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08年美国数学建模C题

时间:2013-01-28

Team # 3310 For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
Team Control Number

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3310
Problem Chosen

C

Finding the Good in Health Care Systems
Abstract
Access to health care is a fundamental human right. This paper analyzes a variety of health care systems, and probes into the six given tasks. To solve Task 1 and Task 2, we give an overall review of various health care systems. 156 metrics and 193 counties are selected, among which 11 metrics and 12 countries are singled out with the method of entropy law. These countries are scored and ranked preliminarily by means of principal component analysis. To solve Task 3, six key metrics are first selected by means of principal component analysis. Then the raw data are standardized by means of normal distribution function. After defining the potential coefficients, a method called Artificial Partial Differential Equations is devised to work out the coefficient’s functional correspondence to present values and the change rates of the metrics. Use the weighted sum of the potential coefficients to calculate the ranks of the countries in terms of their potentials in meeting the future needs of medical care. With principal component analysis to improve the fuzzy factors, the method of fuzzy comprehensive evaluation finally leads to each country’s integrated scores which are determined by the changes in time. To solve Task 4 and Task 5, the weighted sum of potential coefficients is employed to compare the health care systems in America and that in Germany and the Republic of Korea. It leads to the conclusion that the potential of the American health care system is superior to that of Germany, and the potential of the Korean health system is superior to that of America. The solution to Task 6 refers to the method which is applied to solving Task 3. A computer simulation system is developed with MATLAB, which is able to simulate the present and future integrated scores of a certain country if any changes occur to its health care system. Then a neural network is constructed to simulate various changes in the metrics measuring the American health care system. Finally, some suggestions are offered to the American health care system.

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Contents
Introduction ................................................................................ 3 Symbols and Definitions ............................................................ 4 Analysis of the Tasks and The Flow Chart of our Ideas ........ 5
1 2 1 2 3 1 2 3 1 2 3 4 1 2 Analyzing the Tasks ........................................................................................... 5 The Flow Chart of our Ideas .............................................................................. 5 Describing the Metrics ....................................................................................... 6 Metrics to Evaluate the Potential Health Care Systems..................................... 7 Combining Different Metrics. ............................................................................ 8 Collecting National Samples.............................................................................. 8 Selecting the Data and Metrics .......................................................................... 8 Ranking the Sample Countries......................................................................... 11 singling out the metrics .................................................................................... 14 Standardizing Data ........................................................................................... 15 Health Care System’s Potentials with the Variation of Time ........................... 18 The General Evaluation ................................................................................... 25 An introduction and evaluation of the Health Care System in the U.S. .......... 31 An introduction and Evaluation of the Health Care System in Germany ...... 323 A comparative analysis Between America and Germany ................................ 33 An introduction and evaluation of the Health Care System in the Korea. ....... 35 A Comparative Analysis between Korea and America. ................................... 36 improve the United States's health care system ............................................... 38 Test of the Change of Each Metric .................................................................. 40

Task 1........................................................................................... 6

Task 2........................................................................................... 8

Task 3......................................................................................... 14

Task 4......................................................................................... 30

Task 5......................................................................................... 35
1 2 1 2

Task 6......................................................................................... 38 Suggestion ................................................................................. 43 Strengths and weaknesses ....................................................... 45
1 2 Strong Points .................................................................................................... 45 Weak Points...................................................................................................... 45

References ................................................................................. 45 Appendix ................................................................................... 47

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Introduction
It is one of the god-given rights for the citizens to receive a proper health care. Every one in the world is entitles to a healthy life, no matter he was born disabled or not, no matter he is physically strong or not. He has the right to ask for a healthy life from both the state and the society. Health promises everything one can enjoy in his life. Yet in the real world, not every one has his access to the medical service provided by the state. Many people in illness fail to receive a proper medical treatment because of his economic status. So every one is concerned with the medical care offered in his country, from the health care systems to the clinical facilities, from the average medical cost to the availability of medical insurance. On the other hand, the health care system in a country illustrates its conditions of human rights. It decides whether a country can develop in a sustainable way. In one word, the health care system gives a promise to the country’s future. However, media and government reports may not give adequate information on whether the country’s health care system operates efficiently, whether one is given access to physical health by the state, or whether his fundamental rights are protected or derived by the state. When we are given the opportunity to attend this mathematics model building contest, we visited various websites and collected numerous data. With the help of the mathematic knowledge, we worked out a mathematic model to access the current health care system in a variety of country. It is expected that this model contributes to a good knowledge of the health care system operating in a certain country, and the basic human rights to medical care is well protected.

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Assumptions
? The samples selected represent the most typical examples of the health care systems in the world, which are available in both the developed and developing countries. The metrics listed in this paper are based on the unbiased and reliable data issued on line or by the authorities concerned. The ranking of health care systems in various countries is based on the WHO reports. The health care systems referred to in Task 3 remain constant and unchanged. The metrics are able to give an overall description to all the respects in a health care system.

? ? ? ?

Symbols and Definitions
Fi --------------------------The metric to evaluate the i th health care system Gi --------------------------The general potential of the i th health care system
? yij --------------------------The value of the j th metric of the i th country yij --------------------------The dimensionless value derived from the value of the

j th metric of the i th country

?ij -------------------------- The standardized value of the j th metric of the i th
country

? ij --------------------------- The potential coefficient of the i th health care system
corresponding to the annual changes in the j th metric

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Analysis of the Tasks and the Flow Chart of our Ideas
1 Analyzing the Tasks

Health care system is deeply related to people's immediate needs. In this paper, We carry out an in-depth research into the six given tasks. According to the tips, we believe that the establishment of an effective and reasonable health care system is our goal. The selection and reasonable combination of the various evaluating metrics are the bottleneck in completing the tasks. We start with Task1 and Task 2. By searching various web sites we find a large amount of data for the solution of Task 3. We use SPSS software for data processing and principal component analysis for satisfactory metrics. Meanwhile, we define potential coefficient, and use fuzzy mathematic theory to build mathematical models. The calculation and solution are completed in Task 4 and Task 5. while solving Task 6,suggestions are offered on the basis of the findings in the previous five tasks.

2

The Flow Chart of our Ideas
Task1

Description

Raw Data The Entropy Law National ranking 11 metrics

Task2

6 metrics National (National , Metrics) data Year (Year , Metrics) data

Task3

Potential coefficient 7 years later (National , Metrics) data

Comparison of Germany and the United States

Task4

Task5

Fuzzy Evaluation 7 years later Composite scores in various countries

Comparison of Republic and the United States

Neural Network Forecasting

Predictive Models
Task6

Suggestion

Figure 0 The Flow Chart of our Ideas

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Task 1
1 Describing the Metrics

Metrics to evaluate the health care systems are complicated systems of multi-goal, multi-function, multi-level and multi-component. They should describe the special features of health care statistics, and clear the ground for justifying, accessing, controlling and optimizing the medical service. So far, there is no record of a well-established metric in this field. ? to ease the patients from their illness and improve their health status. Health status should not be measured on the basis of improving traditional life expectancy, but on the basis of the Average healthy life expectancy. The focus of this objective is to minimize the unfair distribution of health status and to give the best support to the underdeveloped area. to maximize the availability of health care. Medical care should cover as many people as possible. It should be within both the economic and geographic reach of people at all levels, especially those who have an immediate and desperate need for medical support. to improve fairness in medical care. People of different races, genders, or socio-economic classes should have equal access to the basic medical care. The medical services should be reasonably distributed, funded and practiced

? ?

?

The degree to which the three objectives are achieved are measured by the following metrics. The first objective is measured respectively by the metrics of Mortality, Morbidity, Health Service Coverage and Risk Factors, the second objective respectively by Health Systems and Communication Technology, and the third respectively by Demographic and Socioeconomic Statistics, and Information and Communication Technology. Given the influence of these component on the scores of each health care system, these metrics are further divided into 29 subordinates, which are illustrated in Table1.1.
Table 1.1 Systems of Metrics
superordinates subordinates Life expectancy at birth Healthy life expectancy (HALE) at birth Mortality Probability of dying Infant ,Neonatal ,Maternal mortality rate Age-standardized mortality rate units years years per 1 000 population per 1 000 live births per 100 000 population

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Children under five years of age Morbidity Prevalence of tuberculosis Incidence of tuberculosis

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per 100 000 population per 100 000 population per 100 000 population per year % % % % % % % density per 1000 population density per 1000 population density per 1000 population % % per 10000 population per 1000 population % PPP international $ % per woman % per 100 inhabitants per 1000 inhabitants

One-year-olds immunized with one dose of measles Health Service Coverage Contraceptive prevalence rate Births by Caesarean section Prevalence of adults(15 years and old) who are obese Risk Factors Population with sustainable access to improved sanitation Population using solid fuels Prevalence of current tobacco use in adolescents(13-15 years of age) Physicians Public and environmental health works Health Systems Dentists General government expenditure on health as percentage of total expenditure on health Private expenditure on health as percentage of total expenditure on health Hospital beds Population (in thousands) total Population annual growth rate Demographic and Socioeconomic Statistics Net primary school enrolment ratio Total fertility rate Total expenditure on health as percentage of gross Information and Communication Technology domestic product Main telephone lines Internet users Gross national income per capita

2

Metrics to Evaluate the Potential Health Care Systems

We give a full consideration to the feasibility of comparing the existing and potential systems of health care. With the help of WHO statistics, we adopt the metric of Health Systems to evaluation the existing and potential health care systems. Firstly, there are a sufficient set of statistics concerning Health Systems, which contributes positively to the comparison. Secondly, Health Systems plays a constantly important role in the medical care systems. The WHO members vary significantly in

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this item. Therefore, Health Systems is good at indicating the changes between the existing and the potential health care systems. Finally, Health Systems covers the expenditures in complementary health care. A probe into this will reveal the efficiency of a certain health care system, and illustrate the trend from the existing to the potential systems of health care.

