# Machine Learning Model and Statistical Methods for COVID-19 Evolution Prediction

Authors: M. D. Alsulami; Hanaa Abu-Zinadah; Anwar Hassan Ibrahim
Journal: Wireless Communications and Mobile Computing
 (2021)

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## Abstract

In this paper, we discuss the statistical processing of COVID-19 data. COVID-19 was initially recognized in Wuhan, China, on December 31, 2019. It then spread to other parts of the world, so it became known as a pandemic. It has received interest due to its sudden emergence as a deadly human pathogen. The effect is not only confined to morbidity and mortality but also extends to social and economic consequences. Statistical analysis is required to measure the damage done to humans and take the necessary measures to limit this damage. The objective of the work was to examine the effects of various factors on the deaths due to COVID-19. To achieve this goal, we applied a logistic regression (LR) model, as a statistical method, and a decision tree model, as a machine learning method, to model the deaths due to COVID-19 in France, Germany, Italy, and Spain. The predictive abilities of these two models were compared. The overall accuracies of the decision tree and LR were 94.1% and 93.9%, respectively. It was also observed that countries with high population densities tended to have more cases than those with smaller population densities. There were more female deaths than male deaths in the United Kingdom, and more deaths occurred for those aged 65 years and older. The data were collected from the World Health Organization’s official website from January 11, 2020, to May 29, 2020. The results obtained were in agreement with the previous results obtained by others.


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## Body

## 1. Introduction

The spread of the COVID-19 virus was first confirmed in Italy on January 31, 2020, after Chinese tourists that visited tested positive in Rome [1]. After seven days, a male tourist from Italy returned home from Wuhan, China. He was hospitalized and proved to be the third case in Italy [2]. On February 21, 2020, more cases were detected, beginning with 16 proven cases in Lombardy [3]. The following day, an additional 60 cases and the first death were reported [4]. In early March, COVID-19 moved across Italy [5]. As of July 19, 2020, there were 12,440 active cases in Italy. During the peak of the pandemic, the number of active cases in Italy was among the highest in the world [6]. There were 244,434 confirmed cases and 35,045 deaths, an average of 578 deaths per million inhabitants [7], while there were 196,949 cases of recovery or dismissal. By July 19, Italy tested about 3,741,000 residents [8].The pandemic has caused significant damage to the Italian economy. The tourism, residential, and food service sectors were the most severely affected by the travel restrictions from foreign countries to Italy. Moreover, a national closure was imposed by the government on March 8, 2020 [9]. By April, the Minister of Finance, Roberto Gualtieri, expected the gross domestic product (GDP) to drop by 6% for 2020. The first five proven cases in France were people that arrived from China [10, 11].On January 28, a tourist from China was hospitalized in Paris but died on February 14. This was the first death from COVID-19 in France and outside of Asia [12, 13]. The main factor in the spread of COVID-19 across the metropolitan area was the yearly gathering of the Christian Open-Door Church on February 17–24, in Mulhouse, which was attended by nearly 2,500 people. About 50% of the attendees were thought to be infected with COVID-19 [14]. On June 21, there were 29,640 deaths, 160,377 confirmed cases, and 74,372 cases in which the person recovered after staying in hospitals in France.A group of epidemiologists from France reported that less than 5% of France’s population (about 2.8 million residents) could test positive for COVID-19, which is considered a high percentage in Île-de-France and Alsace [15]. France has faced a major recession due to the impact of the COVID-19 pandemic, which has affected the country’s full production capacity, decreased global demand, and raised concerns about the availability of the raw materials. As a result, the country’s manufacturing and other industrial sectors have temporarily ceased their industrial operations [16]. The first positive patient was reported near Munich, Bavaria, in Germany on January 27, 2020 [17].Most of the cases arose in January and early February from the same auto parts manufacturer, and these were reported to be the earliest cases. Several cases of the Italian outbreak were discovered in Baden-Wurttemberg on February 25 and 26. A large group was associated with a carnival in Heinsberg, North Rhine-Westphalia, with the first reported death on March 9, 2020 [18, 19]. Some groups appeared across Heinsberg as well as China, Iran, and Italy [20]. By July 18, 2020, the Robert Koch Institute (RKI) officially reported 202,572 cases, 9,162 deaths, and about 197,200 recoveries [21]. On June 10, 2020, the RKI reported that the total confirmed number of cases was 184,861, of which 41.2% were in the age group of 35 to 59 years, i.e., called the youth age. The number of deaths reached 8,729, of which 85.3% were in the older age group (70 to 99 years) [22].By January 31, 2020, the virus was first 1reported in Spain when a traveler from Germany with SARS-CoV-2 was diagnosed in La Gomera, Canary Islands [23]. Post-ad hoc genetic analysis revealed that about 15 strains of the virus were brought in, and infection started from the community by mid-February [24]. On March 13, 2020, 1,531 confirmed cases and 37 deaths were reported in the country. By July 17, 2020, 260,255 cases were confirmed and 28,420 deaths were reported [25].Eleven vital blood indices were extracted using the random forest (RF) method to design an assistant discrimination tool [26]. This method yielded accuracies of 96.97% and 97.95% for the test and cross-validation sets, respectively. A convolutional neural network (CNN) was employed for feature extraction, and long short-term memory was used for the classification of patients based on X-ray images [27].


