Document Type: Research Paper

Authors

1 Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

2 Department of Industrial Engineering, Golpayegan University of Technology, Golpayegan, Iran

Abstract

The COVID-19 pandemic has affected many people around the globe. Europe, as one of the most seriously affected continents, has been struggling with the novel coronavirus for several months. Obviously, outbreak response management plays a critical role in the impact of the disease. Therefore, in this paper, Malmquist Productivity Index is used to evaluate the performance of the most severely affected European countries based on the average contagion rate. The results rank the countries and provides insight for the future.

Keywords

Main Subjects

1       Introduction

In December 2019, the novel coronavirus, also known as 2019-nCoV, was observed for the first time in Wuhan, China (Wuhan City Health Committee (WCHC), 2020). The virus then spread to almost all of the countries around the world infecting hundreds of thousands of people and claiming thousands of lives. By 10 April 2020, there were more than 1,500,000 confirmed cases, and over 90,000 death cases globally, while the numbers were about 800,000 and 66,000 for the European region, respectively (World Health Organization, 2020). With more than 50% of the number of confirmed cases and more than 70% of the death cases in Europe, this continent is by far the most acutely stuck region in the world. Therefore, outbreak response management performance evaluation is critical to control the situation and provide insight for future epidemic crises in Europe.

The performance of a national outbreak response management system should be measured according to the conditions under which the system is operating. More specifically, the number of confirmed cases and the rate at which the epidemic spreads in a country depends on the features of that country. Although some indicators, such as confirmed Case Fatality Rate (cCFR) and confirmed Case Recovery Rate (cCRR), are already defined as used for performance evaluation of countries (Jouzdani, 2020), they may be insufficient for capturing the situation in which a country faces the outbreak. Few researches have addressed the outbreak response management performance evaluation from this perspective. Shirouyehzad, Jouzdani, and Khodadadi (2020) analyzed the performance of the countries, most significantly impacted by COVID-19, based on medical treatment of the patients and contagion control. They proposed a Data Envelopment Analysis (DEA) model to calculate the efficiency values in two consecutive steps. They considered several factors including population density, health care system condition, the number of confirmed cases, the number of deaths, and the number of recovered cases. They presented an evaluation of the outbreak response management performance in the countries, and provided a classification of the countries based on medical treatment and contagion control.

In this paper, the aim is to determine the relative growth/decline rate of COVID-19 contagion in the European countries that are most significantly affected by the disease. To achieve this goal, DEA, as a tool with the potential of providing relative comparisons, is utilized. Contact frequency among people is known as one of the major factors affecting the spread of diseases. A crucial factor that can increase the frequency of contact in a country is the population density which is a measurement of population per unit area. Therefore, the population density is considered as an input for the DEA model. To provide an appropriate basis for the comparison, the number of days since the confirmation of the first case is also regarded as an input for the model. 30 European countries in which, on 31 March 2020, more than a month is passed since the confirmation of their first case are considered as Decision-Making Units (DMUs), and the DEA model is run for the last two weeks of March 2020, and the Malmquist Productivity Index (MPI) is used to determine the relative growth/decline of average contagion rate in the countries. The results would be to distinguish the countries with critical relative progress and average contagion rate.

The exposition of the paper is as follows. In the next section, the methodology of this research is presented. Section 3 discusses the results, and Section 4 discusses the results and concludes the paper and suggests future research topics.

2       Methodology

The data envelopment analysis (DEA) technique is used to identify the strengths and weaknesses of a set of DMUs than can be evaluated using several different indicators including the relative efficiency, rankings, pattern coordinates, congestion in inputs, Malmquist productivity index, return on the scale, profit efficiency, and cost efficiency. For each DMU, belonging to a set of observed units, an independent optimization problem should be solved in order to achieve the aforementioned objectives (Lotfi, Ebrahimnejad, Vaez-Ghasemi, & Moghaddas, 2020). 

MPI is known to be a well-known and widely-used tool for studying the performance progress or regress. As known, DEA models are linear programming (LP) models with which relative efficiency can be obtained. One of the important feature of DEA methodology is the estimation of production frontier. As regards, if a unit locates on the frontier, it is considered efficient, and inefficient otherwise. It can be said that the efficient units construct the frontier. Thus, as changes happen in DMUs’ performance, from one period relative to another, the frontier may also change. In the MPI method, efficiency changes of DMUs and technology changes, are simultaneously considered. It is possible to estimate the MPI while DEA methodology is being utilized. In this regards, the efficient frontier may change from one time period to another, and for each time period, the frontier can be calculated by DEA (Lotfi, Jahanshahloo, Vaez-Ghasemi, & Moghaddas, 2013).