3

Combining Different Metrics.

Since a single metric can only measure one aspect of a country’s health care system, an overall evaluation calls for an active combination of all the possible metrics. To achieve this end, we integrate the metrics by means of Principal Component Analysis and work out the scores and ranks of each country’s health care system.

Task 2
1 Collecting National Samples

●Countries for evaluation are selected on the following principles. ●The samples include the most typical systems of health care. ●The samples include countries in various economic status. ●The samples include countries in similar conditions to that in the United States.

2

Selecting the Data and Metrics

From the eight superordinate metrics and 156 subordinate metrics given to us, we take advantage of Entropy Law and select the representative subordinates from their superordinates. All together 11 subordinates under 8 superordinates are selected.

2.1.

The Model of Entropy Law

In information theory, entropy is a measurement of uncertainty. The characteristics of entropy decide the discrete degrees of the metrics. The greater the difference coefficient of the metrics are, the greater influence they leave on the comprehensive evaluation. ●Take the six subordinates under the superordinate of Health Systems in 12 country’s health care systems. Let
xij

be the value of the j th metric in the i th

country’s health care system( i ? 1, 2?12; j ? 1, 2?6 ). The correspondence between them is illustrated in the following table.
Table 2.1 The Correspondence between Countries and Metrics

Team # 3310 Health Systems of the i th country 1 2 3 4 5 6 7 8 9 10 11 12 China Germany France America Singapore Russia Britain Brazil Poland Japan on health Canada Republic of Korea

Page 9 of 51 Metrics xij of Health Systems

xi1 :The density of Physicians xi 2 : The density of dentists
xi 3 : The density of health workers

xi 4 :General government expenditure on

health as percentage of total government expenditure
xi 5 : Out-of-pocket

expenditure

as

percentage of private expenditure

xi 6 :Hospital beds

●Calculate the weight of Health Systems in the j th metric in the i th country.
pij ? xij , (i ? 1, 2?12; j ? 1, 2? 6)

?x
i ?1

12

ij

●Calculate the entropy value of the j th metric.
e j ? ?k ? pij ln( pij ), 其中k ? 0, k ?
i ?1 6

1 ,ej ? 0 ln(12)

Table 2.2 The Entropy Values of the Various Metric.

e1

e2

e3

e4

e5

e6

0.967

0.920

0.950

0.985

0.96

0.94

●coefficient of the j th metric. The greater the difference is, or the greater the discrete degrees are, the greater role the metric plays in evaluation, and the smaller the entropy value is. Define the difference coefficient:

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gj ? 1? ej m ? Ee
6 6

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, 式中Ee ? ? e j , 0 ? g j ? 1, ? g j ? 1
j ?1 j ?1

Table 2.3 The Difference Coefficients of Various Metrics

g1

g2

g3

g4

g5

g6

0.118

0.290

0.178

0.055

0.145

0.214

According to the data in Task2.2 and Task2.3, we have the three subordinate metrics which leave the greatest influence on the health care system: the Density of Dentists, the Density of Health Workers, and Hospital Beds. Identifying the Metrics ● In the same way, we find that the subordinate of Healthy Life Expectancy (HALE) at Birth, and the subordinate of Infant, Neonatal, Maternal Mortality Rate have the smallest entropy in the superordinate of Mortality. ● The subordinate of Incidence of Tuberculosis has the smallest entropy in the superordinate of Morbidity . ● The subordinate of One-year-olds Immunized with One Dose of Measles has the smallest entropy in the superordinate of Health Service Coverage. ● The subordinate of Prevalence of Adults (15 years and old) Who are Obese has the smallest entropy in the superordinate of Risk Factors. ● The subordinate of Population Annual Growth Rate and the subordinate Total Expenditure on Health as Percentage of GDP have the smallest entropy in the superordinate of Demographic and Socioeconomic Statistics. ● Information and Communication Technology has the smallest entropy in the superordinate of Main Telephone Lines per 1000. With the model of entropy law, we have the following 12 subordinates: ? Healthy Life Expectancy (HALE) at Birth ? Infant , Neonatal , Maternal mortality rate ? Incidence of Tuberculosis ? One-year-olds Immunized with One Dose of Measles ? Prevalence of Adults (15 years and old) Who are Obese ? Public and Environmental Health Works ? Dentists ? Hospital Beds

Team # 3310 ? Population Annual GrowthRate

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? Total Expenditure on Health as Percentage of GDP ? Main Telephone Lines per 1000

3

Ranking the Sample Countries

We build a principal component analysis model with the help of the selected metrics and data to rank the 12 sample countries.

3.1.

Source of the Data

America and another 11 countries are selected as the subjects in evaluating their respective systems of health care in 2004. All the data are supplied by the WHO websites. The raw data of the evaluating metrics are shown in Table2.4.
Table 2.4 The Raw Data of for the Metrics to Evaluate Various Countries’ Health Care Systems
Total Healthy Life expectancy Maternal (HALE) mortality of measles at birth rate are obese works domestic product tuberculosis with one dose old) who Infant, One-year-olds of Neonatal, Incidence Immunized of years and health rate of gross inhabitants adults(15 environmental Dentists beds growth percentage 100 and Hospital annual as lines per Population on health telephone Prevalence Public expenditure Main

China

64

97

100.3

86.0

5.8

0.7

0.1

22

0.8

4.7

46

Germany

72

16

7.2

93.0

25.9

5.2

0.8

84

0.1

10.6

436

France

72

23

12.9

87.0

42.1

4.2

0.7

75

0.4

10.5

314

USA

69

35

4.5

93.0

64.3

5.1

1.6

33

1.0

15.4

551

Singapore

70

18

28.7

96.0

12.0

2.3

0.3

28

2.2

3.7

504

Russia

58.5

83

119.0

99

16.8

4.1

0.3

97

-0.3

6.0

41

UK

70.5

19

14.2

82

28.0

6.3

1.0

39

0.3

8.1

423

Brazil

59.5

301

59.6

99

22.0

2.1

1.1

26

1.5

8.8

82

Poland

65.5

21

26.1

98

35.6

2.8

0.3

53

0

6.2

230

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Japan 75 14 28.2 99 5.2 4.5 0.7

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129 1.3 7.8 449

Canada

72

13

4.7

94

19.8

5.3

0.6

36

1.0

9.8

513

ROK

68

30

96.4

99

4.7

1.4

0.3

66

0.6

5.5

552

3.2.

Processing the Raw Data

Different units are transformed into dimensionless values by dividing the average value of a certain metric with value in the same metric of one particular country.
yij ? ? 11? yij , i ? 1, 2?12

? y?
j ?1

11

ij

3.3.

