20 12 "Shenzhen cup" summer camp for national college students. Question A: Predict the population and medical needs of Shenzhen, and find the answer (the approximate answer is good.

Question A: Forecast of population and medical needs in Shenzhen.

abstract

Shenzhen is one of the fastest growing cities in China. In recent years, with the reform and opening up and the changes in Shenzhen's industrial structure, the population of Shenzhen has also undergone tremendous changes. It is particularly important to predict the changing trend of Shenzhen population. In this paper, the population changes and the future demand for medical beds in Shenzhen are predicted. Proceed from reality, based on some reasonable simplifying assumptions, establish a mathematical model, make full use of matlab and other mathematical software to simplify calculations, and solve related problems in a targeted manner.

1. Aiming at the problem 1: Analyze the changing characteristics of registered population and non-registered population in Shenzhen in recent ten years. Use matlab programming to draw their relationship curve with the total population-this curve conforms to the following function:

Registered population: f (x) = a * exp (b * x)+c * exp (d * x) A = 2.85e-87, b=0. 102 c=0, d=8.3 1e-02.

Non-registered population: f (x) = a * exp (b * x) a =1.805e-026, b = 0.0328 1.

2. Aiming at Question 2: Forecast the development trend of Shenzhen's population and structure in the next decade. Collect data (see attached table), draw the population change curve with matlab programming, find the function, and predict the population change with grey prediction method. The results are as follows:

Table 1 population change in the next decade (10,000 people)

Year (year): 201120122014201520162017201820.

The non-registered population is1076.11210/266.

Population with registered residence: 799.6571.825.3555851.8988898889

The total population is1076.112168.21217.1/kloc-0.

In the same way, we can get the trend of population change in different age groups, regions and sexes.

3. For Question 3: Forecast the future demand for medical beds in the whole city and all districts. Firstly, the data of the relationship between medical beds and years is found through the internet; Then, the feasibility analysis is carried out according to the grey prediction method, and the known data are programmed by this method to get the simulation value and drawn into a graph. Then, the beds in the whole city and all districts in the next ten years are predicted, and the method is found to be feasible after posterior difference test. The data obtained are as follows:

Table 2 Bed prediction units in the whole city and districts in the next ten years (Zhang)

Year 201120122013201420152016201720/kloc-.

Shenzhen 24894 26825 28905 31146 33562 36164 38969 4199145247 48756.

Luohu District 602 632 663 696 730 766 803 843 884 928

Futian district 902 925 948 971995102010451071098125.

Nanshan District18651982 2106 2238 2377 2526 2684 2852 3030 3220

Yantian District 368391416 442 470 499 530 564 599 637

Baoan District 5058 5330 5618 5920 6239 6576 6930 7304 7698 816 5438+03

Longgang District 2656 2775 2899 3028 3163 3304 34513605 3766 3934

4. Aiming at Question 4: Predict the bed demand of hypertension, cancer and cerebral hemorrhage.

The future development trend function of hypertension, cerebral hemorrhage and cancer was obtained by using matlab least square fitting.

Hypertension: y 1=246.6x+ 1083,

Cancer: y2= 1067.3x+6657.2,

Cerebral hemorrhage: y3= 100.5x+804.5.

Then according to the proportional function, the bed demand of hospitals at all levels is obtained, so as to predict the bed demand of a disease in different types of medical institutions.

Keywords: Shenzhen population development, demand for medical beds, grey forecasting method, logarithmic model,

Matlab least square method

I. Restatement of the problem

Shenzhen is one of the fastest-growing cities in China. In the past 30 years, the health service has made great progress, forming a medical service system for cities, districts and communities, and solving the problem of medical treatment for the existing population.

