferred. However, they were removed by the software due to exact multicollinearity that exists among the independent variables. Also, the Durbin-Watson statistic shows that the models possess autocorrelation problems; and that the residuals are non-normal except in linear model. Thus, the quartic form linear regression model is identified as the most preferred model and hence classified as the best model. The parameter estimation of the most preferred model using OLS estimator is available in Table 2 . Result reveals that the data set has an autocorrelation problem (P-value of DW Statistic <0.01); and this was addressed using CORC, HILU, and PW estimators. All these estimators indicated that time factors have a significant contribution to the COVID-19 confirmed cases reported. However, their residuals were not normally distributed (P-value of Shapiro-Wilk <0.001); and this eventually brought in the idea of using the LAD estimator as an alternative estimator. Of all these estimators, the HILU estimator is best. We used HILU and LAD estimator for forecasting. The forecast values for May and June 2020 for the two (2) estimators are provided in Appendix A and pictorially presented in Fig. 5, Fig. 6. From the appendix and Figs. 5 and 6, it is expected that the increase in the next two (2) months shall be alarming; increase from 1,932 cases to 107,678 cases by the HILU estimator and from 1,932 cases to 64,070 cases by the LAD estimator. Therefore, there are needs for a tactical and robust approach for COVID-19 confirmed case number not to get out of control.

Table 2.

Results of the most preferred model with the estimators: COVID-19 Confirmed Cases.

Estimator Estimation Methods
OLS CORC HILU PW LAD
β^0 Estimate 82.7245 973.484 2202.75 26.5725 86.4171
Std. Error 22.9895 282.385 657.795 44.5336 53.7316
T-value 3.598 3.447 3.349 0.5967 1.608
P-value 0.0007*** 0.0011*** 0.0014*** 0.553 0.1131
β^1 Estimate -29.3698 -137.069 -236.525 -21.3927 -26.1172
Std. Error 4.8198 34.8878 65.3742 8.8188 11.6074
T-value -6.094 -3.929 -3.618 -2.426 -2.250
P-value 9.04e-08*** 0.0002*** 0.0006*** 0.0184** 0.0282**
β^2 Estimate 2.4042 7.09748 10.2454 2.1892 2.0848
Std. Error 0.29825 1.53021 2.4873 0.5831 0.7606
T-value 8.061 4.638 4.119 3.754 2.741
P-value 4.3e-011*** 2.1e-05*** 0.0001*** 0.0004*** 0.0081***
β^3 Estimate -0.0673 -0.1533 -0.1984 -0.0676 -0.0587
Std. Error 0.0069 0.028 0.0414 0.0137 0.0185
T-value -9.791 -5.483 -4.791 -4.926 -3.166
P-value 5.6e-014*** 9.5e-07*** 1.2e-05*** 7.1e-06*** 0.0024
β^4 Estimate 0.0007 0.001243 0.0015 0.0007 0.0006
Std. Error 5.2438e-05 0.0002 0.0003 0.0001 0.0001
T-value 13.00 6.885 5.920 6.861 4.103
P-value 5.7e-019*** 4.6e-09*** 1.8e-07*** 4.7e-09*** 0.0001***
ρ^ 0.889991 0.896892
Adj. R2 0.995909 0.994873 0.998779 0.998562 0.994562
DW Stat-value 0.3204 1.7542 1.8352 1.5832 0.3035
P-value 4.8e-013***
SW Stat-value 0.9695 0.8667 0.8484 0.9010
P-value 0.113699 6.3e-006*** 1.7e-006*** 8.7e-005***

Note: (i)** and *** imply significance at alpha = 0.05 and 0.01 respectively.

Fig. 5.

Fig 5:

COVID-19 Confirmed Cases for First Sixty Four Days and its forecast values for May and June, 2020: HILU Estimator.

Source:Appendix A

Fig. 6.

Fig 6:

COVID-19 Confirmed Cases for First Sixty Four Days and its forecast values for May and June, 2020: LAD Estimator.

Source:Appendix A

3.2. COVID-19 Discharged Cases

By the adjusted coefficient of determinations (Adj.R2) presented in Table 3 , we generally preferred the Quartic form of the models except in Logarithm and Power model. At these instances, the simple form is most preferred. The most preferred model is the Linear Regression Model even though those of Compound, Growth and Exponential compete favourably. Furthermore, we observed that all the models have an auto-regressive error of order one (P-value of DW<0.01) and that the residuals of the models, except Linear and Inverse, are not normally distributed (SW P-value<0.1).