Identifying the Principal Components

We adopt the principal Component analysis based on a Correlation coefficient matrix. We then use SPSS to solve the coefficient relative matrix and calculate the eigenvalue in the matrix, as is shown in Table 6。A mong all the qigenvalues, the variance cumulative contribution rate of the first a few eigenvalues should be greater than, or equal to a certain percentage, which in real practice is often identified as greater than 80%.. This principle helps to make sure the number of selected principal components. This paper takes the first two principal components in Table 6 whose variance Cumulative contribution rates reach 87.966 %. These two principal components can replace the original metrics in the evaluation of various health care systems. This act of replacement has a reliability of 87.966 %.
Table2.5 Total Variance Explained
Componen t Eigenvalu e % of Varianc e Cumulative % Componen t Eigenvalu e % of Variance Cumulative %

F1 F2 F3 F4 F5 F6

4.6471 2.124 1.7464 1.1703 0.5539 0.3246

42.2467 19.3095 15.8765 10.6392 5.035 2.9505

42.2467 61.5562 77.4327 88.0719 93.1069 96.0574

F7 F8 F9 F10 F11

0.2505 0.098 0.0738 0.0077 0.0038

2.2771 0.8905 0.6705 0.0704 0.0341

98.3345 99.225 99.8955 99.9659 100

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Calculate the eigenvector to have the linear expression of the principal components.
T1 =(0.3645, -0.2928, -0.421, -0.1874, 0.2962, 0.3879, 0.313, 0.0392, -0.0253, 0.3722, 0.3037) T2 =(-0.3609, 0.4728, -0.0078, -0.1947, 0.3829, 0.0123, 0.3813, -0.3189, -0.02, 0.2999, -0.3523) T3 =(0.1333, 0.08, -0.1279, -0.014, -0.177, -0.2333, 0.0992, -0.5395, 0.696, -0.0528, 0.2921) T4 =(-0.0318, 0.2409, 0.0678, 0.7116, -0.1009, 0.114, 0.3354, 0.3919, 0.2649, 0.2569, 0.0674)

With the eigenvector we can have the linear expressions of F1 ,the first principal components, F2 , second principal components, F3 , third principal components, the the and F4 , the fourth principal components. Constructing the comprehensive assessment index. Use the variance contribution rate of the first,the second,the third and the fourth principal components as the coefficients to construct p , the comprehensive assessment index.
P ? A1 ? F 1 ? A2 ? F2 ? A3 ? F3 ? A4 ? F4

That is

P ? 42.24% ? F 1 ? 19.30% ? F2 ? 15.87% ? F3 ? 10.63% ? F4

F F and Put the principal components F1 , 2 , 3 , F4 in correspondence to various metrics

into the equation, and we have p , the comprehensive scorns and ranks of the 12 countries, which are shown in Table 2.6.
Table 2.6 The Comprehensive Scores and Ranks of the 12 Countries Order 1 2 3 4 5 6 Country Germany Japan France UK USA Canada Score 74 72.99 68.36 65.16 63.25 60.44 Order 7 8 9 10 11 12 Country Poland ROK Singapore Russia China Brazil Score 43.15 36.46 35.53 26.44 19.02 9.87

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3.4.

Comparing the Ranks of the Sample Countries

This paper finally identifies 11 metrics to rank the 12 sample countries. From the WHO website we are given the latest ranks of them, which are shown in Table 2.7.
Table 2.7 The On-line Ranks of the 12 Countries Given by WHO Order 1 2 3 4 5 6 Country France Singapore Japan UK Germany Canada Order 7 8 9 10 11 12 Country USA Poland ROK Brazil Russia China

Comparing the two sets of ranks, we can see that most countries are in agreement in both ranks except Singapore. Singapore lags behind because it fails to invest enough in the metric of Total Expenditure on Health as Percentage of GDP, which weighs a lot in the evaluating systems. Its lagging behind can be predicted as its rank is calculated with limited index.

Task 3
1

singling out the metrics

We single out 11 of the most representative metrics from Task 2. But these metrics produces redundancy in processing the data. We adopt the method of principal component analysis, which is similar to that used in Part II, to find out the metrics that best measure the health care systems in various countries. To find out the common metrics that best evaluate each country, we exchange the abscissa and the ordinate in Table 2, with countries along the abscissa and the metrics along the ordinate. Then we carry out a principal component analysis with SPSS to the metrics, and work out the metrics that are able to measure the common features of all countries. The calculation is similar to that in 2.3.3, 2.3.4 and 2.3.5. Table 3.1 shows the scores of each metrics.

Team # 3310 Table 3.1 the scores of each metrics
Metrics Healthy life expectancy (HALE) at birth Public and environmental health works Main telephone lines per 100 inhabitants Total expenditure on health as percentage of gross domestic product Hospital beds Prevalence of adults(15 years and old) who are obese Scor e 123. 3 110.8 103. 5 54.5

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Metrics The density of dentists One-year-olds immunized with one dose of measles Population annual growth rate Infant ,Neonatal ,Maternal mortality rate

Score 9.5 -39.1 -62.2 -159. 5

26.8 21.9

Incidence of tuberculosis

-199. 6

It is illustrated in Table 3.1that the scores of Healthy life expectancy (HALE) at birth, the density of health workers, main telephone lines per 100 inhabitants, Total expenditure on health as percentage of gross domestic product, hospital beds and prevalence of adults(15 years and old) who are obese are higher than others. Therefore they should be the principal metrics to evaluate a certain health care system.

2

Standardizing Data

The raw data should be normalized for the reason that they vary from each other in dimension, that the data have relatively great difference, and that the metrics have different qualities(the greater life expectancy is the better it is, and the smaller the mortality is the better it is). While processing the data, we focus on their relative values instead of their absolute values. Therefore we decide to standardize them with probability density in normal distribution.

2.1.

Metrics that are favored when maximized (with life expectance as an example)

We assume X , the life expectancy in each country, is in normal distribution, and then use Matlab to apply a normal distribution test to it.

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The figure of normal distribution 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 55

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60

65 70 average life expectancy

75

80

Figure 3.1: the figure of normal distribution

Figure 3.1 shows that X is in a good agreement with normal distribution. The assumption is verified. Let the expectancy of X be ? X ,and let its variance be ? X , then we have X ~ N ( ? X , ? X ) . Let the probability density corresponding to a country’s life expectancy be ?i , the standard value of its life expectancy , then

?i ? Norm( xi ) ?

1 2?? X

?

xi

?

( t ? ? X )2
2 2? X

??

e

dt

(3-1)

?i can be worked out with MATLAB, which is shown in Table 3.2.
Table 3.2 The Raw Data and the Standard Value of Life Expectancy Raw Data Standard Raw Data Standard

Country

Country

China Germany France America Singapore Russia

64 72 72 69 70 58.5

0.219 0.781 0.781 0.5778 0.651 0.033

English Brazil Poland Japan Canada Korea

70.5 59.5 65.5 75 72 68

0.686 0.05 0.314 0.912 0.781 0.5

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2.2.

Metrics that are favored when minimized (with prevalence of adults who are obese as an example)

The standardized data are distributed within 0~1with 0.5 as the center. Therefore, when it comes to the metrics that are favored when minimized, subtract its probability density with 1. Since the normal distribution is symmetric, the transformed metrics are equal to the metrics that are favored when maximized. So the standardized data in normal distribution have the following merits. 1. They eliminate the negative influence caused by using different units. 2. They eliminate the negative influence caused by different qualities of 3. They describes the relativity of the data, which helps evaluate the difference between countries. 4. They eliminate the negative influence caused by extremums, and stabilize the data. Standardize the data with normal distribution, and we have ?ij , the standard value of the j th metric in the i th country which is shown in Table 3.3.
Table 3.3 the standard value of the j th metric in the i th country.
Healthy Life Prevalence of Public And Hospital beds Total expenditure on health as percentage of gross domestic 0.147 product 0.782 0.772 0.988 0.087 0.258 0.501 0.587 0.279 0.464

?ij

expectancy (HALE) at birth

adults (15 years environmental and old) who are obese 0.844 0.446 0.144 0.01 0.744 0.649 0.399 0.534 0.245 0.852 health works 0.046 0.808 0.619 0.792 0.219 0.597 0.932 0.187 0.311 0.682

Main telephone lines per 100 inhabitants

China Germany France USA Singapore Russia UK Brazil Poland Japan

0.219 0.781 0.781 0.577 0.651 0.033 0.686 0.05 0.314 0.913

0.145 0.787 0.701 0.233 0.19 0.882 0.292 0.174 0.448 0.984

0.065 0.677 0.437 0.851 0.789 0.062 0.653 0.091 0.28 0.701

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Canada ROK 0.781 0.5 0.584 0.859 0.823 0.099 0.262 0.602

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0.702 0.211 0.802 0.853

3

Health Care System’s Potentials with the Variation of Time

Due the limitation in the current medical facilities, a country may not have high integrated score. This, however, does not mean that the present health care system is not good. Collect the values that change along with time in a certain country, and we can have the potential of this country’s health care system concerning this metrics.

3.1.

Statistics

Firstly collect the variation of time in each metric of each country. Take life expectancy as an example, we can have the data concerning the life expectancy in each country between 2001 and 2005,which can be seen in Table 3.4.
Table 3.4 Changes in Healthy life expectancy in various countries with the variation of time 2000 China Germany France USA Singapore Russia UK Brazil Poland Japan Canada ROK 70.8 78 79.1 76.8 78.4 65.2 77 68.4 73.9 81.3 79.1 74.6 2001 71.2 78.2 79.3 77 78.8 65.2 77.5 68.7 74 81.4 79.3 74.9 2002 71.1 78.7 79.8 77.3 79.6 64.6 78.2 68.9 74.7 81.9 79.8 75.5 2003 71.1 79.1 80 77.5 79.9 64.5 78.6 69.4 74.8 82 80 76.4 2004 71.9 79.2 79.7 77.6 79.6 64.9 78.7 70.2 75 82.3 80.3 76.8 2005 72.4 79.3 80.4 77.9 80.2 65.2 78.9 71.1 75 82.2 80.5 78.5

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3.2.