## 2. Methods

In this study, data were collected from the WHO database for four European countries. The data for COVID-19 in each country from January 11, 2020, to May 29, 2020, were correlated to other attributes: the real GDP growth (annual percentage change), national health expenditure per capita (current international $), and projected old-age dependency ratio per 100 persons. The total unemployment of the youth (percentage of the total labor force of ages 15–24, modeled International Labor Office (ILO) estimate) was estimated, and new cases were reported. Machine learning [26–28] and logistic regression (LR) models were employed.


## 3. Decision Tree

(i)
The decision tree classifier is a supervised machine learning method [29, 30]. To develop a model, researchers input training data corresponding to correct output labels. The model was learned from the patterns in the training data [31, 32]. After this, data that the model had not encountered yet were input to determine how the model performed [33]. The decision tree model included three kinds of components [34, 35] as follows:(a)
Nodes represent decisions over the values of certain features(b)
Edges represent answers from nodes and are used to build connections to subsequent nodes(c)
Leaf nodes represent exit points for the result of the decision tree


## 4. Logistic Regression

The LR contains the linear regression equation within a sigmoid function [30, 36–41].The formula of the LR takes the following form:(1)fz=11+exp−β0+β1x1+⋯+βnxn.A sigmoid function is employed to map the values from a large range to the range of 0 to 1.


## 5. Data Analysis

### 5.1. Decision Tree

The growth method and the dependent and independent variables of the model are summarized in Table1.Table 1
Summary of the model.
ConditionsGrowing techniqueCHAIDDependent variableDeathIndependent variablesNew_cases, domestic general government health expenditure per capita, PPP (present international $), joblessness, youth total (% of the total workforce aged 15-24) (modeled ILO estimate), real GDP growth (annual percent change), projected old-age dependency ratio per 100 personsValidationNoneMaximum depth3Lowest number of cases in parent node100Lowest number of cases in child node50ResultsIndependent variables includedNew cases, projected old-age dependency ratio per 100 personsNo. of nodes8No. of terminal nodes5Depth2Table2 is the classification table that shows that 94.1% of the training samples were classified correctly.Table 2
Classification.
ObservedPredictedNo deathDeathPercent correctNo death1331589.9%Death1433095.9%Overall percentage29.9%70.1%94.1%Growing method: CHAIDDependent variable: deathFigure1 shows the tree diagram with 7 nodes.Figure 1
The tree diagram with 7 nodes.