Table 3.

Results of Preferred Model with OLS estimator in each of the Nine Curve Estimation models: COVID-19 Discharged Cases.

Models Form Adj.R2 DW-test
SW-test
Value P-value Value P-value
Linear Quartic 0.9925 0.6965 4.69e-009 *** 0.9724 0.3819
Logarithm Simple+ 0.5613 0.0656 7.029e-01*** 0.8965 0.001***
Inverse Quartic 0.7682 0.3143 1.798e-010*** 0.9733 0.4078
Power Simple+ 0.8857 0.2762 3.954e-012*** 0.8803 0.0003***
Compound Quartic 0.9918 1.448 0.005*** 0.9503 0.0613*
S-Curve Quartic 0.9826 1.172 0.0007*** 0.9128 0.0031***
Growth Quartic 0.9918 1.4478 0.005*** 0.0613 0.0613*
Exponential Quartic 0.9918 1.4478 0.005*** 0.0613 0.0613*
Logistic(u=350) Quartic 0.9916 1.3065 0.0010*** 0.9694 0.3003

NOTE: (i) Bold implies most preferred of the nine models.

(ii) + implies exalt multicollinearity made other forms of the variable to be omitted.

(iii) The maximum COVID-19 discharged cases for the period of study was 319.

The results of the parameter estimation of the most preferred model using OLS estimator and the other three (3) estimators are available in Table 4 . From the OLS results, the two observed problems are in the residual. These are autocorrelation problem (P-value of DW Statistic < 0.05) and problem of non-normality (P-value of SW Statistic < 0.1).

Table 4.

Results of the most preferred model with the estimators: COVID-19 Discharged Cases.

Estimator Estimation Methods
OLS CORC HILU PW LAD
β^0 Estimate 8.8236 87.4791 91.4391 7.13149 0.4897
Std. Error 9.3703 69.7831 72.8257 13.8694 5.2657
T-value 0.9417 1.254 1.256 0.5142 0.093
P-value 0.3523 0.2179 0.2171 0.6101 0.9264
β^1 Estimate -3.0062 -19.9917 -20.6673 -3.6692 0.6712
Std. Error 2.8784 14.5542 15.0457 4.403 2.1814
T-value -1.044 -1.374 -1.374 -0.8333 0.3077
P-value 0.3029 0.1778 0.1778 0.4099 0.76
β^2 Estimate 0.1972 1.4509 1.4928 0.344 -0.1777
Std. Error 0.2618 1.0268 1.0551 0.4165 0.2679
T-value 0.7532 1.413 1.415 0.8259 -0.6633
P-value 0.456 0.166 0.1655 0.414 0.5111
β^3 Estimate 0.0037 -0.0339 -0.035 -0.0036 0.0169
Std. Error 0.0089 0.0294 0.0301 0.0143 0.0117
T-value 0.4131 -1.154 -1.164 -0.2496 1.443
P-value 0.6819 0.2558 0.2517 0.8042 0.1572
β^4 Estimate -6.89e-05 0.0003 0.0003 3.28e-05 -0.0002
Std. Error 0.0001 0.0003 0.0003 0.0002 0.0002
T-value -0.687 1.101 1.114 0.2032 -1.39
P-value 0.4963 0.2779 0.2726 0.8401 0.1726
ρ^ 0.7133 0.719 0.6968
Adj. R2 0.992512 0.993402 0.993402 0.993328 0.9932
DW Stat-value 0.6965 2.0548 2.0669 1.9497 2.06048
P-value 4.7e-009***
SW Stat-value 0.9724 0.8717 0.8676 0.8622 0.8434
P-value 0.3819 0.0002*** 0.0002*** 0.0001*** 3.6e-005***

Note: (i) *** implies significance at alpha = 0.01.

Addressing these problems respectively with CORC, HILU and PW estimators; and the LAD estimator, the best estimators, are identified to be CORC and HILU estimators in that they have the highest Adj.R2.

Meanwhile, the effect of time as the independent variable is not significant in all the estimators (P-value >0.1). It might be due to the inevitable multicollinearity problem. Furthermore, the non-normality of the residuals of the autocorrelation problem handling estimators necessitated the use of LAD as an alternative estimator. Thus, we adopted the CORC, HILU and the LAD estimators for forecasting and their forecast values, in Appendix B, are pictorially presented in logarithm form in Fig. 7, Fig. 8, Fig. 9. If existing measures and structures are maintained and improved upon, the recovery cases will increase from 319 to about 13,000 cases. However, the LAD estimator reveals a situation whereby, instead of having recovery cases increasing, it may be static since the cumulative cases can't decrease.

