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Epidemiological Analysis and Time Prediction Models of Coronavirus (COVID-19/SARS-CoV-2) Spread in Selected Epicentres around the World: Nigeria as a Case Study
Favour Deborah Adaugo Onyelowe 1, Kennedy Onyelowe 2
1 Ebonyi State University
P. M. B. 053, Abakaliki, Nigeria
2 Kampala International University
Box 20000, Ggaba Road, Kansanga, Kampala, Uganda
Abstract. The spread of coronavirus disease (COVID-19/SARS-CoV-2) in Nigeria from index to community cases is becoming alarming that what the future holds should be brought to bear. An analytical study and time prediction model have been conducted on the epidemiological spread of coronavirus (COVID-19/SARS-CoV-2) with data collected from records of selected epicentres in Nigeria. The data was collected between March 1 and May 31, 2020. It can be shown that the highest daily infection in March was recorded on the 28th with 32 infections while the highest fatality rate was recorded on 24th with a rate of 2.3% and recorded daily infection of 10. As at the 31st, a total number of 139 confirmed cases were recorded in Nigeria with a fatality and discharge rates of 1.4 and 6.5% respectively. It can be deduced that the highest daily infection in Nigeria in April was recorded on 30th, with daily infection of 204 confirmed cases. The highest discharge rate of 34.4% was recorded on 16th, with a fatality rate of 2.9% while the highest fatality rate of April was 3.5% recorded on 18th, which has a discharge rate of 30.6% and a daily infection record of 49. As of April 30, 2020, Nigeria had recorded a total of 1932 confirmed cases with 58 deaths. It can also be deduced that the highest daily infection in Nigeria in May was recorded on 30th, with daily infection of 553 confirmed cases. It can also be observed that the highest discharge and fatality rates for May 2020 are 29.6% and 3.6% recorded on 31st and 2nd respectively. As of May 31, 2020, the total infection stood at 10162 confirmed cases and there seems to be a continuing upward trajectory for the situation under investigation. It can also be observed that the rate of discharged cases continued to surpass those of the fatality for the months of investigation. No doubts that the COVID-19/SARS-CoV-2 was first recorded in the Ogun State of Nigeria, but Lagos state has surpassed both the daily infections and the cumulative infections for the country. With collected data, MLR simple linear regression extension was used to estimate an outcome or target variable based on two or more independent variables. The variables which are the three months data collected from daily infections, totally confirmed case, total deaths and total discharged cases between March 1, 2020, and May 31, 2020, were used to propose regression equations for the prediction of the cases under study for anytime period.
Keywords: Coronavirus; Time Prediction Model; Epidemiological Spread; Epicentre of Viral Infection; Confirmed Cases; Discharged Cases; Intravascular Coagulation; Biomedicine; Pneumonia; Symptomatic Infections; Asymptomatic Infections; Community Infections.
DOI: 10.22178/pos.60-4
LCC Subject Category: WC500-593
Received 26.06.2020 Accepted 28.07.2020 Published online 31.07.2020
Corresponding Author: Kennedy Onyelowe [email protected]
© 2020 The Authors. This article is licensed under a Creative Commons Attribution 4.0 License IOL.
INTRODUCTION
Coronavirus disease is a potentially severe acute respiratory infection caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). According to WHO, 44 cases of pneumonia of unknown microbial etiology entangled with Wuhan city, Hubei province china on 31 December 2019 [12, 5]. According to [2] 87 % of confirmed cases were aged 30 to 79 years, 1 % were aged 80 years or older. Approximately 51 % of patients were male and 49 % were female. In the US older patients aged greater than or equal to 65 years accounted for 31 % of all cases, 45 % of hospi-talizations, 53 % of intensive care unit admissions and 80 % of deaths, with the highest inci-
dence of severe outcomes in patients aged greater than or equal to 85 years [4]. According to findings, weather conditions may influence the transmission of COVID-19, with cold and dry conditions appearing to increase transmission, and warm and humid conditions reducing the risk of cases and deaths in some countries [11]. Most common symptoms of COVID-19 include fever, cough, dyspnea, myalgia, fatigue, altered sense of taste/smell, while less common symptoms include sore throat, confusion, dizziness, headache, rhinorrhea, or nasal congestion, hemoptysis, chest pain, conjunctivitis, cutaneous manifestations [14] (Figure 1).