Standardizing the Data

We work out a chart of Healthy life expectancy in various countries with the variation of time
Goal 100 80 60 40 20 0

China Germany France America Singapore Russian UK Brazil Poland Japan Canada Korea

Country

Figure 3.2 Healthy life expectancy in various countries with the variation of time

Figure 3.2 shows that the life expectancy increase generally in each country. If the increase in a certain country is higher than the world average, it means that this country’s health care system is featured by a good life expectancy. If the increase in a certain country is lower than the world average, it means that this country’s health care system is featured by a bad life expectancy. So we should focus upon the difference between the data and the average, and give consideration to the difference in the units of the data and the difference in the qualities of the data. We standardize with the method used in the normal distribution of data in 3.2. from it we have the standard value of various countries’ life expectancy with the variation of time, as is shown in Table 3.5. And then we can have the average between the yearly increase of life expectancy and the increase of life expectancy in 5 years, as is shown in Table 3.6.
Table 3.5 the standard value of various countries’ life expectancy with the variation of time 2000 China Germany France USA 0.1814 0.7168 0.7882 0.6279 2001 0.1912 0.713 0.7846 0.6241 2002 0.1805 0.709 0.7771 0.6106 2003 0.17 0.7156 0.7708 0.6045 2004 0.1883 0.7144 0.7471 0.5981 2005 0.188 0.6925 0.7655 0.5876 Average 0.1832 0.7102 0.7722 0.6088

Korea Canada Japan Poland Brazil UK Russian Singapore America France Germany China

2005 2004 2003 Year 2002 2001 2000

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Singapore Russia UK Brazil Poland Japan Canada ROK 0.744 0.0195 0.6433 0.0801 0.3931 0.895 0.7882 0.4495 0.7534 0.0177 0.6623 0.0829 0.3824 0.8885 0.7846 0.4544 0.7654 0.0152 0.6752 0.0906 0.413 0.8784 0.7771 0.4738 0.7649 0.0135 0.6825 0.1006 0.4016 0.8691 0.7708 0.5222

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0.7407 0.0115 0.6797 0.1109 0.3943 0.8814 0.7837 0.5356 0.753 0.0098 0.6637 0.1257 0.3586 0.8613 0.7717 0.6338 0.7536 0.0145 0.6678 0.0985 0.3905 0.879 0.7794 0.5116

Table 3.6 The yearly increase in various country’s life expectancy 00~01 China Germany France USA Singapore Russia UK Brazil Poland Japan Canada ROK 0.0098 -0.0038 -0.0036 -0.0038 0.0094 -0.0018 0.019 0.0028 -0.0107 -0.0065 -0.0036 0.0049 01~02 -0.0107 -0.004 -0.0075 -0.0135 0.012 -0.0025 0.0129 0.0077 0.0306 -0.0101 -0.0075 0.0194 02~03 -0.0105 0.0066 -0.0063 -0.0061 -0.0005 -0.0017 0.0073 0.01 -0.0114 -0.0093 -0.0063 0.0484 03~04 0.0183 -0.0012 -0.0237 -0.0064 -0.0242 -0.002 -0.0028 0.0103 -0.0073 0.0123 0.0129 0.0134 04~05 -0.0003 -0.0219 0.0184 -0.0105 0.0123 -0.0017 -0.016 0.0148 -0.0357 -0.0201 -0.012 0.0982 Average 0.0066 -0.0243 -0.0227 -0.0403 0.009 -0.0097 0.0204 0.0456 -0.0345 -0.0337 -0.0165 0.1843

Similarly, we can have the average values of other metrics in five years, as is shown in Table 3.7.

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Table 3.7 the average values in five years in the j th metric of the i th country
Healthy Life Prevalence of Public And Total expenditure on health as percentage of 0.176 0.73 0.673 0.393 0.17 0.854 0.295 0.176 0.376 0.992 0.289 0.488 0.201 gross domestic 0.858 product 0.742 0.986 0.094 0.247 0.459 0.487 0.287 0.5 0.71 0.172 0.061 0.842 0.727 0.839 0.497 0.11 0.752 0.085 0.193 0.635 0.862 0.612

Main telephone lines per 100 inhabitants

sij

expectancy (HALE) at birth

adults (15 years environmental Hospital beds and old) who health are obese 0.132 0.73 0.27 0.983 0.133 0.62 0.765 0.432 0.579 0.135 0.814 0.231 works 0.238 0.863 0.83 0.741 0.221 0.984 0.298 0.27 0.446 0.288 0.382 0.112

China Germany France USA Singapore Russia UK Brazil Poland Japan Canada ROK

0.183 0.71 0.772 0.609 0.754 0.015 0.668 0.098 0.391 0.879 0.779 0.512

Table 3.8

the average(%) of the yearly changes of the j th metric in the i th country
Main

Healthy Life

Prevalence of adults (15 yearsand older) who are obese

Public and Hospital environmental health beds works

Total expenditure on health as percentage of gross domestic product

telephone lines per 100 inhabitants

pij (%)

expectancy (HALE) at birth

China Germany France USA Singapore Russia UK Brazil

-0.33 -1.12 -0.45 0.21 0.9 -1.75 1.96 -2.59

0.07 -0.85 -0.06 0.23 -0.14 -1.99 0.35 3.24

-0.59 -1.58 1.57 1.66 0.27 0.04 0.56 3.41

-0.72 -1.37 -0.59 3.64 0.39 -2.44 -0.93 -0.19

0.13 -0.49 -0.45 -0.81 0.18 -0.19 0.41 0.91

0.84 3.01 0.35 -0.7 -2.53 -0.35 -0.02 -0.2

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Poland Japan Canada ROK 0.58 -1.25 0.2 1.13 -1.96 -0.12 -1.17 1.13 -1.12 -2.48 -1.35 -0.67 -0.08 0.15 -0.35 2.47

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-0.69 -0.67 -0.33 3.69 0.09 -5.9 -0.55 4

3.3.

Potential Coefficient—Artificial Partial Differential Equations

The evaluation of a country’s health care system in a certain metric is decided by its variation with time in this system. If it increases with time, it means that the health care system works well in this metric. And then this system has a great potential. Then we define the concept of Potential Coefficient. 4.3.3.1 Definition: ? ij , the Potential Coefficient, refers to the potential changes in

j th metric in the i th country’s health care system. If ? ? 1 , it means that the country
has a good health care system in this metrics. If ? ? 1 , it means that the country has a bad health care system in this metrics. It has the following features. 1. The potential of a country’s health care system in a certain metric, ? ij namely, is related to its present conditions, that is sij , and the yearly changes, pij namely. In one word, ? ? f (s, p) 2. The greater the increase pij is, the better health care system the i th country has in the j th metric. The greater the potential coefficient ? ij is. In one word: 3.
?f ( s, p) ?0 ?p

(3-2)

4. Suppose the present life expectancy in Country I is 80 years, and the present life expectancy in Country II is 75 years. With a greater base, Country I has more difficulty than Country II in increasing another 0.5 years in its life expectancy. So to have an equal increase of pij , the greater the present

Team # 3310 condition sij is, the greater the potential coefficient is. 5.
?f ( s, p) ?0 ?s

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(3-3)

6. When the present condition sij equals the average, and the yearly change pij is 0, its potential coefficient is 1. that is, f (0.5,0) ? 1 . 7. According to the Theory of the Biggest Entropy of A.G.Wilson, ? ? f (s, p) is in the form of

? ? e g ( s , p ) . So we can assume that the change rate of

potentials is in direct proportion with itself. That is,
? ?f ( s, p ) ? ?p ? k1 f ( s, p ) ? ? ? ?f ( s, p ) ? k f ( s, p ) 2 ? ?s ?