Fig. 7.

Fig 7:

COVID-19 Discharged Cases for First Sixty Four Days and its forecast values for May and June, 2020: CORC Estimator.

Source:Appendix B

Fig. 8.

Fig 8:

COVID-19 Discharged/ Recovery Cases for First Sixty Four Days and its forecast values for May and June, 2020: HILU Estimator.

Fig. 9.

Fig 9:

COVID-19 Discharged Cases for First Sixty Four Days and its forecast values for May and June, 2020: LAD Estimator.

3.3. COVID-19 Death Cases

We employed the OLS estimator to analyse the nine statistical models in Table 5. From the table, the preferred form of the model is generally Quartic except in Logarithm and Power where exact multicollinearity prevented others forms to be used in the analysis. All these preferred models have autocorrelation problem (P-value of DW Statistic < 0.01); only the residuals of Logarithm, Inverse, Power and Logistic do not follow normal distribution (P-value of SW Statistic < 0.1). Thus, the most preferred model is the Linear Regression Model with Quartic form having explained 99.53% of the variation in COVID-19 death cases.

Table 5.

Results of Preferred Model with OLS estimator in each of the Nine Curve Estimation models: COVID-19 Death Cases.

Models Form Adj. R2 DW-test
SW- test
Value P-value Value P-value
Linear Quartic 0.9953 1.3563 0.0021*** 0.9581 0.153984
Logarithm Simple+ 0.4988 0.0703 3.63e-011*** 0.8552 0.0001***
Inverse Quartic 0.6856 0.2494 1.798e-015*** 0.9449 0.0553*
Power Simple+ 0.842 0.2441 1.798e-015*** 0.945971 0.0602*
Compound Quartic 0.9896 1.6627 0.0345106** 0.97267 0.4513
S-Curve Quartic 0.9518 0.6449 7.704e-008*** 0.9751 0.5301
Growth Quartic 0.9896 1.6627 0.0345106** 0.97267 0.4513
Exponential Quartic 0.9896 1.6627 0.0345106** 0.97267 0.4513
Logistic(u=60) Quartic 0.9824 1.2658 0.00074*** 0.941344 0.0422**

NOTE: (i) Bold implies most preferred of the nine models.

(ii) + implies exact multicollinearity made other forms of the variable to be omitted.

(iii) The cumulative death cases recorded within the period was 58.

The parameter estimation of the most preferred model using OLS estimator is available in Table 6. From the results, there is the presence of autocorrelation. Addressing the autocorrelation problem with CORC, HILU and PW only produced estimates slightly better than the OLS. Moreover, the quartic time variable only has a significant impact (P-value<0.1) on cumulative of COVID-19 death cases using the OLS and PW estimators. Consequently, it became necessary to adopt the LAD estimator, a robust estimation method for comparison. Eventually, we employed the PW and LAD estimators for forecasting because of their performance. The results are provided in Appendix C and shown in Fig. 10, Fig. 11. The forecast results for the next two months revealed that death cases would increase from 58 to 1800 and 2567, respectively, with the use of LAD and PW estimator. Moreover, forecast values from LAD estimator indicate a situation whereby cumulative COVID-19 death cases may be static since it can't decrease. This increase in death cases is alarming and therefore, effective planning and action are required to be able to avert this incidence.

Table 6.

Results of the most preferred model with the estimators: COVID-19 Death Cases.