Figure 1 - COVID-19/SARS-CoV-2 origin, infectious and effect factors on humans [8]
Approximately 90 % of patients present with more than one symptom, and 15 % of patients present with fever, cough, and dyspnea. On January 7, a novel coronavirus was identified by the Chinese centre of Disease Control and Prevention (CDC) from the throat swab sample of a patient and was subsequently named 2019-nCoV by WHO [12, 5]. According to [8], COVID-19 can cause multiple system infections in respiratory tract infections in humans, such as Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS). The following research was carried out in china on patients with SARS-CoV-2 according to age. 10 % of these patients were less than or equal to 39 years old, 22 % of these patients were 40-49 years old, 30 % - 50-59 years old, 22 % - 60-69 years old, 15 % - greater than or equal to 70 years old. The same research was carried out according to sex. There were 32 % of female patients and 68 % of male patients.
Epicentres/severely affected countries on the epidemiological spread of COVID-19/SARS-CoV-2 across continents. According to [10] between late February and the early march of 2020, the individual data of laboratory-confirmed cases of COVID-19 were retrieved from 10728 publicly available reports released by the health authorities of and outside china and from 1790 publications identified in PubMed and CNKI. According to [13], Europe has become the new epicentre of the COVID-19 pandemic. Italy was initially the county hit the hardest by far Spain, the Netherlands and other followed. France and Germany had experienced the first importation of cases already in January. On 10 March, the total number of fatalities in Italy exceeded 3,000, topping the total number of reported fatalities in china. Outside Europe, Iran faced a rapid surge of COVID-19 followed by the exportation of cases mostly to countries in the Middle East [3]. The United States in North America and Europe in the United Kingdom emerged as new epicentre with 124,655 cases plus 1,019 fatalities respectively, reported by 29 March [6]. Recently increasing case numbers have also been seen in Africa and Asian countries outside China [9].
The novel coronavirus has two modes of transmission which includes droplets with a particle size of 5-10 [im and transmissible distance of <3 ft. SARS-CoV-2 survives on surface materials like copper with a half-life of 1 hour and a total time of detectability of 8 hours, cardboard with a halflife of 3 hours and a total time of detectability of
48 hours, and plastic with a half-life of 7 hours and a total time of detectability of 72 hours. SARS (Severe Acute Respiratory Syndrome) started onset November 2002 [9]. Its last known case was 2004. MERS (Middle East Respiratory Syndrome) started onset 2012 in Saudi Arabia. Saudi Arabia outbreak in 2004 recorded 402 cases and 27 % mortality. South Korea outbreak in 2015 recorded 105 cases and 17% mortality. United States outbreak recorded 2 cases in 2014, including health care workers travelling from Saudi Arabia [15].
COVID-19 Timeline showed that from December 31-January 3, 2020, 44 cases of pneumonia of unknown cause was reported in Wuhan [3, 13]. On January 7, 2020, new coronavirus was identified. On January 13, 2020: Thailand, on January 15, 2020: Japan, on January 20, 2020: South Korea, on January 23, 2020: the United States and on April 4, 2020, worldwide cases surpassed 1 million [10].
The novel COVID-19 was declared a global pandemic by the World Health Organization (WHO) on the 11 March 2020. The WHO has reported an incubation period for COVID-19 between 2 and 10 days. However, according to research incubation period can last for longer than two weeks. However, according to [3, 1], cases reported in china according to location and patients include; Mainland china - 364 (72 %), Beijing -133 (26 %), Shaanxi - 87 (17 %), Hubei - 41 (8 %), Tianjin - 22 (4 %), Yunnan - 19 (4 %). And the mortality rate around the world vary by country as of the first week of April 2020 as follows; China - 4.0 %, South Korea - 1.8 %, Italy -12.5 %, Spain - 9.7 %, Iran - 6.2 %, United States - 3.2 %, worldwide - 5.6 %. As of April 7th 2020, 1,353,361 confirmed cases worldwide, 79,235 confirmed deaths, 212 counties, areas or territories with cases.