(3-4)

It can be deprived form the above that

? ? e p ? k ( s ?0.5)

(3-5)

4.3.3.2 Identifying the value of k , the weight coefficient.

k represents the weight of the present value of sij and the change of pij . There is no
theoretic solution to its value. But its range can be estimated artificially. It is estimated that the present value is 0.9, much greater than the average level. To increase it by 1% shares the same difficulty with an increase of 2% when the present value is 0.55, which is slightly greater than the average. That is,
f (0.9,0.01) ? f (0.55,0.02)

Similarly, it is estimated that
? f (0.9, 0.01) ? ? f (0.9, 0.01) ? ? ? ? f (0.8, 0.01) ? ? f (0.8, 0.01) ? ? ? f (0.8, 0.01) ? ? f (0.5, 0.02) f (0.45, 0.02) f (0.6, 0.015) f (0.65, 0.015) f (0.7, 0.015)

Put it into equation (3-5), and we can make sure that the range of

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k is 0.0285 ~ 0.0333 . If k ? 0.031 , then

?ij ? e

pij ? 0.031( sij ? 0.5)

(3-6)

Put pij of Table 3.8 and sij of Table 3.7 into (3-6), we can have the potential coefficient of the i th country in the j th metric, as is shown in Table 3.9.
Table 3.9 the potential coefficient of ? ij of the i th country in the j th metric.

Prevalence Healthy Lifeexpectancy (HALE) at birth of adults (15 years and old) who are obese

Public and environmental health works Hospital beds

Total expenditure on Main telephone health As percentage lines per 100 inhabitants

? ij

of gross domestic product

China Germ any Franc e USA Singa pore Russi a UK Brazil Polan d Japan Cana da ROK

0.987 0.9953 1.004 1.0055 1.017 0.968 1.0251 0.9624 1.0025 0.9992 1.0107 1.0117

1.0108 1.0014 1.0078 0.9829 1.0128 1.0163 0.9883 0.9702 1.0173 1.0126 1.002 0.997

0.9861 0.9955 1.0263 1.0244 0.9941 1.0155 0.9994 1.0273 0.9872 0.9691 0.9829 0.9814

0.983 0.9934 0.9995 1.0337 0.9937 0.9867 0.9844 0.9881 0.9954 1.0168 0.9901 1.0246

0.9921 1.0063 1.003 1.007 0.9893 0.9903 1.0028 1.0088 0.9866 0.9933 1.0032 1.0271

0.9948 1.0415 1.0106 1.0035 0.9749 0.9845 1.0076 0.9853 0.9914 0.9467 1.0058 1.0445

Then the standard value of raw data in the t th year is

?ijt ? ?ij ??ij t

(3-7)

Team # 3310 Table 3.1 shows that the weight factor of each metric is

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B ? ?123.3,110.8,103.5,54.5,26.8,21.9?

Then the integrated potential of the i th country’s health care system is
Gi ? ? ??ij ? B j ?
6 j ?1

(3-8).

Then we can have a table of potentials of each country’s health care system, as is shown in Table 3.10.
Table 3.10 potentials of each country’s health care system Country Potentials Country Potentials China 437.8 UK 442.1 Germany 440.8 Brazil 435.1 France 445.3 Poland 441 America 444.3 Japan 438.6 Singapore 442.7 Canada 440.4 Russia 439.1 ROK 443.2

448 446 444 442 440 438
Potential

436 434 432 430 428
America Singapore Poland China Russia Brazil Germany Canada France Japan UK ROK

Figure 3.3 potentials of each country’s health care system

This graph shows that France has the greatest potentials.

4

The General Evaluation

There are any approaches to a general evaluation, including Fuzzy Comprehensive Evaluation, Analytical Hierarchy Process, Data Envelopment

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Analysis, Cluster Analysis, Factor Analysis and so on. The less subjective Fuzzy Comprehensive Evaluation is very similar to the human thought patterns. It is also the most theoretically mature. Therefore, we adopt Fuzzy Comprehensive Evaluation to measure the health care systems in various countries.

4.1.

The preliminary procession of data.

Standardize the raw data of xij with equation 3-2.

?ij ? Norm( xij )
The standard value of the raw data in the t th year is

?ijt ? ?ij ??ij t

(3-9)

4.2.

The fuzzy Procession and Comprehensive Evaluation of the Data

Build a factor set of U ? ?U1 ,U 2 ,U 3 ,U 4 ,U 5 ,U 6 ,? , in which U1 is Healthy Life Expectancy (HALE)at Birth, U 2 is Prevalence of adults(15years and old) who are
U U U obese, 3 is Public and environmental health works, 4 is Hospital beds, 5 is Total

expenditure on health as percentage of gross domestic product,and U 6 is Main telephone lines per 100 inhabitants, the evaluation set V={ Good,Satisfactory, Middling, Bad }

1.

Selecting Membership Function

The membership function selects the most common trigonometric membership function.

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D

C

B

A

A : excellent B : good C : satisfactory D : poor

0

0.25

0.5

0.75

1

Figure 3.4 Membership function diagram

Function expression:
?0 ?8 ? UV 1 ? ? ( x ? 0.5) ?3 ?1 ? 0 ? x ? 0.5 0.5 ? x ? 0.875 0.875 ? x ? 1 UV 2 0 ? ?8 ? ? ? ( x?0 . 5 ) ?3 1 ? ? x? 0.5 0 ?5 ? . x 0.875

x? 0.875

UV 3

8 ? x 0 ? x ? 0.375 ? 3 ? ?8 ? ? (0.75 ? x) 0.375 ? x ? 0.75 ?3 0 0.75 ? x ? 1 ? ? ?

UV 4

1 ? ?8 ? ?? (0.5 x ) ? ?3 0 ? ?

x? 0.125 0 . 1? x ? 25 x? 0.5 0.5

2.

The Fuzzy Procession of the Data

Before the fuzzy evaluation, a fuzzy procession of the data is necessary. Take the year of 2004, in which t ? 0 , for example. Table 3.3 indicates the standard data of various metrics in America, which are shown in Table 3.11.
Table 3.11 the standard data of various metrics in America
Total Public and environmental health works Hospital beds expenditure on Main telephone health as percentage of gross domestic product lines per 100 inhabitants

Healthy Life expectancy (HALE) at birth

Prevalence of adults(15 years and old) who are obese

USA

0.5768

0.001

0.7919

0.2334

0.9883

0.8514

The standard life expectancy in America is x ? 0.5768 . Put it into membership

Team # 3310 function , we have

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UV 1 ? 0.133,UV 2 ? 0.567,UV 3 =0.3,UV 4 ? 0

So the fuzzy of vector life expectancy is R1 ? ? 0.133,0.567,0.3,0? Similarly, the fuzzy of vector Prevalence of adults who are obese is R2 ? ? 0,0,0.026,0.974? the fuzzy of vector Public and environmental health works is R3 ? ? 0.584,0.416,0,0? the fuzzy of vector Hospital beds is R4 ? ? 0,0,0.467,0.533? the fuzzy of vector Total expenditure on health as percentage of gross domestic product is R5 ? ? 0.97,0.03,0,0? the fuzzy of vector Main telephone lines per 100 inhabitants is R6 ? ? 0.703,0.297,0,0? therefore the fuzzy evaluation matrix is
? R1 ? ? 0.133 0.567 0.3 0 ? ?R ? ? 0 0.026 0.974 ? ? 2? ? 0 ? ? R3 ? ?0.584 0.416 0 0 ? R?? ??? ? 0 0.467 0.533? ? R4 ? ? 0 ? R ? ? 0.97 0.03 0 0 ? ? 5? ? ? 0 0 ? ? R6 ? ? 0.703 0.297 ? ?

3.

Various Weighted Factors

There are many approaches to the Weighted Factors. In this case the less subjective principal component analysis is adopted. In Table 3.1 it has been adopted to achieve the scores of various metrics. We use the scores of the metrics as its fuzzy weighted factors. From Table 3.1 it is proved that the fuzzy weighted factors of B ' is
B ' ? ?123.3,110.8,103.5,54.5,26.8,22?

After normalization, the weighted factors of various metrics is
B ? ? 0.28,0.251,0.235,0.124,0.061,0.05?

Team # 3310 4. The general scores

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A , the result of the comprehensive evaluation, equals the fuzzy multiple of the fuzzy evaluation matrix and the weighted factors. Therefore,
0 ? ? 0.133 0.567 0.3 ? 0 0 0.026 0.974 ? ? ? ?0.584 0.416 0 0 ? A ? B ? R ? ? 0.28,0.251,0.235,0.124,0.061,0.05? ? ? ? 0 0.467 0.533? ? 0 ? 0.97 0.03 0 0 ? ? ? 0 0 ? ? 0.703 0.297 ? ? 0.271,0.319,0.319,0.091?