Estimator Estimation Methods
OLS CORC HILU PW LAD
β^0 Estimate 1.1464 1.9173 1.9189 1.3449 1.0711
Std. Error 1.0108 2.447 2.4494 1.2579 0.8036
T-value 1.134 0.7835 0.7834 1.069 1.333
P-value 0.2647 0.4389 0.439 0.2925 0.1915
β^1 Estimate -0.117 -0.3897 -0.3902 -0.2352 -0.0958
Std. Error 0.3407 0.7087 0.7093 0.43189 0.3297
T-value -0.3434 -0.5499 -0.5502 -0.5446 -0.2907
P-value 0.7334 0.5861 0.5859 0.5896 0.7731
β^2 Estimate 0.0308 0.0591 0.0592 0.0462 0.0252
Std. Error 0.034 0.0639 0.0639 0.0437 0.0384
T-value 0.9052 0.9258 0.926 1.058 0.6576
P-value 0.3717 0.3613 0.3612 0.2973 0.5152
β^3 Estimate -0.0009 -0.002 -0.002 -0.0015 -0.0005
Std. Error 0.0013 0.0022 0.0022 0.0016 0.0016
T-value -0.6694 -0.8767 -0.8770 -0.9354 -0.2741
P-value 0.5078 0.3870 0.3868 0.3562 0.7857
β^4 Estimate 2.7e-05 4.13e-05 4.13e-05 3.66e-05 2.007e-05
Std. Error 1.56e-05 2.63e-05 2.63e-05 2.03e-05 2.323e-05
T-value 1.717 1.569 1.569 1.801 0.8643
P-value 0.095* 0.1262 0.1262 0.0805* 0.3935
ρ^ 0.347 0.347 0.3389
Adj. R2 0.995342 0.995638 0.9956 0.995737 0.995047
DW Stat-value 1.3563 1.7146 1.7151 1.7056 1.23802
P-value 0.0021***
SW Stat-value 0.9581 0.9576 0.9576 0.9571 0.918514
P-value 0.15398 0.1585 0.1581 0.1428 0.0078***

Note: (i)*and *** imply significance at alpha = 0.1 and 0.01respectively.

Fig. 10.

Fig 10:

Death COVID-19 Cases for First Sixty Four Days and its forecast values for May and June, 2020: PW Estimator.

Source:Appendix C

Fig. 11.

Fig 11:

Death COVID-19 Cases for First Sixty Four Days and its forecast values for May and June, 2020: LAD Estimator.

Source:Appendix C

3.4. Models Assessment with Observed/True values (TV)

The COVID-19 data for the first five days in May 2020 were further collected and compared with the forecast value (FV). These values are presented as follows in Table 7. From the table, we observed that the observed original values are in agreement with the forecast values except on few cases especially on the fifth day. Notwithstanding, the actual values and forecast values of LAD estimator are most frequently in agreement; and so, we recommend the estimator.

Table 7.

Comparison of forecast values with the true values.

Image, table 7

4. Conclusion

This study provided the statistical curve model for the daily cumulative reported COVID-19 confirmed cases, discharged cases and death cases in Nigeria using data collected by the Nigeria Centre for Disease Control (NCDC) for the first sixty-four days of the incidence using five estimation methods. It further identified the best model for each of the variables and used the same to forecast for May and June 2020. Comparing the actual values with the forecast ones in the first five days of May 2020, we recommended the forecast values of the LAD estimator because of its precision. The forecast values are alarming and therefore require serious planning and intervention by the Government to avoid the pandemic becoming a huge health problem for the country.

CRediT authorship contribution statement

Kayode Ayinde: Conceptualization, Methodology, Formal analysis, Software, Writing - original draft. Adewale F. Lukman: Conceptualization, Methodology, Resources, Writing - original draft. Rauf I. Rauf: Conceptualization, Methodology, Resources, Supervision. Olusegun O. Alabi: Conceptualization, Methodology, Supervision. Charles E. Okon: Conceptualization, Methodology, Writing - original draft. Opeyemi E. Ayinde: Conceptualization, Methodology, Resources.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Forecast vales of COVID-19 confirmed cases for May and June, 2020

