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

© 2020 The Authors. This article is licensed under a Creative Commons Attribution 4.0 License 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.


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 hospitalizations, 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 µm 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].
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 epidemiological statistics of COVID-19/SARS-CoV-2 cases in Nigeria for three months duration are presented in Table 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: 0 ... :

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.     It can be shown from   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.
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 Pvalue > 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 > 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.
where y is the dependent or target variables, 0  is the constant term, n    ,... , 2 1 is the regression coefficients and n x x x ,... , 2 1 is the independent or predictor variables.
The model parameters are presented in Table 9.
Since linear regression models are not always appropriate in terms of prediction performance, the evaluation of the appropriateness of the 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.  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.