Epicentres/severely affected states on the epidemiological spread of COVID-19/SARS-CoV-2 Nigeria. The report has shown that coronavirus is one of the major pathogens that mainly targets the human respiratory system [7]. The first case of COVID-19 was reported in December 2019. From December 18, 2019, through December 29, 2019, five patients were hospitalized with acute respiratory distress syndrome. By January 2, 2020, 41 admitted hospital patients had been identified as having laboratory-confirmed COVID-19 infections, less than half of the patients had underlying diseases including diabetes, hypertension,
and cardiovascular diseases. Different bodies including the WHO and the US Centres for Disease Control and Preventions (CDC) have issued advice on preventing further spread of COVID-19. They have advised that travel to high-risk areas should be avoided, and contact with symptomatic patients should also be avoided. Basic hand hygiene measures are also recommended including frequent hand washing. The SARS-CoV-2 possesses a single strand, positive-sense RNA genome ranging from 26-32 kilobases in length. Coronavirus has been identified in various mammals including camels, bats, masked palm civets, mice, dogs and cats. The COVID-19/SARS-CoV-2 was first recorded in the Ogun State of Nigeria, but Lagos state has surpassed both the daily infections and the cumulative infections for the country. On May 30, 2020, Lagos state recorded a daily total of 378 confirmed cases and Kano state has continued to follow in the rate at which cases are confirmed in Nigeria and followed by the other 8 states. Also beyond these 10 states in view, the tide is changing towards the south-south and south-east regions of Nigeria and this demands urgent study.
METHODOLOGY
Data Collection. The data for this work was collected using sampling method and released information from the WHO, CDC and NCDC on daily monitoring of the recorded cases of events across the world and particularly Nigeria. The collation of the data took three months spanning between
March 1 and May 31, 2020. The cumulative daily cases of infection, discharged and deaths were collated and the rates of discharge and deaths were computed by common calculation. A literature search was also incorporated and lastly, a graphical analysis of the epidemiological spread of the COVID-19/SARS-CoV-2 was conducted.
Model Development and Statistical Hypothesis. MLR is a simple linear regression extension used to estimate an outcome or target variable based on two or more independent variables. The expected parameter to be estimated is termed the dependent or outcome variable, which is total case discharged, total deaths and total case confirmed within a study period. The variables or factors utilized to produce the estimation results are termed the predictor/independent/criterion variables or explanatory variables, which are the three months data collected from daily infections, totally confirmed case, total deaths and total discharged cases between March 1, 2020, and May 31, 2020. MLR aids in the determination of the variance explained (overall fit) of the model in terms of respective contributions of each explanatory parameter to the total variance explained. It is also used to assess the relationship strength which exists between two or more variables and its respective target variables.
The descriptive statistics of the data utilized for the model development which consist of epide-miological statistics of COVID-19/SARS-CoV-2 cases in Nigeria for three months duration are presented in Table 1.
Table 1 - Statistical parameters of data sets for
he model development
Model Variables SE Mean SD Range SV Minimum Maximum
Duration 2.78 46.50 26.70 91 713.00 1 92
Daily infections 13.43 110.61 128.84 553 16601.03 0 553
% discharge 1.12 16.26 10.71 34.4 114.80 0 34.4
Total discharged 86.52 541.86 829.85 3007 688659.22 0 3007
Total deaths 9.17 65.90 87.96 287 7737.47 0 287
Total confirmed cases 309.33 2188.36 2966.98 10161 8802971.75 1 10162
Statistical Hypothesis:
Null Hypothesis: all the parameters of predictors are not significantly different from zeros which implies that the model is not statistically significant. This is expressed mathematically in Formula 1:
H0: ß =ß2...ßn = 0 (1)
Alternate Hypothesis: at least one predictor parameter is significantly different from zero that is the model is statistically significant. This is expressed mathematically in Formula 2:
HY : ß *ß2...ßn * 0 (2)
RESULTS AND DISCUSSION
Epidemiological timeline of COVID-19/SARS-CoV-2 spread in Nigeria from March 1, 2020 to May 31, 2020. Tables 2-3 and Figures 2-7 represent the epidemiological timeline of COVID-19/SARS-CoV-2 spread in Nigeria from March 1, 2020, to
May 31, 2020, which show the epidemiological statistics of COVID-19/SARS-CoV-2 cases and discharge and death rates in Nigeria within the studied period.