HILU LAD
99% C.I. 99% C.I.
DATE F.V L.V U.V F.V L.V U.V
1/5/2020 2134.49 2090.91 2178.07 1997.93 1776.17 2219.7
2/5/2020 2355.38 2297.04 2413.71 2177.03 1912.4 2441.67
3/5/2020 2595.81 2528.02 2663.59 2369.03 2055.6 2682.45
4/5/2020 2856.95 2782.53 2931.37 2574.54 2206.24 2942.84
5/5/2020 3140.03 3060.75 3219.31 2794.21 2364.7 3223.72
6/5/2020 3446.29 3363.36 3529.22 3028.69 2531.36 3526.02
7/5/2020 3777.02 3691.3 3862.73 3278.65 2706.58 3850.72
8/5/2020 4133.53 4045.68 4221.38 3544.77 2890.7 4198.84
9/5/2020 4517.19 4427.68 4606.7 3827.75 3084.07 4571.43
10/5/2020 4929.38 4838.58 5020.18 4128.3 3287.02 4969.58
11/5/2020 5371.54 5279.72 5463.35 4447.15 3499.89 5394.41
12/5/2020 5845.12 5752.51 5937.73 4785.03 3723.02 5847.05
13/5/2020 6351.63 6258.4 6444.86 5142.71 3956.74 6328.69
14/5/2020 6892.6 6798.88 6986.32 5520.96 4201.4 6840.51
15/5/2020 7469.61 7375.5 7563.71 5920.55 4457.35 7383.75
16/5/2020 8084.25 7989.84 8178.66 6342.29 4724.93 7959.65
17/5/2020 8738.17 8643.52 8832.83 6787 5004.49 8569.5
18/5/2020 9433.05 9338.21 9527.9 7255.5 5296.4 9214.59
19/5/2020 10170.6 10075.6 10265.6 7748.63 5601.01 9896.25
20/5/2020 10952.6 10857.5 11047.7 8267.26 5918.7 10615.8
21/5/2020 11780.7 11685.5 11876 8812.26 6249.82 11374.7
22/5/2020 12656.9 12561.7 12752.2 9384.52 6594.76 12174.3
23/5/2020 13583 13487.7 13678.4 9984.93 6953.9 13016
24/5/2020 14560.9 14465.5 14656.3 10614.4 7327.62 13901.2
25/5/2020 15592.4 15497 15687.8 11273.9 7716.32 14831.5
26/5/2020 16679.6 16584.2 16775.1 11964.4 8120.38 15808.4
27/5/2020 17824.5 17729 17920 12686.8 8540.2 16833.3
28/5/2020 19029.1 18933.6 19124.6 13442 8976.2 17907.8
29/5/2020 20295.4 20199.9 20390.9 14231.2 9428.77 19033.6
30/5/2020 21625.6 21530.1 21721.1 15055.2 9898.34 20212.1
31/5/2020 23021.8 22926.2 23117.3 15915.1 10385.3 21445
1/6/2020 24486.2 24390.6 24581.7 16812 10890.1 22733.9
2/6/2020 26020.9 25925.4 26116.5 17746.9 11413.2 24080.6
3/6/2020 27628.4 27532.8 27723.9 18720.8 11955 25486.7
4/6/2020 29310.7 29215.2 29406.3 19734.9 12516 26953.9
5/6/2020 31070.3 30974.8 31165.9 20790.2 13096.5 28483.9
6/6/2020 32909.5 32814 33005.1 21887.8 13697 30078.7
7/6/2020 34830.7 34735.2 34926.3 23028.9 14318.1 31739.8
8/6/2020 36836.4 36740.8 36931.9 24214.6 14960 33469.2
9/6/2020 38928.8 38833.3 39024.4 25446.1 15623.5 35268.7
10/6/2020 41110.7 41015.2 41206.3 26724.4 16308.7 37140.1
11/6/2020 43384.5 43288.9 43480.1 28050.9 17016.4 39085.3
12/6/2020 45752.8 45657.2 45848.3 29426.6 17746.9 41106.3
13/6/2020 48218.1 48122.5 48313.7 30852.8 18500.7 43205
14/6/2020 50783.2 50687.6 50878.7 32330.8 19278.3 45383.3
15/6/2020 53450.6 53546.2 53355.1 33861.7 20080.2 47643.3
16/6/2020 56223.2 56127.6 56318.8 35446.9 20906.9 49986.9
17/6/2020 59103.6 59008 59199.2 37087.6 21758.9 52416.2
18/6/2020 62094.7 61999.1 62190.2 38785 22636.8 54933.2
19/6/2020 65199.2 65103.6 65294.7 40540.5 23541 57540
20/6/2020 68420 68324.4 68515.6 42355.4 24472 60238.8
21/6/2020 71760 71664.4 71855.6 44231 25430.4 63031.6
22/6/2020 75222.1 75126.6 75317.7 46168.7 26416.8 65920.6
23/6/2020 78809.4 78713.8, 78904.9 48169.8 27431.5 68908
24/6/2020 82524.7 82429.1 82620.2 50235.6 28475.3 71996
25/6/2020 86371.1 86275.5 86466.6 52367.7 29548.6 75186.8
26/6/2020 90351.6 90256.1 90447.2 54567.3 30652 78482.7
27/6/2020 94469.5 94373.9 94565.1 56836 31786 81886
28/6/2020 98727.8 98632.2 98823.3 59175 32951.2 85398.9
29/6/2020 103130 103034 103225 61585.9 34148.1 89023.8
30/6/2020 107678 107583 107774 64070.2 35377.4 92763