From the structural point of view, the remarkable feature of Shenzhen's population is that the floating population far exceeds the registered population, and the young population has an absolute advantage. The floating population in Shenzhen is mainly front-line workers and commercial service personnel engaged in secondary and tertiary industries. Young people are strong and have fewer diseases. Therefore, although the per capita medical facilities in Shenzhen are lower than the average level of similar cities in China, they can still meet the medical needs of the existing population. However, with the passage of time and the adjustment of policies, the proportion of the elderly population in Shenzhen will gradually increase, and the change of industrial structure will also affect the number of migrant workers. All these may lead to a great difference between Shenzhen's future medical needs and the present ones.

Future medical needs are related to population structure, quantity and economic development. Reasonable prediction can make the construction of medical facilities correctly match the future population health security needs, which is an important condition to ensure the sustainable development of Shenzhen's social economy. However, the existing population and social development model is difficult to meet the requirements of population and medical forecast faced by Shenzhen. In order to solve this problem, please collect data according to the population development trend and the input of medical and health resources (medical facilities, medical personnel structure, etc.) in Shenzhen. ), according to the specific situation in Shenzhen, establish a mathematical model to predict the future population growth and medical needs in Shenzhen, and solve the following problems:

Firstly, the changing characteristics of registered population and non-registered population in Shenzhen in recent ten years are analyzed.

Secondly, the development trend of Shenzhen's population size and structure in the next decade is predicted.

Then, on this basis, predict the future demand for medical beds in the whole city and districts;

Finally, the bed demand of hypertension, cancer and cerebral hemorrhage is predicted according to the previous knot.

Second, the problem analysis

4. 1 Question 1 Analysis:

Due to the rapid economic development and great changes in population growth in Shenzhen, we select the population of Shenzhen over the years for quantitative analysis, then find out the change curves of registered population, non-registered population and total population in Shenzhen, and then fit a similar function according to the curves, from which we can analyze the change characteristics of registered population and non-registered population.

4.2 Analysis of Question 2:

Analyze the trend curve of the total population in Shenzhen in recent ten years, find out the closest function curve, get the function by matlab programming, and then fit the registered population and the non-registered population twice to get the total function, and predict the change of the total population in the next ten years. In the same way, we can find out the population change trend of different ages, different regions and different sexes.

4.3 Analysis of Question 3:

The demand for medical beds is closely related to the change of population, and the change of beds can be found from the second question.

4.4 Analysis of Question 4:

It is required to predict the bed demand of different types of medical institutions. According to the age structure and condition of the whole city obtained in questions 1, 2 and 3, the bed demand of different types of medical institutions for hypertension, tumor and cerebral hemorrhage is divided according to the size of hospitals in Shenzhen, and then the bed demand of different medical institutions is obtained through the relationship between the bed demand of different hospitals and the number of patients with a certain disease and the number of hospitals at the same level.

Third, the model hypothesis.

1. It is assumed that all the collected data are correct.

2. Assume that the secondary and tertiary industries develop steadily, the government policies are relatively stable, and the number of migrant workers increases according to the normal proportion.

Suppose everyone has at most one disease.

The incidence of various diseases remains unchanged.

5. The supply and demand of hospital beds are balanced with the number of inpatients (that is, there will be no vacancies in beds, and people will be hospitalized when they leave the hospital).

6. Bed has nothing to do with the type of disease (as long as there is an empty bed, patients can be accommodated).

7. After hospitals are classified by grade, it is assumed that the number of beds in hospitals of the same grade is the same.

8. Choose three representative diseases to study: hypertension, cancer and cerebral hemorrhage. It is assumed that hypertension can be treated in general hospitals, specialized hospitals and street (town) hospitals, while cancer and cerebral hemorrhage can only be treated in general hospitals and specialized hospitals, and both of them should be hospitalized.

9. This paper only selects the relationship between population and age, region, household registration and gender, and ignores the influence of natural disasters for the time being.

Fourth, symbolic convention.

1.x forecast variable: indicates the year.

2.f(x) stands for population. See the establishment and solution of the model for details.

3. Number of hospitals at all levels

4. Number of patients per year

5. Number of beds in different types of medical institutions

The establishment and solution of verb (verb's abbreviation) model

(on your own)