The method of research in this paper is based on the reliable data from the well-known international sources and the DEA and MPI as tools. In this research, an efficiency evaluation of the European countries, in which, on 31 March 2020, at least one month is passed from their first confirmed case, is performed. The MPI is utilized to determine the relative growth or decline of the contagion in two last weeks of March. The MPI was first introduced by Caves, Christensen, and Diewert (1982). Malmquist Index (MI) is initially introduced to compare the production technology of two economies; however, it can be utilized to address situations in which a comparison of DMUs based on performance needs to be done. The general steps of this study are as follows.

1)    Defining the DMUs: In this study, the countries are considered as the DMUs because they are relatively compared. Countries from a single continent or multiple continents or even provinces within a country may be chosen for the study; however, because of the critical situation in Europe and in order to create a bed for a just comparison among similar DMUs, European countries with the aforementioned conditions are selected.

2)    Determining the inputs and outputs: When the number of inputs or the number of outputs is large, DEA usually does not yield satisfying results for analysis. Therefore, this study considers two inputs and one output. More specifically, population density and the number of days passed since the observation of the first confirmed case are considered as the inputs, and the average contagion rate is taken as the output, as shown in Figure 1.

 

Figure 1. The general scheme of the DEA model

3)    Calculating the productivity progress/regress index: The MPI is utilized to determine the progress/regress index. It should be noted that according to the definitions of the inputs and the outputs, the efficient DMUs, i.e. countries, are the ones with a critical situation regarding the COVID-19 average contagion rate. In addition, when the MPI shows progress or a regress, it is an indicator of a growth or a decline in the average contagion rate. In order to calculate the MPIs, the efficiency values are calculated for the two weeks. Based on these values, the relative efficiency of each country is calculated in each week, giving analysis for each time period. In addition, the MPI is calculated to present the growth or decline of the average relative contagion rates for the countries.

4)    Analysis of the results: In this final step, the situations of the countries regarding the growth or decline of average contagion rates are discussed. In addition, the efficient countries in each of the two weeks, which are the ones with critical situations, are determined.

3       Data Analysis

The data, on the aforementioned countries (Table 1), are provided by the United Nations Statistics Division gathered from national statistical offices, and used to estimate the urbanization. Those estimates are presented in World Urbanization Prospects United Nations Statistics Division (The United Nations Statistics Division, 2020). To evaluate the efficiency of the countries in contagion control, the total number of confirmed cases of COVID-19 can be used. The data are provided by the World Health Organization (2020)

Table 1. The countries in the study

NO.

Country

NO.

Country

NO.

Country

NO.

Country

NO.

Country

1

Andorra

7

Denmark

13

Iceland

19

Monaco

25

Russia

2

Austria

8

Estonia

14

Ireland

20

Netherlands

26

Spain

3

Belarus

9

Finland

15

Italy

21

North Macedonia

27

Sweden

4

Belgium

10

France

16

Latvia

22

Norway

28

Switzerland

5

Croatia

11

Germany

17

Lithuania

23

Portugal

29

Ukraine

6

Czech

12

Greece

18

Luxembourg

24

Romania

30

United Kingdom

The data for the inputs and the output for the two last weeks of March 2020 are presented in Table 2. It should be noted that the contagion rate is calculated by differencing the number of confirmed cases on every two consecutive days, and the average contagion rate for each week is obtained by calculating the mean value of daily contagion rates throughout that week. 

Table 2. The input and output data for the two time periods

NO.

Country

First Week

Second Week

Days since the first confirmed case (input1)

Population Density (input2)

Average contagion rate (output)

Days since the first confirmed case (input1)

Population Density (input2)

Average contagion rate (output)