The evaluation of final results show that: 7.1% of the people evaluate the United States as outstanding, 31.9% as good, 31.9% as general, 9.1% as poor. The grades are quantized into numbers from 4 to 1, as is shown in Table 3.12.
Table 3.12 the scores of different grades Grad Score A 4 B 3 C 2 D 1

Therefore American’s integration scores in 2004 is
S ? A ? C T ? ? 0.271,0.319,0.319,0.091? ? [4,3, 2,1]T ? 2.77

Similarly, the general scores of each country after the year 2004,as table3.13.
Table 3.13 the general scores of each country after the year 2004 2004 China Germany Canada USA Singapore 1.5 3.23 2.82 2.77 2.54 2005 1.5 3.31 2.84 2.78 2.58 2006 1.5 3.23 2.85 2.8 2.58 2007 1.5 3.09 2.87 2.81 2.58 2008 1.5 3.02 2.88 2.81 2.58 2009 1.5 2.95 2.89 2.81 2.58 2010 1.5 2.95 2.9 2.81 2.58 2011 1.5 2.95 2.91 2.81 2.58 2012 1.5 2.95 2.92 2.81 2.58 2013 1.5 2.95 2.91 2.81 2.58

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Russia UK Brazil Poland Japan France ROK 2.3 2.95 2.16 1.75 3.02 3.05 2.48 2.34 2.96 2.16 1.88 2.95 3.05 2.48 2.38 2.96 2.16 1.95 2.85 3.05 2.48 2.43 2.96 2.16 2.01 2.81 3.04 2.51 2.47 2.96 2.16 2.05 2.79 3.04 2.52 2.47 2.95 2.16 2.05 2.77 3.04 2.55

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2.47 2.94 2.16 2.05 2.76 3.04 2.59 2.46 2.94 2.16 2.05 2.73 3.03 2.61 2.46 2.93 2.16 2.05 2.66 3.01 2.61 2.46 2.92 2.16 2.05 2.58 2.97 2.61

Form table 3.13 we can see that Germany ranks first in 2004 in the general scores. The United States ranks No. 6. Its growth will slow down if the United States does not initiate reforms in its health care system. It would rank No. 5 in 2007 and No. 4 in 2017. But the United States has the greatest investment in the health care system, which leads to the conclusion that the health care system in America has problems. We can measure the potentials of various health care systems with their general scores with the variation of time. Although our model is good, its effectiveness is conditioned by the collection of the necessary data. Luckily, all the data of the major metrics from 2001 to 2005 are available on line, which contribute to a satisfactory result in our modeling.

Task 4 A Comparative Analysis between America and Germany
There are basically three types of health care systems in the world. The National Health System in U.K., the Healthy Care System in Germany, and the Free Enterprise System in the U.S., which runs on the principle of market. The system in Korea is much similar to that in U.K.[8],[9],[10] Germany has an equal economic might with America, but it manages to offer a more remarkable health care to the residents in German.

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1

An introduction and evaluation of the Health Care System in the U.S.

America is one of the few countries in the west which does not offer universal health care service to all its residents. The health care system in America has two categories. One is the public health insurance offered by the state, the other is the commercial health insurance run by businesses or NGOs. Evaluation of the health care systems in America ? Lack of fairness and efficiency. When it comes to the working class, there is only commercial health insurance, but not any public health insurance designed for them. So the American health care systems lack in fairness. Meanwhile, the total health care expenditure takes up 13.6% of its GDP, which tops any other countries in the world. This illustrates the low efficiency of the system. Efforts to reform the hospitals did not bring any positive changes to this situation. Lack of availability. Public health insurance programs, including health care, health assistance, and the free health care systems designed for the minority , do not hold an important position in the overall health care system in America. They fail to cover all the population. In America, 80% of the government employees and 74% of the employees in the private sector are covered by commercial insurance programs, but not the public health insurance programs. Heavy public expenditure. Statistics show that medical care expenditures in 2000 by the government takes 16.7% of the total federal expenditures, higher than that in Britain, which offers universal free medical care to all its citizens. Heavy medical cost for the patients. Statistics show that the individual medical cost in 2000 takes 7.3% of its GDP, much more than that in Britain(2.4%) and Singapore(2.3%).

?

?

?

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-Low popularity

+Medicare and Medicaid -Including the limited crowd , unfair

availability

-Patients with no medical insurance got hard economic burden

Fairness

Marketdriven commercial medical insurance

Patients economic burden

-Heavy financial burden -health expenditure in the GDP higher

Governme nt financial burden

Efficiency

-There are still 20% of the country people do not have health protection

Figure 4.1 the Model of the American Health Care System

2

An introduction and Evaluation of the Health Care System in Germany

German is the first in the world to have its social welfare systems. It is persistent in a compulsory health care system which relies more on public health insurance programs N than on the commercial programs. The German health care system is supported by the Statutory Health Insurance (SHI) , S a compulsory medical insurance started in 1883. It states that people with annual income under a certain standard must participate this program. Those who earn more than that decide by themselves to participate either this program or buy the commercial medical insurance. In general, SHI covers 99.8% of its population. Evaluation of the health care systems in Germany ? Remarkable fairness. Its compulsory health care system covers nearly all of its residents. The insurance premium is charged according to the residents’ economic status, while services are offered according to the real needs. More availability. The patients have an easy access to medical care. All the policy-holders, both in rural and urban areas, are entitled equally to much the same medical service, which is paid by SHI. SHI not only pays for the treatment of serious illness and chronic illness, but also for the medical care needed for recovery. Average efficiency, but improved by the last reforms. There is a certain degree of
W E

?

?

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competition among the clinical institutes. The policy-holder can choose them by their own will. On the other hand, the clinical institutes are trouble by a waste of resource and sharp increase of medical costs. Germany has the most expensive medical care system in the world. Fortunately, the reforms in its health insurance system manage to check the steady and constant increase of medical costs. ? Thanks to its successful universal and compulsory health insurance system, both the government and the individuals are able afford the medical costs.

+Almost universal social health insurance +Convenience for Treatment +The principle of “solidarity ”
+According to capacity to pay +According to Demand -Access to medical services

availability

+Patients with get appropriate economic burden

Fairness
Mandatory social health insurance system

Patients economic burden

+appropriate economic burden

Governme nt financial burden

Efficiency

+Almost universal social health insurance +Rational competition among Disease Foundations +Focus on disease prevention, health cost savings -There is a certain waste of resources

Figure 4.2 the Model of the German Health Care System

3

A comparative analysis Between America and Germany
N

The current conditions
W E

Table 3.9 are S comparisons between the two countries, based the data in 2004. Task the shows that the current system in Germany is superior to that in America. Potentials in General Table 4.1 shows ? ij , the coefficient of potential of both Germany and America

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Table 4.1 ? ij the coefficient of potential of both Germany and America.

?

Total Prevalence of Healthy Life Physicians expenditure on Main adults (15 Hospital beds expectancy density per health as telephone years and per 10000 (HALE) at 1000 percentage of lines per 100 older) who population birth population gross domestic inhabitants are obese product 1.0055 0.9953 0.9829 1.0014 1.0244 0.9955 1.0337 0.9934 1.007 1.0063 1.0035 1.0415

America Germany

Table 4.2 shows the weight of the indexes
Table 4.2 The Weight of the Index B Total expenditure on Main telephone health as lines per 100 percentage of inhabitants gross domestic product

B

Prevalence of Healthy Life Physicians Hospital beds adults (15 years expectancy density per per 10000 and older) who (HALE) at birth 1000 population population are obese

Weight coefficient

123.3

110.8

103.5

54.5

26.8

21.9

In conclusion, the general potential in America ( ??1 ? B ? 444 ), is higher than that in Germany ( ??2 ? B ? 441 .) Historic Changes We use the theory of fuzzy mathematics in Table 3.9 to make a prediction of the data 10 years later in America and Germany. The predicted figures are shown in Figure 4.3.

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3.5 3.4 3.3 3.2 3.1 3 2.9 2.8 2.7 2.6 2.5 1

Germany & the United States development trends

2

3

4

5

6

7

8

9

10

11

Year

Germany

the United States

Figure 4.3 Trends in Germany and the United States

Figure 4.3 shows that Germany has a rise at first, but a slow fall in the following years. America is in a slow increase. So it will take a long time for America to surpass Germany if there is not any change in the current health care system in America.

Task 5 A comparative analysis between America and Korea.
1 An introduction and evaluation of the Health Care System in the Korea.
As a developing country, Korea aims to build a welfare country. It follows the western public health care systems on one hand, and designs its own medical insurance system on the other. Although it is less developed than the western countries, Korea makes some remarkable progress in its health care system. An Evaluation on the Korean Health Care System[12],[13],[14] ? ? Wider Coverage. The Korean compulsory health care system covers the majority of its population. Better fairness and Availability. The Korean health care system states that its

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citizens, poor or rich, have an equal access to the public health care. Government offers the fund for both the urban and rural medical service, so as to provide as many people as possible the medical care they need. ? ? ? more reasonable services The medical support varies from person to person. The jobless has free welfare support while the working class pays partially for the medical care. The public insurance system in Korea is given sufficient legal support. Relevant laws are passed before the enforcement of every public insurance system.