Table 2 - March 2020 epidemio ogical statistics o' COVID-19/SARS-CoV-2 cases in Nigeria
Date Total confirmed cases Daily infections Total discharged % discharge Total deaths % deaths
1 1 1 0 0 0 0
2 1 0 0 0 0 0
3 1 0 0 0 0 0
4 1 0 0 0 0 0
5 1 0 0 0 0 0
6 1 0 0 0 0 0
7 1 0 0 0 0 0
8 1 0 0 0 0 0
9 1 0 0 0 0 0
10 2 1 0 0 0 0
11 2 0 0 0 0 0
12 2 0 0 0 0 0
13 2 0 0 0 0 0
14 2 0 0 0 0 0
15 2 0 0 0 0 0
16 3 1 1 33.3 0 0
17 3 0 1 33.3 0 0
18 8 5 1 12.5 0 0
19 12 4 1 8.3 0 0
20 12 0 1 8.3 0 0
21 22 10 2 9.1 0 0
22 24 2 2 8.3 0 0
23 33 9 2 6.1 1 3
24 44 10 2 4.5 1 2.3
25 51 7 2 3.9 1 2
26 65 14 3 4.6 1 1.5
27 65 0 3 4.6 1 1.5
28 97 32 3 3.1 1 1
29 111 14 3 2.7 1 0.9
30 131 20 8 6.1 2 1.5
31 139 8 9 6.5 2 1.4
Table 3 - April 2020 epidemiological statistics of COVID-19/SARS-CoV-2 cases in Nigeria
Date Total confirmed cases Daily infections Total discharged % discharge Total deaths % deaths
1 174 35 9 5.2 2 1.1
2 184 10 20 10.9 2 1.1
3 210 26 25 11.9 4 1.9
4 214 4 25 11.7 4 1.9
5 232 18 33 14.2 5 1.5
6 238 6 35 14.7 5 2.1
7 254 16 44 17.3 6 2.4
8 276 22 44 15.9 6 2.2
9 288 12 51 17.7 7 2.4
10 305 17 58 18.8 7 2.3
11 318 13 70 22.0 10 3.1
12 323 5 85 26.3 10 3.1
13 343 20 91 26.5 10 2.9
Date Total confirmed cases Daily infections Total discharged % discharge Total deaths % deaths
14 373 30 99 26.5 11 2.9
15 407 34 128 31.4 12 2.9
16 442 35 152 34.4 13 2.9
17 493 51 159 32.3 17 3.4
18 542 49 166 30.6 19 3.5
19 627 85 170 27.1 21 3.3
20 665 38 188 28.3 22 3.3
21 782 117 197 25.2 25 3.2
22 873 91 197 22.6 28 3.2
23 981 108 197 20.1 31 3.2
24 1097 116 208 19.0 32 2.9
25 1182 85 222 18.8 35 3.0
26 1273 91 239 18.8 40 3.1
27 1337 64 255 19.1 40 3.0
28 1532 195 255 16.6 44 2.9
29 1728 196 307 17.8 51 3.0
30 1932 204 319 16.5 58 3.0
Table 4 - May 2020 epidemiological statistics of COVID-19/SARS-CoV-2 cases in Nigeria
Date Total confirmed cases Daily infections Total discharged % discharge Total deaths % deaths
1 2170 238 351 16.2 68 3.1
2 2388 218 358 15.0 85 3.6
3 2558 170 400 15.6 87 3.4
4 2802 244 417 14.9 93 3.3
5 2950 148 481 16.3 98 3.3
6 3147 197 534 17.0 103 3.3
7 3526 379 601 17.0 107 3.0
8 3912 386 679 17.4 117 3.0
9 4151 239 745 17.9 128 3.1
10 4399 248 778 17.7 143 3.3
11 4641 242 902 19.4 150 3.2
12 4787 146 959 20.0 158 3.3
13 4971 184 1070 21.5 164 3.3
14 5162 193 1180 22.9 167 3.2
15 5445 288 1320 24.2 171 3.1
16 5621 176 1472 26.2 176 3.1
17 5959 338 1594 26.7 182 3.1
18 6175 216 1644 26.6 191 3.1
19 6401 226 1734 27.1 192 3.0
20 6677 284 1840 27.6 200 3.0
21 7016 339 1907 27.2 211 3.0
22 7261 245 2007 27.6 221 3.0
23 7526 265 2174 28.9 221 2.9
24 7839 313 2263 28.9 226 2.8
25 8068 229 2311 28.6 233 2.9
26 8344 276 2385 28.6 249 3.0