Appendix B. Forecast vales of COVID-19 confirmed cases for May and June, 2020

CORC HILU LAD
99% C.I. 99% C.I. 99% C.I.
DATE F.V L.V U.V F.V L.V U.V F.V L.V U.V
1/5/2020 337.634 315.966 359.302 337.826 316.158 359.494 291.609 198.702 384.516
2/5/2020 358.013 331.397 384.628 358.406 331.718 385.094 298.421 184.439 412.404
3/5/2020 380.186 351.378 408.994 380.802 351.858 409.747 304.034 165.471 442.596
4/5/2020 404.237 374.375 434.098 405.109 375.065 435.154 308.304 141.456 475.152
5/5/2020 430.275 399.892 460.659 431.445 400.847 462.043 311.085 112.018 510.152
6/5/2020 458.431 427.786 489.077 459.948 429.068 490.828 312.225 76.7531 547.696
7/5/2020 488.853 458.075 519.631 490.772 459.748 521.797 311.566 35.2337 587.897
8/5/2020 521.703 490.858 552.548 524.088 492.989 555.188 308.945 -12.9903 630.879
9/5/2020 557.155 526.276 588.035 560.076 528.938 591.214 304.193 -68.3885 676.775
10/5/2020 595.396 564.499 626.293 598.928 567.77 630.086 297.138 -131.449 725.726
11/5/2020 636.621 605.715 667.526 640.848 609.68 672.016 287.6 -202.677 777.878
12/5/2020 681.035 650.125 711.946 686.048 654.874 717.221 275.395 -282.594 833.385
13/5/2020 728.855 697.942 759.767 734.748 703.572 765.925 260.333 -371.74 892.407
14/5/2020 780.301 749.387 811.215 787.181 756.003 818.358 242.219 -470.669 955.107
15/5/2020 835.606 804.692 866.521 843.583 812.405 874.762 220.853 -579.951 1021.66
16/5/2020 895.01 864.095 925.924 904.204 873.025 935.382 196.029 -700.172 1092.23
17/5/2020 958.76 927.845 989.674 969.297 938.118 1000.48 167.535 -831.934 1167
18/5/2020 1027.11 996.196 1058.03 1039.13 1007.95 1070.31 135.157 -975.853 1246.17
19/5/2020 1100.33 1069.41 1131.24 1113.97 1082.79 1145.15 98.6706 -1132.56 1329.9
20/5/2020 1178.68 1147.77 1209.59 1194.1 1162.92 1225.28 57.8505 -1302.71 1418.41
21/5/2020 1262.45 1231.53 1293.36 1279.8 1248.62 1310.98 12.4636 -1486.96 1511.89
22/5/2020 1351.92 1321 1382.83 1371.38 1340.2 1402.56 -37.7276 -1685.99 1610.53
23/5/2020 1447.39 1416.47 1478.3 1469.14 1437.96 1500.32 -92.9663 -1900.49 1714.55
24/5/2020 1549.15 1518.24 1580.07 1573.39 1542.21 1604.56 -153.501 -2131.17 1824.17
25/5/2020 1657.53 1626.62 1688.45 1684.44 1653.26 1715.62 -219.585 -2378.75 1939.58
26/5/2020 1772.84 1741.92 1803.75 1802.64 1771.46 1833.81 -291.478 -2643.98 2061.02
27/5/2020 1895.39 1864.48 1926.31 1928.3 1897.12 1959.48 -369.445 -2927.61 2188.72
28/5/2020 2025.54 1994.62 2056.45 2061.79 2030.61 2092.97 -453.755 -3230.4 2322.89
29/5/2020 2163.61 2132.7 2194.53 2203.45 2172.27 2234.62 -544.682 -3553.14 2463.77
30/5/2020 2309.96 2279.05 2340.88 2353.63 2322.45 2384.81 -642.509 -3896.63 2611.61
