The P opulation of Shenzhen and T he M edical D emand PredictionFrist editorSecond editorThird editorYour school nameAdvisor:********Abstract::AbstractIn this paper,using the establishment of the Malthus index of population growth model,gray model and linear regression model predict the population growth and beds demand for medical care in Shenzhen city.For question One:first of all,through the analysis the household register population,the non-registered population,the change of the number of the population characteristics of Shenzhen in recent ten years,we build the Malthus index of population growth model on the household registration population.To predict the number of the non-registered population,we use the cubic exponential smoothing method.We establish the gray model GM(1,1)based on different age groups,moreover，we verify the feasibility of the ing the model,we predict the number of Shenzhen resident non-registered population numbers and different age population in the next ten years.Then,using linear fitting method forecasts the value of beds demand.For question Two:we mainly consider the relationship between age structure and prevalence characteristics.According to each kind of disease in high-risk population,we determine the effect of age structure of population.Then,combined with the incidence rate,we analyzed the number of sick.According to the clinic characteristics of medical institutions of different types,we figure out the bed-space requirements of various kinds of diseases in different types of medical institutions by MATLAB software.Keywords:Malthus index of population growth model,Cubic exponential smoothing method,GM(1,1),MATLAB software1.IntroductionShenzhen is one of the fastest growing city in economy development.In recent years,with the reform and opening up and the changes of industrial structure in Shenzhen,the population of Shenzhen is undergoing tremendous changes.Therefore，it is particularly important to predict the population’s trend of Shenzhen.2.Problem analysisAiming at a population prediction problem,the population is divided into the household register population and the non-registered population.Due to the mobility of the population is relatively low,and the time of the prediction is relatively short,so we can develop the Malthus index of population growth model to estimate the number of registered population.The non-registered population population growth is much affected by various factors and the non-domicile population increased by second-degree curve,so we can use the cubic exponential smoothing method to predict the number of non-registered population.For the problem of a bed demand prediction,in a certain extent,the total numberof beds can reflect the demand of beds in 1979-2010years .Because of serious tendency of the aging population of Shenzhen city ,the number of beds are still needed on the original basis and keep a year-on-year increase of population at least in the future.For problem two,we do analysis on children pneumonia and hypertension,children pneumonia is characterized by pneumonia in children,which only for the age is in 0-4years old group.Meanwhile,hypertension is mainly in the elderly population.3.Model assumptions1.The data are accurate and reliable;2.Shenzhen city population prevalence is in the average rate of medium-sized city National hospital.3.The district of Shenzhen city population distribution is not changed greatly in 10years.4.Assuming that economic development in Shenzhen city level maintain a stable in the future of a period of time.5.The population policy and the medical system does not change .6.There is not considering the impact of major disease and war effect on population.4.Symbolic descriptionpopulation Permanent :y populationRegistered :1y populationregistered -Non :2y 5.Establishing and Analyzing the Models5.1the Prediction of P opulation of Shenzhen (2011-2020)We assume that the number of the population of Shenzhen is y in t year,of which the household registration population is 1y and the non-registered population is 2y .We can get :21y y y +=.Next,we forecast on the registration population and non -household population.5.1.1the Prediction M odel of the Registered P opulationIn consideration of the household registration population,owing to the mobility population is low relatively and Δt is short,so there is no need to consider the blocking effect of natural resources,environmental conditions and other factors on population growth,so using Malthus index of []1growth population model to estimate the population.)(110)0()(t t r e y t y −=(1)According to the formula (1)and the number of register population （Appendix I attached),,Using nonlinear least squares fitting by MATLAB software can get the r parameter value is 0.0677.Get the model :)1979(0667.0126.31)(−=t e t y (2)According to the formula (2),we get the number of estimated population,its residual error and relative error from 1979to 2010.The results are shown in the following T able 1:Year Actual number of registered population Estimated number of registered population Residual error Relative error (%)197931.2631.2600198032.0933.4496-1.3596 4.236833905198133.3935.7925-2.40257.195268044198235.4538.2996-2.84968.038363893198340.5240.9823-0.4623 1.140918065198443.5243.8528-0.33280.764705882198547.8646.92450.9355 1.954659423198651.4550.2113 1.2387 2.407580175198755.653.7283 1.8717 