1

Andorra

16

164

18

23

164

30

2

Austria

22

109

564

29

109

700

3

Belarus

19

47

6

26

47

10

4

Belgium

43

383

432

50

383

1215

5

Croatia

22

73

45

29

73

69

6

Czech

17

139

143

24

139

273

7

Denmark

20

137

99

27

137

189

8

Estonia

20

31

21

27

31

54

9

Finland

49

18

67

56

18

89

10

France

54

119

2130

61

119

4315

11

Germany

51

240

3390

58

240

5546

12

Greece

21

81

51

28

81

82

13

Iceland

19

3

61

26

3

70

14

Ireland

18

72

158

25

72

272

15

Italy

47

206

5381

54

206

5231

16

Latvia

16

30

21

23

30

29

17

Lithuania

19

43

26

26

43

47

18

Luxembourg

18

242

137

25

242

154

19

Monaco

18

26338

2

25

26338

4

20

Netherlands

20

508

553

27

508

1012

21

North Macedonia

21

83

17

28

83

26

22

Norway

21

15

200

28

15

254

23

Portugal

16

111

273

23

111

726

24

Romania

21

84

87

28

84

207

25

Russia

46

9

54

53

9

263

26

Spain

46

94

4020

53

94

8005

27

Sweden

47

25

157

54

25

307

28

Switzerland

22

219

1025

29

219

961

29

Ukraine

15

75

12

22

75

78

30

United Kingdom

47

281

886

54

281

2474

To solve the model for each of the two weeks, the input-oriented BCC is utilized. Furthermore, the return-to-scale is variable. The results of solving the model for each of the weeks are presented in Table 3 in which the average efficiency for each country is obtained by calculating the average of the efficiencies of the first week and the second week. It should be emphasized that the more efficient a country the larger the relative average contagion rate in that country. In other words, the country with a lower population density, fewer days passed since its first confirmed case, and higher rate of contagion is considered as efficient. In this Table, the countries are ranked based on their average efficiency number. Specifically, Iceland, Italy, Latvia, Portugal, Spain, and Ukraine are on the efficiency frontier and have the highest rank. This means that considering their population density and the number of days passed since the observation of their first confirmed case, they have had a relatively high rate of contagion introducing them critical countries from this perspective. Obviously, the situation is the opposite for Finland, Sweden, Belgium, and the United Kingdom.

Table 3. Weekly efficiency of the countries and their ranks

NO.

Country

First Week Efficiency

Second Week Efficiency

Average Efficiency

Average Efficiency Rank

1

Andorra

0.939

0.957

0.948

6

2

Austria

0.830

0.816

0.823

18

3

Belarus

0.832

0.876

0.854

16

4

Belgium

0.395

0.500

0.447

28

5

Croatia

0.714

0.774

0.744

23

6

Czech

0.912

0.929

0.920

7

7

Denmark

0.767

0.821

0.794

19

8

Estonia

0.825

0.868

0.847

17

9

Finland

0.382

0.457

0.419

30

10

France

0.578

0.635

0.607

25

11

Germany

0.686

0.739

0.713

24

12

Greece

0.742

0.796

0.769

21

13

Iceland

1.000

1.000

1.000

1

14

Ireland

0.899

0.913

0.906

9

15

Italy

1.000

0.770

0.885

11

16

Latvia

1.000

1.000

1.000

1

17

Lithuania

0.837

0.879

0.858

14

18

Luxembourg

0.860

0.885

0.872

13

19

Monaco

0.833

0.880

0.857

15

20

Netherlands

0.885

0.896

0.890

10

21

North Macedonia

0.731

0.794

0.762

22

22

Norway

0.917

0.921

0.919

8

23

Portugal

1.000

1.000

1.000

1

24

Romania

0.750

0.807

0.778

20

25

Russia

0.413

0.641

0.527

26

26

Spain

1.000

1.000

1.000

1

27

Sweden

0.409

0.485

0.447

29

28

Switzerland

0.935

0.827

0.881

12

29

Ukraine

1.000

1.000

1.000

1

30

United Kingdom

0.421

0.559

0.490

27

The increase/decrease index of the countries is calculated using the MPI, which is obtained by multiplying the technical efficiency change (TEC) index by the factor specific change (FS) index. TEC gives the progress/regress of a DMU compared to itself from one time period to another and FS calculates its relative progress/regress compared to the corresponding population. An MPI greater than 1 shows an efficiency progress while an MPI lower than 1 is an indicator of efficiency regress. In other words, for the former case, shows a growth in contagion rate from one week to the other, while the latter indicates a decline. The results of applying the MPI are presented in Table 4. According to this Table, Russia, France, Germany, the United Kingdom, Spain, and Belgium have had a growth in the relative contagion rate. Iceland shows a constant status, and other countries have had a decline in relative contagion rates.

In addition, Figure 2 depicts the TEC, FS, and MPI for the countries. In this Figure, the horizontal line with the constant value of 1 is the basis for analysis. For any country, a point for TEC, FS, or MPI above 1 is considered as a sign of relative contagion rate growth. More specifically, the countries with a TEC above 1 are the ones in which relative contagion rate has grown, meaning that compared to their first week, their contagion rate in the second week is increased. For the countries with a FS above 1, the relative contagion rate has grown compared to other countries. 

Table 4. The growth/decline of contagion rate of the countries and their ranks

NO.