+Almost universal social health insurance +Enforcement system

+Government financing
+Equality

availability

+ Social security support

Fairness
The creation of social welfare

Patients economic burden

+appropriate economic burden

Governme nt financial burden

Efficiency

+Introduction to the law, enforcement -With obvious Industries -Employment insurance system was implemented too late

Figure 5.1 the Model of Health Care System in the Republic of Korea

2

A Comparative Analysis between Korea and America.
N

The Current Conditions Task 3 and Table 5 are the comparisons between the two countries, based the data of W E 2004. Task shows that the current system in America is superior to that in Korea.
S

Potentials in General Table 5.1 shows ? ij , the coefficient of potential of both Korea and America

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Table 5.1 ? ij , the coefficient of potential of both Korea and America.

?

Prevalence of Physicians Hospital beds adults (15 years Life expectancy density per per 10000 and older) who 1000 population population are obese

Total expenditure on health as Main telephone percentage of lines per 100 gross domestic inhabitants product 1.007 1.0271 1.0035 1.0445

America Korea

1.0055 1.0117

0.9829 0.997

1.0244 0.9814

1.0337 1.0246

Table 5.2 shows the weight of the indexes
Table 5.2 The Weight of the Index B Total expenditure on health as Main telephone percentage of lines per 100 gross domestic inhabitants product 26.8 21.9

B

Prevalence of Physicians Hospital beds adults (15 years Life expectancy density per per 10000 and older) who 1000 population population are obese

weight

123.3

110.8

103.5

54.5

In conclusion, the general potential in America ( ??1 ? B ? 444 ), is lower than that in Korea( ??2 ? B ? 451 .) Historic Changes We use the theory of fuzzy mathematics in Table 3 to make a prediction of the data 10 years later in America and Germany. The predicted figures are shown in Figure

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2.9

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Republic of Korea & the United States to develop trends

2.8

2.7

2.6

2.5

2.4

2.3 1 2 3 4 5 6 7 8 9 10 11 Republic of Korea the United States

Year

Figure 5.2 Trends in Republic of Korea and the United States

Figure 5.2 shows that Both America and Korea have a rising trend. But Korea increases at a speed much greater than America.

Task 6
1 improve the United States's health care system

Based on further analysis of the problem, we have decided to use the six indicators based on Task 3 to restructure in order to improve its health care system. Financing for the health protection of the United States and purchase and provision of services are to be charged by the four different "health management" systems. They are public and social security departments of government protection of public health (Medicare), public security and compensatory medical assistance (Medicaid), public security and compensatory medical assistance (Medicaid), as well as employers to pay medical insurance (Indemnity insurance). (Concrete structure of Figure 1)
Federal public health protection Public health care assistance protection Employer health compensation insurance
The Fundraising People

Health Department financial management Government medical aid group Employers and employees

Fund Manager

Private Insurance Companies

Health Management Organization (HMO, PPO)

Health Planning Organization

Public and private health-care providers(Hospital, doctors etc. )

Healthcare Providers

Civil Service, Over age 60, Disabled people, Poor

Employees and Their Families

Consumers

Fig6.1

United States health protection system

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Based on the understanding of United States health protection system and the comparison between United States and Germany and the Republic of Korea in Task 4 and Task 5 , we can conclude: The fairness of United States health care protection is comparatively poor, the coverage of national medical insurance is low, and the state financial burden is heavy. In order to change and forecast the health care system easily, we use the toolbox GUIDE of MATLAB to develop a computer simulation system based on the model of fuzzy comprehensive evaluation of Task 3 (core code, see Appendix 1). The flow chart of programs:
Raw Data

Potential coefficient

Data Processing Amended data Normal Distribution Standardiz ed data Membership function Fuzzy Matrix

Year

Weight factor Scoring

Interface:

Team # 3310 Introduction of functions

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We can increase or decrease indicators or countries, also can change data of an indicator of a country. Through computer simulation, we can get the country's overall score randomly for any year after 2004 after the change of the data. As is shown in the above Figure, when HALE from the United States turns into a 75-year-old, the United State’s score in 2004 is 2.772. Through building the model of computer simulation system, we can get the country's score now and in the future respectively when the health care system changes.

2 2.1.

Test of the Change of Each Metric
The Building of the Model

A nervous network is established with the input layer having 6 nerve nodes to evaluate the health care system. (See Fig 12)

Fig 6.3.

Schematic of biological neuron

With the state’s health care system as output nerve nodes, and middle layer has 7 nodes, we build a BP neural network. (See Fig 13)

Fig 6.4

Before the network structure

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2.2.

Solution to the Model

We use China, Japan, Korea, Singapore, Canada, Brazil, France, Germany, Poland, Russia, amd the United Kingdom as the input values. Then we train the BP neural network and get a better result (See Figure 3)
3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 fitting data primordial data

0

2

4

6

8

10

12

We then used the United States as input data to test the model, the United States scores 2.758. Actually, the USA real data is 2.772. Their relative error is
2.758 ? 2.772 2.772 ?100% ? 0.50% , hence, the error was permissible, and the

correctness of the model is therefore verified.

2.3.

An effective varying range of metrics

We modify the six metrics of health care system, then we use BP neural network to obtain six pictures, which change as metrics do, as shown in Figure 1-Figure 6 below:

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3.4 3 3.2 3 2.5 2.8 2 2.6

4 3.5 3 2.5 2

65 70 75 80 85 Figure 1

40

60 Figure 2

80

0

10 Figure 3

20

3 2.9

3.5

3 2.9

3 2.8 2.7 2.6 20 40 Figure 4 60 2.5 2 2.8 2.7 3 4 5 Figure 5 x 104 2.6 500 550 Figure 6 600

Figure 1. Healthy life expectancy (HALE) at birth Figure 2. Prevalence of adults (15 years and older) who are obese Figure 3 . Public and environmental health works Figure 4. Hospital beds per 10000 population Figure 5. Total expenditure on health as percentage of gross domestic product Figure 6. Main telephone lines per 100 inhabitan as follow. When 1,000 Mobidity is less than Hospital Beds per 1,000, it is pointless to increase the hospital beds. Otherwise, it will be a waste of money, and weaken the health care system's scores. Figure5 show that the Percentage of Health Care Expenditure in the GDP should be under 15%; According to Figure 6, we know that the best number of telephones per 1000 should be around 600. Because when telephone coverage reaches a peak, any more increase may have little impact on the quality of the health care systems.as follow. When 1,000 Mobidity is less than Hospital Beds per 1,000, it is pointless to increase the hospital beds. Otherwise, it will be a waste of money, and weaken the health care system's scores. Figure5 show that the Percentage of Health Care Expenditure in the GDP should be under 15%; According to Figure 6, we know that the best number of telephones per 1000 should be around 600. Because when telephone coverage reaches a peak, any more increase may have little impact on the quality of the health care systems. When the system adjusts itself, if the six metrics vary within its effective range, then we can conclude that the adjustment contributes to improving the comprehensive quality of the health care system.

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3.4 3 3.2 3 2.5 2.8 2 2.6

4 3.5 3 2.5 2

65 70 75 80 85 Figure 1

40

60 Figure 2

80

0

10 Figure 3

20

3 2.9

3.5

3 2.9

3 2.8 2.7 2.6 20 40 Figure 4 60 2.5 2 2.8 2.7 3 4 5 Figure 5 x 104 2.6 500 550 Figure 6 600

Suggestion
The establishment of ideal, harmonious, and efficient health care systems can not be done in a short time. It needs continuous reform and the cumulative experience, and gradually achieves the goal. From our analysis and comparison, we can see that if the health care system of the United States gets better, focus should be placed on reforming the medical insurance system and the tackle of high medical expenditure. ● solution to high medical expenditure In the past 20 years, the United States Government and the health-care institutions has made much effort in health care spending, but the result is not clear. In the health care industry in the United States, the demand for commodities does not decrease with the rise of price. Since the "invisible hand" failed to curb health insurance expenditures, health care market needs governmental intervention. United States Government should establish a unified medical insurance system to curb health care spending and raise the level of the overall health. ●reform of medical security system: Medical insurance issue is "whether to adopt the national insurance system”, and "how to assure everyone to get the treatment." Inhibition of medical expenses is whether to adopt a total limit budgeting or to enforce the management competition. The current American program is that to execute a weak-protection policy in the medical insurance with the goal to realize the national health insurance, that is, to benefit people, guarantee freedom of choice, and control the prices of

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integrated programs. But now the program is facing problems concerning four aspects: a considerable population without medical insurance, aging of the population, the growing medical costs and the contradictions between government and private medical institutions for medical expenses, and he lack of medical personnel. Therefore, this program needs to be improved immediately. Now many developed countries are using national insurance system and have achieved better results. The United States is the only developed country without using this program, so we think that it is inappropriate to directly use national insurance system to reform the medical security system in United States, because the United States has such features as a multiracial and multiethnic structure, and the developed non-governmental charitable organizations and so on. Therefore, we propose that we should make some little modification to ensure the existing health insurance system, and be conscious to fine-tune the existing system while bearing the goal in mind, especially take into account the potential feasibility of the system, in order to improve the existing medical security system in a shorter period of time. After studying the six issues comprehensively, we learn better about national health systems in Germany and South Korea and design an ideal model of the national health system, as shown in Figure 21
System objectives

All enjoy the right to health and survival

Government financial burden Fairness Universal Efficiency

Patients economic burden

System module

National health system

WHO medical system
*Perfect community health services *Reasonable hospital system *Scientific mechanism of competition *Perfect oversight mechanisms *Adequate information and smooth information channel

Health insurance system

*Fair and reasonable health care financing and use

System environment

*Reasonable system design *Raising the level of education ??