### 5.2. Logistic Regression

The LR sought to predict deaths based on the following factors:(1)
x1: projected old-age dependency ratio per 100 persons(2)
x2: real GDP growth (annual percent change)(3)
x3: joblessness, youth total (percentage of the total workforce aged 15–24, modeled ILO estimate)(4)
x4: national health expenditure per capita(5)
x5: new casesThe regression equation for the LR is as follows:(2)P1=eY′1+eY′.As shown in Table3, the analysis included 492 samples, with no missing data.Table 3
Summary of case processing.
Unweighted CasesaNPercentChosen casesIncluded in analysis492100.0Missed cases00.0Total492100.0Unselected cases00.0Total492100.0The analysis procedure was as follows:(i)
Step 1. Variable(s) input: new cases(ii)
Step 2. Variable(s) input: national health expenditure per capita (current international $)(iii)
Step 3. Variable(s) input: joblessness, youth total (percentage of the total workforce aged 15–24, modeled ILO estimate)(iv)
Step 4. Variable(s) input: real GDP growth (annual percent change)Table4 shows the variables selected in the model and their statistical significance.Table 4
The variables selected in the model.
BS.E.WalddfSig.Exp(B)Step 1aNew_cases0.0080.00170.06510.0001.008Constant-1.6990.21363.89610.0000.183Step 2bNew_cases0.0090.00165.84410.0001.009National health expenditure per capita, PPP (current international $)-0.0010.0006.21110.0130.999Constant0.1300.7360.03110.8601.139Step 3cNew_cases0.0090.00165.99210.0001.009Joblessness, youth total (% of total work force aged 15-24) (modeled ILO estimate)-0.2690.1324.13410.0420.764National health expenditure per capita, PPP (current international $)-0.0020.0017.21810.0070.998Constant6.7463.3324.09910.043850.538Step 4dNew_cases0.0100.00161.48710.0001.010Real GDP growth (annual percent change)1.3720.4887.90510.0053.945Joblessness, youth total (% of total work force aged 15-24) (modeled ILO estimate)-0.4910.1599.49710.0020.612National health expenditure per capita, PPP (current international $)-0.0040.00113.50910.0000.996Constant26.5987.96211.16010.001355839592019.724Table5 shows the omnibus test results of the model coefficients based on the chi-squared test. When the p value was <0.001, the null hypothesis was rejected. This finding suggests that the model best fits the data.Table 5
Omnibus tests of model coefficients.
Chi-squaredfSig.Step 1Step392.94410.000Block392.94410.000Model392.94410.000Step 2Step6.56310.010Block399.50820.000Model399.50820.000Step 3Step4.26710.039Block403.77530.000Model403.77530.000Step 4Step8.74010.003Block412.51540.000Model412.51540.000Table6 shows that the overall percentage of correct classification was 93.9%.Table 6
Classification table.
ObservedPredictedDeathPercentage correctNo deathDeathStep 1DeathNo death143596.6Death2332193.3Overall percentage94.3Step 2DeathNo death144497.3Death2332193.3Overall percentage94.5Step 3DeathNo death143596.6Death2531992.7Overall percentage93.9Step 4DeathNo death144497.3Death2631892.4Overall percentage93.9


## 5.1. Decision Tree

The growth method and the dependent and independent variables of the model are summarized in Table1.Table 1
Summary of the model.
ConditionsGrowing techniqueCHAIDDependent variableDeathIndependent variablesNew_cases, domestic general government health expenditure per capita, PPP (present international $), joblessness, youth total (% of the total workforce aged 15-24) (modeled ILO estimate), real GDP growth (annual percent change), projected old-age dependency ratio per 100 personsValidationNoneMaximum depth3Lowest number of cases in parent node100Lowest number of cases in child node50ResultsIndependent variables includedNew cases, projected old-age dependency ratio per 100 personsNo. of nodes8No. of terminal nodes5Depth2Table2 is the classification table that shows that 94.1% of the training samples were classified correctly.Table 2
Classification.
ObservedPredictedNo deathDeathPercent correctNo death1331589.9%Death1433095.9%Overall percentage29.9%70.1%94.1%Growing method: CHAIDDependent variable: deathFigure1 shows the tree diagram with 7 nodes.Figure 1
The tree diagram with 7 nodes.