Country

TEC

FS

MPI

Efficiency Progress Statues

Contagion Rate Status

Efficiency Progress/Regress Rank

1

Andorra

1.019

0.802

0.817

Regress

Decline

19

2

Austria

0.983

0.827

0.813

Regress

Decline

21

3

Belarus

1.052

0.768

0.809

Regress

Decline

22

4

Belgium

1.268

0.808

1.025

Progress

Growth

6

5

Croatia

1.085

0.715

0.776

Regress

Decline

30

6

Czech

1.019

0.817

0.833

Regress

Decline

17

7

Denmark

1.071

0.745

0.797

Regress

Decline

25

8

Estonia

1.052

0.780

0.821

Regress

Decline

18

9

Finland

1.196

0.740

0.885

Regress

Decline

11

10

France

1.098

1.269

1.394

Progress

Growth

2

11

Germany

1.077

1.180

1.272

Progress

Growth

3

12

Greece

1.073

0.731

0.785

Regress

Decline

27

13

Iceland

1.000

1.000

1.000

Constant

Constant

7

14

Ireland

1.016

0.824

0.837

Regress

Decline

16

15

Italy

0.770

1.166

0.898

Regress

Decline

10

16

Latvia

1.000

0.857

0.857

Regress

Decline

13

17

Lithuania

1.050

0.778

0.816

Regress

Decline

20

18

Luxembourg

1.029

0.777

0.800

Regress

Decline

24

19

Monaco

1.056

0.754

0.796

Regress

Decline

26

20

Netherlands

1.012

0.866

0.876

Regress

Decline

12

21

North Macedonia

1.086

0.719

0.780

Regress

Decline

29

22

Norway

1.004

0.844

0.848

Regress

Decline

15

23

Portugal

1.000

0.915

0.915

Regress

Decline

9

24

Romania

1.075

0.747

0.803

Regress

Decline

23

25

Russia

1.553

1.025

1.591

Progress

Growth

1

26

Spain

1.000

1.107

1.107

Progress

Growth

5

27

Sweden

1.187

0.772

0.917

Regress

Decline

8

28

Switzerland

0.884

0.887

0.784

Regress

Decline

28

29

Ukraine

1.000

0.849

0.849

Regress

Decline

14

30

United Kingdom

1.328

0.902

1.197

Progress

Growth

4

 

Figure 2. The TEC, FS, and the MPI for the countries

Finally, the MPI assesses the overall contagion rate status. In other words, the contagion rate of a country with an MPI over 1 has grown and that of a country with an MPI lower than 1 has declined.

4       Discussion and Conclusions

The results in Table 3 and Table 4, summarized in Table 5, are worth analyzing simultaneously. The Table shows that Russia, Germany, and France did not have high relative contagion rates in either of the two weeks; however, they have experienced a growth in their contagion rate from the first week to the second, both considering them individually or in comparison with other countries. 

Italy is in a different situation from all other countries. In this country, the contagion rate has been high in the first week, while in the second week this is not the case, showing the contagion rate control. In addition, it shows a large improvement when comparing its first week with the second, meaning a decline in the contagion rate compared to itself; however, compared to others, it shows a growth in relative contagion rate.

Spain is also in a unique situation. It has had a relatively high contagion rate in both weeks, while the contagion rate, compared to itself, remained constant, showing no change in contagion rate from one week to the other. On the other hand, the relative contagion rate, compared to other countries, for Spain shows a growth from the first week to the second.

Belgium and the United Kingdom have the same condition. In addition, their relative contagion rate declined from the first week to the other. However, although their contagion rates in the two weeks are not high, when considered individually, their contagion rate shows a growth. This means that considered the two weeks in each of these countries, the contagion rates increased.

Portugal, Ukraine, and Latvia are in the same situation. Although the contagion rate during these two weeks has been high in these countries, the rates within each country, considered individually, are constant, showing no change in the contagion rate. In addition, their contagion rates declined from the first week to the second. Therefore, these are the countries that performed well in controlling the growth of the contagion rate.

Table 5. The overall status of the European countries

NO.

Country

Relative Contagion Rate

Relative Contagion Rate Status

First Week (based on first week’s efficiency)

Second Week (based on second week’s efficiency)

Compared to Self (based on TEC)

Compared to Others (based on FS)

Overall (based on MPI)

1

Belgium

Not High

Not High

Growth

Decline

Growth

2

France

Not High

Not High

Growth

Growth

Growth

3

Germany

Not High

Not High

Growth

Growth

Growth

4

Iceland

High

High

Constant

Constant

Constant

5

Italy

High

No High

Decline

Growth

Decline

6

Latvia

High

High

Constant

Decline

Decline

7

Portugal

High

High

Constant

Decline

Decline

8

Russia

Not High

Not High

Growth

Growth

Growth

9

Spain

High

High

Constant

Growth

Growth

10

Ukraine

High

High

Constant

Decline

Decline

11

United Kingdom

Not High

Not High

Growth

Decline

Growth

Finally, Iceland with a unique situation among all the countries have had a constant contagion rate during the two weeks. This, along with the fact that it has had high relative contagion rates during the two weeks, puts this country in a situation that needs to be investigated to define actions to cause the contagion rate to decline. In addition, it should be noted that the reason for the high contagion rate in this country may be partly due to its low population density, meaning that considering its low population density, the contagion rate is relatively high in comparison with other countries.

For future research, other influential inputs may be considered, and several time periods can be taken into account. With more than two periods of time, Window DEA can be applied to provide more insight into the dynamics of the outbreak response management performance.