27 8733 389 2501 28.6 254 2.9
28 8915 182 2592 29.1 259 2.9
29 9302 387 2697 29.0 261 2.8
30 9855 553 2856 29.0 273 2.4
31 10162 307 3007 29.6 287 2.8
140 120 I 100
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Figure 4 - April 2020 epidemiological timeline of COVID-19/SARS-CoV-2 spread in Nigeria
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Figure 5 - April 2020 epidemiological timeline of COVID-19/SARS-CoV-2 discharge and death rates in Nigeria
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Figure 7 - May 2020 epidemiological timeline of COVID-19/SARS-CoV-2 discharge and deaths rates in Nigeria
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It can be shown from Table 2 and Figures 2-3 that the highest daily infection was recorded on the 28th of March with 32 infections while the highest fatality rate was recorded on March 24th with a rate of 2.3 % and recorded daily infection of 10. As of March 31, 2020, a total number of 139 confirmed cases were recorded in Nigeria with a fatality and discharge rates of 1.4 and 6.5 % respectively.
Table 3 and Figures 4-5 present the studied cases for April 2020. It can be deduced that the highest daily infection in Nigeria in April was recorded on April 30, 2020, with daily infection of 204 confirmed cases. The highest discharge rate of 34.4 % was recorded on April 16, with a fatality rate of 2.9% while the highest fatality rate of April was 3.5 % recorded on April 18, 2020, which has a discharge rate of 30.6 % and a daily infection record of 49. As of April 30, 2020, Nigeria had recorded a total of 1932 confirmed cases with 58 deaths.
Table 4 and Figures 6-7 present the studied cases for May 2020. It can be deduced that the
highest daily infection in Nigeria in May was recorded on May 30, 2020, with daily infection of 553 confirmed cases. It can also be observed that the highest discharge and fatality rates for May 2020 are 29.6% and 3.6% recorded on May 31, 2020, and May 2, 2020, respectively. As of May 31, 2020, the total infection stood at 10162 confirmed cases and there seems to be a continuing upward trajectory for the situation under investigation. From Figures 3, 5, 7, it can be observed that the rate of discharged cases continued to surpass those of the fatality for the months of investigation.
Epicentres/severely affected states of the epidemi-ological spread of COVID-19/SARS-Co V-2 in Nigeria in May 2020. Table 5 and Figures 8-9 represent the epidemiological timeline of COVID-19/SARS-CoV-2 spread in the most affected states (epicentres) in Nigeria for May 2020, which show the epidemiological statistics of COVID-19/SARS-CoV-2 daily infections within the studied period.