3.366366906198860.1457.4916 2.6484 4.403724643198964.8261.5186 3.3014 5.093181117199068.6565.8276 2.8224 4.111289148199173.2270.4385 2.7815 3.798825458199280.2275.3723 4.8477 6.043006731199387.6980.65177.03838.026342798199493.9786.30087.66928.161328083199599.1692.3457 6.8143 6.872025011996103.3898.814 4.566 4.4167150321997109.46105.7354 3.7246 3.4027041841998114.6113.1415 1.4585 1.2726876091999119.85121.0664-1.2164 1.0149353362000124.92129.5464-4.6264 3.7034902342001132.04138.6204-6.5804 4.9836413212002139.45148.33-8.886.367873792003150.93158.7196-7.7896 5.1610680452004165.13169.837-4.707 2.8504814392005181.93181.73310.19690.108228442006196.83194.4625 2.3675 1.2028146122007212.38208.0835 4.2965 2.0230247672008228.07222.6585 5.4115 2.3727364412009241.45238.2545 3.1955 1.3234624152010251.03254.9428-3.9128 1.558698164 Table1the N umber of E stimated P opulationopulation,,Its R esidual E rror and R elative E rrorIt is seen from Table1,the actual population and estimated population are quite close and the absolute relative error is within9%.we can conclude that the model is reliable,efficient and accurate.Through the model to calculate the predictive value of2011-2020,we obtain the following table:Table2the predictive value of2011-2020Year20112012201320142015Predictive value(10000)272.8001291.9082312.3547334.2333357.6444Year20162017201820192020Predictive value(10000)382.6954409.501438.1842468.8765501.71865.1.2the Prediction M odel of the Non-registered P opulationFirst,we analyze in the non-registered population data in Shenzhen city from 1979to2010.The results are shown the flowing Figure1:Figure 1the Trend of the Non-registered P opulationFrom the Figure one ,we can arrival at a conclusion that the non-registered population increased with second-degree curve from 1979to 2010.Meanwhile ,cubic exponential smoothing method can be used to predicted the the trend of the non-registered population from 2011to 2020.Exponential smoothing method is a time sequence ，which based on the analysis and prediction means,in the moving average method.With some time series prediction model of certain phenomena in the future prediction ，it is calculated by exponential smoothing value.Its principle is exponential smoothing any period values are the actual observed and previous period of exponential smoothing weighted average.The forecasting model of cubic exponential smoothing method are shown as follows:],...2,1,2=++=+∧T T c T b a y t t t T t (3)of which⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧+−−=−+−−−−=+−=]2[)1(2])34()45(2)56[()1(233)3()2()1(22)3()2()1(2)3()2()1(t t tt t t t t t t t tS S S c S S S b S S S a ααααααα(4)Where )(k t S is smoothing value with an index of k and α（10<<α）is the weighted coefficient.Here α=0.4,i nitial value ,55.13321)0(3)0(2)0(1=++===y y y S S S .We can gain )1(t S ,)2(t S ,(By Appendix 1).Moreover ,we can get the values asfollows:)3(t S 7867.743)1(32=S ,4296.705)2(32=S ,7718.668)3(32=S .When t=32,from the formula (3),32a ，32b ，32c can be calculated :783.843132=a ，28.214732=b ，0.377632=c ;Therefore,the prediction model is:2113776.02147.288431.783T T y T ++=+∧（5）here t=11.This model can be forecast the number of the the non-registered population from 2011to 2020.As is shown in Table 3:Table 3the n on-on-registeredregistered p opulation from 2011to 2020Year 20112012201320142015Predictivevalue value(10000)(10000)812.43841.78871.88902.74934.35Year 20162017201820192020Predictivevalue value(10000)(10000)966.72999.841033.71068.41103.8When T=3,we took the formula (4)into the prediction model of formula (3).Then:)3(2)2(2)1(221)1(1)1(3)1(33tt tt S S S y αααααα−+−−−−+−=+∧（6）To gain the prediction value ,taking t(from 0to 32)into formula (6).The fitted resultcan be seen in Figure 2:Figure 2Seen from figure 2,the forecasting value basically agrees with the actual value.Therefore,we can predict the number of the Non-registered population.5.1.3t he D evelopment T rend of P opulation S tructureIn order to predict the development trend of Shenzhen population structure,we listed the population age distribution of Shenzhen city according to Annex2,3,4.As shown in the following table:According to the data from the table,we can see the population age structure and sex structure data is only in 2000,2005and 2010,and the interval is 5years.So we can predict the population structure model in 2015and 2020by using the gray prediction theory.In the process of establishing the gray model,we put the data of 32years as the initial sequence:))3(),2(),1((0000x x x x =(7)So we can get )(k λ:)()1(00k x k x k −=λ(8)Checking and calculating of ratio values to test whether they are in ),(2212++−n n e e ,if not,we need to take sequence x (0)to do the necessary transformation to fall into the admissible covering interval .To seek the proper constant C and translation transform:nk c k x k y ,...,2,1,)()(00=+=(9)Frist ,to make the accumulated generating operation (AGO)gain the sequence :)]3()2(),2()1(),1([)]2(),2(),1([)0()1()0()1()1()1()1()1()1(x x x x x x x x x ++==(10)Of which )3,2,1)(()(10)1(==∑=k i x k x ki .3,2),1(5.0)(5.0)()1()1()1(=−+=k k x k x k z (11)Figure3From the Figure3,the change of population and beds is linear on the whole.The population growth faster during1991-2003,while the level of medical development is relatively stable.Especially in the past ten years and the population is linear growth basically.By the MATLAB,the data is