31/5/2020 2464.94 2434.03 2495.86 2512.72 2481.54 2543.9 -747.52 -4261.68 2766.64
1/6/2020 2628.92 2598.01 2659.84 2681.08 2649.9 2712.25 -860.007 -4649.13 2929.12
2/6/2020 2802.27 2771.36 2833.19 2859.09 2827.91 2890.27 -980.265 -5059.82 3099.29
3/6/2020 2985.37 2954.46 3016.29 3047.16 3015.98 3078.34 -1108.6 -5494.6 3277.4
4/6/2020 3178.61 3147.69 3209.52 3245.68 3214.5 3276.86 -1245.31 -5954.35 3463.73
5/6/2020 3382.38 3351.46 3413.29 3455.05 3423.87 3486.23 -1390.72 -6439.97 3658.53
6/6/2020 3597.08 3566.16 3627.99 3675.7 3644.52 3706.88 -1545.14 -6952.36 3862.07
7/6/2020 3823.13 3792.21 3854.04 3908.05 3876.87 3939.23 -1708.89 -7492.43 4074.64
8/6/2020 4060.94 4030.02 4091.85 4152.53 4121.35 4183.7 -1882.31 -8061.12 4296.49
9/6/2020 4310.94 4280.02 4341.85 4409.57 4378.39 4440.75 -2065.73 -8659.38 4527.93
10/6/2020 4573.57 4542.65 4604.48 4679.64 4648.46 4710.81 -2259.48 -9288.18 4769.22
11/6/2020 4849.26 4818.34 4880.17 4963.17 4931.99 4994.35 -2463.91 -9948.5 5020.68
12/6/2020 5138.46 5107.55 5169.38 5260.64 5229.47 5291.82 -2679.38 -10641.3 5282.58
13/6/2020 5441.64 5410.72 5472.55 5572.53 5541.35 5603.71 -2906.23 -11367.7 5555.23
14/6/2020 5759.25 5728.34 5790.17 5899.3 5868.12 5930.47 -3144.82 -12128.6 5838.94
15/6/2020 6091.78 6060.86 6122.69 6241.44 6210.26 6272.62 -3395.53 -12925.1 6134.02
16/6/2020 6439.69 6408.77 6470.6 6599.46 6568.28 6630.64 -3658.73 -13758.2 6440.76
17/6/2020 6803.48 6772.56 6834.39 6973.85 6942.67 7005.03 -3934.78 -14629.1 6759.51
18/6/2020 7183.64 7152.72 7214.55 7365.13 7333.95 7396.31 -4224.08 -15538.7 7090.57
19/6/2020 7580.67 7549.76 7611.59 7773.81 7742.63 7804.99 -4527 -16488.3 7434.27
20/6/2020 7995.1 7964.18 8026.01 8200.43 8169.25 8231.61 -4843.95 -17478.8 7790.94
21/6/2020 8427.43 8396.51 8458.34 8645.51 8614.34 8676.69 -5175.32 -18511.6 8160.92
22/6/2020 8878.19 8847.27 8909.1 9109.61 9078.43 9140.79 -5521.52 -19587.6 8544.55
23/6/2020 9347.92 9317 9378.83 9593.28 9562.1 9624.46 -5882.95 -20708.1 8942.17
24/6/2020 9837.15 9806.24 9868.07 10097.1 10065.9 10128.2 -6260.02 -21874.2 9354.13
25/6/2020 10346.4 10315.5 10377.4 10621.5 10590.4 10652.7 -6653.16 -23087.1 9780.77
26/6/2020 10876.4 10845.4 10907.3 11167.3 11136.1 11198.5 -7062.79 -24348 10222.5
27/6/2020 11427.4 11396.5 11458.4 11734.9 11703.7 11766.1 -7489.34 -25658.3 10679.6
28/6/2020 12000.3 11969.4 12031.2 12324.9 12293.7 12356.1 -7933.25 -27019 11152.5
29/6/2020 12595.5 12564.6 12626.4 12938 12906.8 12969.2 -8394.95 -28431.4 11641.5
30/6/2020 13213.6 13182.7 13244.5 13574.7 13543.5 13605.9 -8874.9 -29896.8 12147