Table 5 - May 2020 epidemiological statistics of COVID-19/SARS-CoV-2 cases in 10 most severely affected
states in Nigeria
Date Lagos Kano FCT Katsina Bauchi Borno Ogun Oyo Jigawa Kaduna
1 30 52 36 - 10 3 - 6 - -
2 62 7 52 - 5 6 - 4 - 31
3 39 29 12 8 18 7 24 1 - 15
4 76 23 19 37 9 18 5 5 32 -
5 43 32 10 9 3 6 6 5 - 3
6 82 30 9 3 - 10 4 8 - 1
7 183 55 - 11 19 9 5 3 44 7
8 176 63 20 31 15 17 13 4 - 3
9 97 29 7 19 44 17 2 5 - 3
10 81 26 13 - 20 26 2 - 35 -
11 88 64 3 49 1 1 9 1 - 13
12 57 27 1 3 8 2 1 4 - -
13 51 14 10 16 16 - - 4 23 5
14 58 46 9 - 1 3 7 - 35 -
15 179 8 7 15 3 13 11 13 15 20
16 95 - 11 - 2 8 - 12 6 -
17 177 64 21 9 3 3 - 11 4 4
18 74 17 4 33 7 8 8 19 - 3
19 131 - 5 - 2 4 25 6 4 7
20 199 5 8 - - 8 - 19 6 -
21 139 28 11 22 4 - 5 28 14 18
22 132 8 1 5 - 12 13 9 16 9
23 133 - 22 - 2 3 23 34 - 5
24 148 13 36 - - - 12 7 - 5
25 90 23 14 27 - 5 9 4 - -
26 161 4 - - 1 - - - - 19
Date Lagos Kano FCT Katsina Bauchi Borno Ogun Oyo Jigawa Kaduna
27 256 13 - 23 - 1 1 2 - 7
28 111 3 16 - 1 1 4 8 - 6
29 254 3 29 - 2 6 - 15 24 11
30 378 9 52 6 - 7 13 5 5 12
31 188 3 44 - 2 - 19 12 - 14
400 350 300
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Figure 8 - May 2020 epidemiological statistics of COVID-19/SARS-CoV-2 cases in 10 most severely affected
states in Nigeria
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Figure 9 - May 2020 epidemiological statistics of COVID-19/SARS-CoV-2 cases in 10 most severely affected
states in Nigeria without Lagos
No doubts that the COVID-19/SARS-CoV-2 was first recorded in the Ogun State of Nigeria, but Lagos state has surpassed both the daily infections and the cumulative infections for the country. On May 30, 2020, Lagos state recorded a
daily total of 378 confirmed cases as shown in Table 4 and Fig. 8. Kano state had continued to follow in the rate at which cases are confirmed in Nigeria and followed by the other 8 states as shown in Table 5.
Analysis of Variance Result (ANOVA). The data sets were statistically analyzed using ANOVA; the experimental duration, daily infections and percentage discharge are the predictor variables while the total discharged, total deaths and total
confirmed cases are the target variables of the regression in the ANOVA, model-independent variables were assessed to the three response or outcome variables as shown in Tables 6-8.
Table 6 - Analysis of Variance for Toi tal Discharged Response
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 45505763 15168588 77.78 0.000
Duration 1 875631 875631 4.49 0.037
Daily infections 1 3474712 3474712 17.82 0.000
% discharge 1 55333 55333 0.28 0.596
Error 88 17162226 195025
Total 91 62667989
Table 7 - Analysis of Variance for Total Deaths Response
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 588680 196227 149.60 0.000
Duration 1 23005 23005 17.54 0.000
Daily infections 1 34200 34200 26.07 0.000
% discharge 1 997 997 0.76 0.386
Error 88 115430 1312
Total 91 704110
Table 8 - Analysis of Variance for Total Confirmed Cases Response
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 659902403 219967468 137.12 0.000
Duration 1 20641294 20641294 12.87 0.001
Daily infections 1 44711208 44711208 27.87 0.000
% discharge 1 467384 467384 0.29 0.591
Error 88 141168026 1604182
Total 91 801070429
The indices used for the statistical analysis are adjusted sum of square adjusted mean squares and P-value. The adjusted mean square helps to evaluate the variation of a model or system that predicts its response. It considers the degree of freedom and provides a platform for the computation of the adjusted coefficient of determination statistics (R2-adj) presented in the model summary. The adjusted sum of squares helps to assess the various measures of different model parameters without taking into account the order of the independent variables of the model. It is also utilized for the computation of the p-value of the factor levels and also the coefficient of the determination statistics (R2); this is used together with the computed p-value for interpretation of model performance.