used to do quadratic fit in nearly ten years,we can conclude the Figure4:Figure 4According to Figure 4,we can calculate that the parameter is 0.0036and -1.4815.Then ,equations can be obtained:()134815.10036.0)(−=n n y By Formula (13),we can calculate the number of the corresponding pared with the actual data,the relative error is shown as following:Figure5R elative E rror of E stimated V alue and A ctual V alue During2000-2010From Figure5,the relative error of estimated value and actual value is almost within0.1,indicating that the prediction equation can simulate the change trend of hospital beds accurately.Therefore the development trend of beds can be predicted 2011-2020in the Shenzhen city,as is shown the follows in the Table7:Table7t he D evelopment Trend of B eds During2010-2020Year20112012201320142015 Predictivevalue(1042455826316281503006332059person)Year20162017201820192020Predictive3414236317385864095843434person)value(104The population distribution of Shenzhen city in2000and2010the district is shown in Figure6and Figure7:Figure6the P roportion of P opulation D istribution in2020000Figure7the P roportion of P opulation D istribution in2010See from Figure 6and Figure 7,the population distribution changes in the proportion of the district is very little in 10years.So we can assume that the population distribution of Shenzhen District remained basically unchanged within ten years ,then the proportion of the population is shown in Table 8:Table 8the P roportion of the P opulation in 2010in Shenzhen City Luohu Distric tFutian District Nan-sh an District Baoan District Long-g ang District Yanhu District ,Guang ming New District Ping-sh an New District K（i）0.090.130.110.390.190.020.050.02The bed demand of each area:)(*)()(i Q i K i q =,here q is the need of beds each area,K(i)isthe proportionof the population in 2010in Shenzhen city,Q(i)is the bed need of Shenzhen and the variable i representing the year.By calculating,we can get the following Table 9:Table 9the Bed Demand Prediction of Each AreaLuohu DistrictFutian District Nan-sha n District Baoan District LonggangDistrictYanhuDistrictGuangm ing New District Ping-sha n New District k(i)0.080.1270.1050.3880.1940.020.0460.032011196431182578952847644911129736201221053342276310210510552612107892013225235752955109225461563129484420142405381831561166458326011382901201525644071336612438.8621964114749612016273143363584132476623682157010242017290546123813140907045726167010892018308649004051149717485771177411572019327652014300158917945819188412282020347455164560168528426868199713035.2the A nalysis of B eds D emand According to D ifferent D isease 5.2.1Infantile PneumoniaInfantile pneumonia is a common clinical disease ；it is easy to occur in four seasons ，especially in winter and spring.If it is not treated thoroughly,easy to repeated attacks and affecting the child's development normally.According to the Shenzhen City Health Bureau of Health Statistics Yearbook from 2001to 2010,the prevalence rate of different years are listed in the following T able 9:T able 9.The prevalence rate and the duration of hospitalization with i nfantilepneumoniaYear 2001200220032004200520062007200820092010P revalenc e rate (%)0.08970.08120.06950.07190.06290.05190.04020.04020.0310.03D uration of hospitalization ation(day (day )6666676667It can be seen from Table 9，along with the modern medical technology improving,the prevalence rate of infantile pneumonia is falling.As stated in 5-1-3,Checking and calculating of ratio values,we can know that they are in ()9680.9666,1.2.Thus we can use the gray model GM (1,1).UsingMATLAB software,the parameters can be obtained.The absolute value of the relative error between the estimated value and the actual value is:Figure 8The absolute value of the relative errorAs you can see from figure 8,the relative error is rather small,so we can estimate the future incidence rate using this model.By this model,we can get the prevalence rate was 0.0163and 0.0087in 2015and 2020.According to table 6,we can get the number of infantile pneumonia were 10529and 8773.5.2.2senile cataractAccording to theShenzhen City Health Bureau of Health Statistics Yearbook in 2001-2010,the prevalence rate of different years are listed in the following table 10:rate rate(%)(%)D uratio n of hospital ization ization((day)444443 2.7Along with the development of Shenzhen City,senile cataract prevalence is increasing year by year from the data in table 10.Then,we predicted the senile cataract prevalence by the cubic exponential smoothing method,and verify the correctness of the model.Moreover,we work out the relative error of the senile cataract prevalence between estimation value and the actual value ,as shown in the following table F igure 8:F igure 8the relative error of the senile cataract prevalenceFrom the table we can see ,owing to having the smaller relative errors between model value and real value,so it is a reasonable model.By using this mode,lwe can estimate the prevalence rate ,and then get that the prevalence rate is 0.00361and 0.01433.According to table 6,the number of old people who suffering from senile cataract were 4394and 29262.5.2.3B ed demand of different type types s hospital According to the statistical yearbook of 2011medical institutions of various kindsvisits and inpatients in Shenzhen city ,health agencies can be divided for the hospital,nursing homes,clinics and so on 。