Appendix C. Forecast vales of COVID-19 death cases for May and June, 2020

PW LAD
99% C.I. 99% C.I.
DATE F.V L.V U.V F.V L.V U.V
1/5/2020 62.1187 59.316 64.9214 60.1645 50.4 69.9291
2/5/2020 67.4243 64.4651 70.3836 65.2303 53.0899 77.3706
3/5/2020 73.4412 70.4645 76.4179 70.6406 55.714 85.5673
4/5/2020 80.0263 77.0476 83.005 76.4128 58.2577 94.568
5/5/2020 87.1501 84.1712 90.1291 82.5647 60.7041 104.425
6/5/2020 94.8222 91.8433 97.8011 89.1144 63.0345 115.194
7/5/2020 103.066 100.087 106.045 96.0807 65.228 126.933
8/5/2020 111.909 108.93 114.888 103.483 67.2626 139.703
9/5/2020 121.384 118.405 124.363 111.341 69.1148 153.566
10/5/2020 131.521 128.542 134.5 119.674 70.7597 168.588
11/5/2020 142.355 139.376 145.334 128.504 72.1715 184.836
12/5/2020 153.92 150.941 156.899 137.851 73.3229 202.379
13/5/2020 166.25 163.271 169.229 147.737 74.1857 221.289
14/5/2020 179.383 176.404 182.362 158.185 74.7306 241.639
15/5/2020 193.354 190.375 196.333 169.216 74.9271 263.506
16/5/2020 208.202 205.223 211.181 180.855 74.7436 286.966
17/5/2020 223.965 220.986 226.944 193.123 74.1476 312.099
18/5/2020 240.683 237.704 243.662 206.047 73.1054 338.988
19/5/2020 258.396 255.417 261.375 219.649 71.5823 367.715
20/5/2020 277.145 274.166 280.124 233.955 69.5425 398.367
21/5/2020 296.974 293.995 299.953 248.99 66.9493 431.031
22/5/2020 317.924 314.945 320.903 264.781 63.7646 465.798
23/5/2020 340.04 337.061 343.019 281.354 59.9497 502.758
24/5/2020 363.366 360.387 366.345 298.735 55.4646 542.006
25/5/2020 387.949 384.97 390.928 316.953 50.2682 583.638
26/5/2020 413.834 410.855 416.813 336.035 44.3185 627.751
27/5/2020 441.07 438.091 444.049 356.009 37.5725 674.445
28/5/2020 469.705 466.726 472.683 376.904 29.986 723.822
29/5/2020 499.787 496.808 502.766 398.75 21.5138 775.985
30/5/2020 531.367 528.388 534.346 421.576 12.1098 831.042
31/5/2020 564.496 561.517 567.475 445.413 1.7266 889.099
1/6/2020 599.225 596.246 602.204 470.291 -9.684 950.266
2/6/2020 635.608 632.63 638.587 496.242 -22.1713 1014.66
3/6/2020 673.699 670.72 676.678 523.297 -35.7858 1082.38
4/6/2020 713.55 710.571 716.529 551.489 -50.5788 1153.56
5/6/2020 755.219 752.24 758.198 580.851 -66.6028 1228.3
6/6/2020 798.76 795.781 801.739 611.415 -83.9112 1306.74
7/6/2020 844.232 841.253 847.211 643.215 -102.559 1388.99
8/6/2020 891.692 888.713 894.671 676.285 -122.601 1475.17
9/6/2020 941.199 938.22 944.178 710.66 -144.094 1565.41
10/6/2020 992.813 989.834 995.792 746.376 -167.096 1659.85
11/6/2020 1046.59 1043.62 1049.57 783.467 -191.665 1758.6
12/6/2020 1102.61 1099.63 1105.58 821.969 -217.862 1861.8
13/6/2020 1160.91 1157.93 1163.89 861.92 -245.747 1969.59
14/6/2020 1221.56 1218.58 1224.54 903.357 -275.381 2082.09
15/6/2020 1284.64 1281.66 1287.62 946.316 -306.828 2199.46
16/6/2020 1350.2 1347.22 1353.18 990.836 -340.152 2321.82
17/6/2020 1418.31 1415.33 1421.28 1036.96 -375.417 2449.33
18/6/2020 1489.03 1486.05 1492.01 1084.71 -412.689 2582.11
19/6/2020 1562.44 1559.46 1565.42 1134.15 -452.036 2720.33
20/6/2020 1638.6 1635.62 1641.58 1185.3 -493.526 2864.13
21/6/2020 1717.58 1714.61 1720.56 1238.21 -537.226 3013.65
22/6/2020 1799.46 1796.48 1802.44 1292.92 -583.209 3169.05
23/6/2020 1884.3 1881.32 1887.28 1349.47 -631.544 3330.49
24/6/2020 1972.18 1969.2 1975.15 1407.9 -682.304 3498.11
25/6/2020 2063.16 2060.18 2066.14 1468.26 -735.562 3672.08
26/6/2020 2157.32 2154.35 2160.3 1530.58 -791.393 3852.56
27/6/2020 2254.75 2251.77 2257.73 1594.92 -849.871 4039.71
28/6/2020 2355.5 2352.52 2358.48 1661.31 -911.074 4233.69
29/6/2020 2459.67 2456.69 2462.64 1729.79 -975.078 4434.66
30/6/2020 2567.32 2564.34 2570.29 1800.42 -1041.96 4642.81

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