The P-value provides the criteria for a rating of statistical significance within a hypothesis testing
which shows where enough evidence exists for the acceptance or rejection of the conjecture or null hypothesis. For results interpretation, if P-value >a then we accept the null hypothesis which means that the corresponding factor is not an important predictor and possesses negligible value within the model but if P-value > a then we accept the alternate hypothesis which means that they are statistically significant to the prediction of the response parameter.
From the computed results, % discharge factor has a p-value of 0.596, 0.386 and 0.591 for the three target responses respectively which indicated that the % discharge factor is not significant while the other factors; % confirmed and % deaths, in the predictor variables are statistically significant.
The Model Summary and Regression Coefficients. The developed regression model performance rating parameters are presented in the model summary for the derivation of the coefficient of determination (R2) which is the variation (in percentage) in the outcome explained by the MLR model. It is used to determine how well the model fits the system database; the higher the values, the better the model performance and its results range from a minimum of 0% to maximum of 100 % signifying that the fitted values are equal to the observed value.
Regression Equation. The regression equation helps to express the relationship between the
The regression equations are presented in Formulas 4- 6 for the three target parameters as follows:
TDs = -369 + 10.42 D + 3.2B7 D/ + 3.BB PD (4) TDt = -40.19 + 1.6BB D + 0.3261 D/- 0.521 PD (5) TCC = -12B4 + 50.6 D + 11.79 D/- 11.3 PD (6)
Where TDs is total discharge, TDt is total deaths, TCC is total confirmed cases, D is duration period, DI is daily infections, and PD is percentage discharge
Residual Plot. The residual plots show the residual values on the y-axis against the independent variable on the x-axis. The model residual results are obtained from the formula 7:
residual = observed—predicted (7)
Since linear regression models are not always appropriate in terms of prediction performance, the evaluation of the appropriateness of the
dependent variable or model response and independent variables; it is expressed in the algebraic form of a regression line which takes the form of:
y = Po +PX + ••• + Pnxn (3)
wherey is the dependent or target variables, P0 is the constant term, Px,P2,...p„is the regression coefficients and x , x ,... x is the independent or predictor variables.
The model parameters are presented in Table 9.
model is achieved by defining and examining the residual plots shown in Figures 10-12.
The plots present the behavioural curves and Histogram charts of residuals which determine the skewness of the data under statistical examination; the normal probability plot of residuals which helps to verify the assumptions that residuals are normally distributed, the residual vs fit plot helps to verify that the residuals possess constant variance and residual versus the order of data which helps to verify that the residuals are uncorrelated with each other.
CONCLUSIONS
From the foregoing epidemiological analysis and time prediction models of coronavirus (COVID-19/SARS-CoV-2) spread in selected epicentres around the world with a focus on Nigeria case, it can be concluded with the following remarks.
1. That the data of total confirmed cases, daily infections, daily discharge case, daily deaths, percentage discharge and deaths were successfully collected for three months through releases from the Nigeria Centre for Disease Control (NCDC).
2. That the collected data were analysed and results presented in graphs to show the behaviour of the virus spread within the period under investigation.
Table 9 - MLR Model Parameters
Model Summary Coefficients of Regression
Response Parameters S R2 (%) R2-Pred (%) R2-adj (%) Constant Duration Daily infections % discharge
Total discharged 441.б17 72.61 69.ББ 71.6В -369 10.42 З.2В7 З.ВВ
Total deaths 36.2174 ВЗ.61 В1.В1 ВЗ.0Б -40.19 1.6ВВ 0.3261 -0.S21
Total confirmed cases 12бб.Бб В2.ЗВ В0.44 В1.7В -12В4 Б0.6 11.79 -11.3
Figure 10 - Residual Plots for Total discharged
Figure 11 - Residual Plots for Total deaths
Figure 12 - Residual Plots for Total confirmed cases
CONCLUSIONS (CONTINUOUS)
3. That a time prediction model was conducted using the MLR and ANOVA algorithms to predict what would be the behaviour of the virus spread in Nigeria in any period and the regression equations were proposed.
That the proposed equations were validated as to established the functions that are more relevant to affect the results of the future predictions and this showed that total confirmed cases and total deaths are the independent variables that showed more effect on the suggested model expressions.
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