Figure 21. The ideal design of the national health care system

The model can fully meet all classes of the society at different levels of demand for medical services, and it has fairness and efficiency which can live up to the country’s expectation. And it helps reduce the state's financial burden. Of course, the ideal model of national health system must

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effectively assume the role public health plays, including such public service fields as immunization, control of infectious diseases, occupational sanitation, environmental sanitation and health education, and public health services, which should be provided by the government to all members of society free of charge.

Strengths and weaknesses
1 Strong Points
1. To achieve more efficiency, the Principal Component Analysis is employed to solve Task 2. It also solves the problem of ranking different countries and the problem of the weights of metrics. Normal distribution is employed creatively to process and standardize the data. It eliminates the negative effects of dimension and various qualities of the metrics on the data. The difference between the data is well noted. The standardized data are granted with more stability. The concept of potential coefficient is applied to the solution of Task 3, which well measures the potential of a country’s health care system. Meanwhile, partial differential equations and artificially-estimated parameters are combined to solve the potential coefficients. It minimized the subjective error in the solution. A computer simulation system is developed to make it easier and more efficient to indicate the changes in the general scores of a country caused by any data changes.

2.

3.

4.

2

Weak Points
1. owing to the limited collection of data, the data procession gives less accurate results than expected. This, however, only results in some minor effects on our analysis of the issue.

References
[1] Ren Ran. Thinking for Performance Assessment of Health System [J]. Medicine and Philosophy, April 2001,Vol.22, No.4, Total No.239 [2] http://en.wikipedia.org/wiki/World-Health-Organisation [3] http://www.who.int/whosis/database/life_tables/life_tables.cfm [4]Wu Qingping1 [,Zhang Dan2]. Comparison of RSR with Some Evaluation Methods [J]. Chinese Journal of Hospital Statistics , Mar.2003, Vol.10,No.1 [5]Yin Aitian1, [Li Chengxiu2,Wu Xiuyun3][,and so on]. Building Metrics on the Quality of Health Care System[J].Chinese Health Quality Management ,Dec 2003,Vol.10,No.6(SN55)

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[6]Wang Dong1,[Zhang Luoman2]. A Review and Analysis of the Metrics on the Quality of Health Care [J]. Chin J Hosp Admin ,Feb 2001,Vol.17,No.2 [7]Li Shuguang1,[Yin Aitian2,Cao Yanmin3]. Interpreting quality evaluation of medical services[J]. Chin J Hosp Admin, Nov 2004 , Vol 20 , No. 11 [9]Wang Jing1,[Zhang Liang2]. A Research of Accessing the Quality of Health Care System [J].Chinese Health Service Management, 2003,Vol.9(SN183) [10]Zhou Shenglai1,[Wang Dexiang2]. A Review of the Expensive Medical Care Costs in America [J]. China Contemporary Medicine,Vol.9,No.2,(SN65) [11]Yu Xiulin1,[Ren Xuesong2]. Multivariate Statistical Aanalysis [M]. Beijing: China Statistics Press,1999 [12]Hao Liren1,[Fan Yuan2, Hao Zeou3].[,and so on]. SPSS Applied Statistics and Analysis [M]. Beijing: China WaterPower Press,2003 [13]Wilson A G..A statistical theory of spatial distribution models[J]. Transportation Res , 1967(1): 253-269 [14]Xiao Mingjie. Application of modified fuzzy comprehensive evaluation in water quality assessment [J]. Water Sciences and Engineering Techology, Apr.2007:6~9 [15]Jin Zhaohui. The Comparison And Evaluation Of International Medical Security Schemes[D]. Beijing. University of International Business and Economics. Apr.2005 [16]Wu Ritu. Comparative Study of International Medical Security Systems and Policy Options for China[D]. Graduate school the Chinese academy of social sciences.May.2003 [17] http://www.who.int/whr/en/index.html [18] World Health Organization .World Health Report 2002 (The).Reducing Risks to Health, Promoting Healthy Life[M].Beijing: People’s Medical Publishing House ,2000.vii

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Appendix
1.1. pingjialiang

for i=1:200 data=[64 97 100.3 25.9 87.0 64.3 96.0 12.0 99 16.8 82 28.0 99 22.0 98 35.6 42.1 86.0 5.8 0.7 0.1 22 0.8 4.7 46 5.2 0.8 84 0.1 10.6 4.2 0.7 75 0.4 10.5 5.1 1.6 33 1.0 15.4 551 436 314

72 16 7.2 93.0 72 23 12.9 69 35 4.5 93.0 70 18 28.7 58.5 70.5 59.5 65.5

2.3 0.3 28 2.2 3.7 504 4.1 0.3 97 -0.3 6.0 41 6.3 1.0 39 0.3 8.1 423 2.1 1.1 26 1.5 8.8 82 2.8 0.3 53 0 6.2 230

83 119.0 19 14.2 301 59.6 21 26.1

75 14 28.2

99 5.2 4.5 0.7 129 1.3 7.8 449 5.3 0.6 36 1.0 9.8 513 1.4 0.3 66 0.6 5.5 552

72 13 4.7 94 19.8 68 30 96.4 ]; z=guiyi(data);

99 0.5*i

for j=[2 3 5] z(:,j)=1-z(:,j); end [hang,lie]=size(z); x=[123.8528 -154.866 -192.053 -36.8912 14.45945 34.83974 -66.9129 59.58863 98.02283]; % x(2)=0;x(3)=0;x(4)=0;x(9)=0; % x(5)=0;%x(7); xsum=sum(x); 105.2654 14.69391

Team # 3310 x=x/xsum; z=z'; y=[]; for j=1:hang yy=mohu(z(:,j)); y(j,:)=mohucheng(x,yy); end xishu=[4,3,2,1]; zonghe=y*xishu'; plot(0.5*i,zonghe(10),'*-r') hold on

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end

1.2.
clear;

guiyi

% data=[]; function y=guiyi(x) [hang,lie]=size(x); y=zeros(hang,lie); for j=1:lie z=x(:,j); [a1,a2]=normfit(z); for i=1:hang y(i,j)=normcdf(x(i,j),a1,a2); end end

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1.3.

mohu

function y=mohu(x) [hang,lie]=size(x); y=zeros(hang,4); for j=1:hang z=x(j,1); y(j,1)=you(x(j,1)); y(j,2)=liang(x(j,1)); y(j,3)=zhong(x(j,1)); y(j,4)=cha(x(j,1)); end for j=1:hang t=sum(y(j,:)); y(j,:)=y(j,:)/t; end

1.4.

mohucheng

function z=mohucheng(x,y) [hang,lie]=size(y); z=zeros(1,lie); for i=1:hang for j=1:lie zz(i,j)=min(x(i),y(i,j)); end end zz=max(zz); z=zz/sum(zz);

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1.5.

you

function y=you(x) if x<=0.5 y=0; elseif x<=0.875 y=8/3*(x-0.5); elseif x<=1 y=1; end

1.6.

zhong

function y=zhong(x) if x<=0.375 y=8/3*x; elseif x<=0.75 y=8/3*(0.75-x); elseif x<=1 y=0; end

1.7.

cha

function y=cha(x) if x<=0.125 y=1; elseif x<=0.5 y=8/3*(0.5-x);

Team # 3310 elseif x<=1 y=0; end

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1.8.

liang

function y=liang(x) if x<=0.25 y=0; elseif x<=0.625 y=8/3*(x-0.25); elseif x<=1 y=8/3*(1-x); end

1.9.

guiyi

function y=guiyi(x) [hang,lie]=size(x); y=zeros(hang,lie); for j=1:lie z=x(:,j); [a1,a2]=normfit(z); for i=1:hang y(i,j)=normcdf(x(i,j),a1,a2); end end


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