## 5.2. Logistic Regression

The LR sought to predict deaths based on the following factors:(1)
x1: projected old-age dependency ratio per 100 persons(2)
x2: real GDP growth (annual percent change)(3)
x3: joblessness, youth total (percentage of the total workforce aged 15–24, modeled ILO estimate)(4)
x4: national health expenditure per capita(5)
x5: new casesThe regression equation for the LR is as follows:(2)P1=eY′1+eY′.As shown in Table3, the analysis included 492 samples, with no missing data.Table 3
Summary of case processing.
Unweighted CasesaNPercentChosen casesIncluded in analysis492100.0Missed cases00.0Total492100.0Unselected cases00.0Total492100.0The analysis procedure was as follows:(i)
Step 1. Variable(s) input: new cases(ii)
Step 2. Variable(s) input: national health expenditure per capita (current international $)(iii)
Step 3. Variable(s) input: joblessness, youth total (percentage of the total workforce aged 15–24, modeled ILO estimate)(iv)
Step 4. Variable(s) input: real GDP growth (annual percent change)Table4 shows the variables selected in the model and their statistical significance.Table 4
The variables selected in the model.
BS.E.WalddfSig.Exp(B)Step 1aNew_cases0.0080.00170.06510.0001.008Constant-1.6990.21363.89610.0000.183Step 2bNew_cases0.0090.00165.84410.0001.009National health expenditure per capita, PPP (current international $)-0.0010.0006.21110.0130.999Constant0.1300.7360.03110.8601.139Step 3cNew_cases0.0090.00165.99210.0001.009Joblessness, youth total (% of total work force aged 15-24) (modeled ILO estimate)-0.2690.1324.13410.0420.764National health expenditure per capita, PPP (current international $)-0.0020.0017.21810.0070.998Constant6.7463.3324.09910.043850.538Step 4dNew_cases0.0100.00161.48710.0001.010Real GDP growth (annual percent change)1.3720.4887.90510.0053.945Joblessness, youth total (% of total work force aged 15-24) (modeled ILO estimate)-0.4910.1599.49710.0020.612National health expenditure per capita, PPP (current international $)-0.0040.00113.50910.0000.996Constant26.5987.96211.16010.001355839592019.724Table5 shows the omnibus test results of the model coefficients based on the chi-squared test. When the p value was <0.001, the null hypothesis was rejected. This finding suggests that the model best fits the data.Table 5
Omnibus tests of model coefficients.
Chi-squaredfSig.Step 1Step392.94410.000Block392.94410.000Model392.94410.000Step 2Step6.56310.010Block399.50820.000Model399.50820.000Step 3Step4.26710.039Block403.77530.000Model403.77530.000Step 4Step8.74010.003Block412.51540.000Model412.51540.000Table6 shows that the overall percentage of correct classification was 93.9%.Table 6
Classification table.
ObservedPredictedDeathPercentage correctNo deathDeathStep 1DeathNo death143596.6Death2332193.3Overall percentage94.3Step 2DeathNo death144497.3Death2332193.3Overall percentage94.5Step 3DeathNo death143596.6Death2531992.7Overall percentage93.9Step 4DeathNo death144497.3Death2631892.4Overall percentage93.9


## 6. Conclusion

The spread of the COVID-19 pandemic in most countries has threatened people and the economy. Therefore, this paper is aimed at evaluating the application of a machine learning model and a statistical model, namely, the decision tree and LR, to study the effects of various factors on the deaths due to COVID-19. This provides some statistical indicators about COVID-19. We determined that the decision tree performed better than LR. The overall accuracies were 94.1% and 93.9% for the decision tree and LR models, respectively, as shown in Tables2 and 6. In addition, the results show that the areas with larger populations tended to have more cases than those with smaller populations. The number of deaths of females was greater than that of males in the UK, and it was greater for those aged 65 years and older.



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