Research Article Comparison of Three Measures to Promote National Fitness in China by Mathematical Modeling

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1 Absrac and Applied Analysis, Aricle ID , 7 pages hp://dx.doi.org/ /2014/ Research Aricle Comparison of Three Measures o Promoe Naional Finess in China by Mahemaical Modeling Pan Tang, 1 Daqing Xu, 1 Qing Dai, 1 and Tinging Huang 2 1 Deparmen of Public Physical Educaion, Hefei Universiy, Hefei , China 2 School of Mahemaical Sciences, Anhui Universiy, Hefei , China Correspondence should be addressed o Pan Tang; pan@hfuu.edu.cn Received 22 January 2014; Acceped 27 January 2014; Published 26 March 2014 Academic Edior: Weiming Wang Copyrigh 2014 Pan Tang e al. This is an open access aricle disribued under he Creaive Commons Aribuion License, which permis unresriced use, disribuion, and reproducion in any medium, provided he original work is properly cied. In his paper we esablished a mahemaical model for naional finess in China. Based on a quesionnaire and daa of he General Adminisraion of Spor of China and he Naional Bureau of Saisics of China, he dynamics for hree classes of people are expressed by a sysem of hree-dimensional ordinary equaions. Model parameers are esimaed from he daa. This sudy indicaed ha naional finess pu ou by he Chinese governmen is reasonable. By finding he key parameer, he bes measure o promoe naional finess is pu forward. In order o increase he number of people who frequenly paricipae in spor exercise in a shor period of ime, if only one measure can be chosen, guiding people who never ake par in physical exercise will be he bes measure. 1. Inroducion To promoe he developmen of mass spors in he new era ofreformandopening-upinchinaandoimprovenaional physical qualiy,he Sae Council launched a naional finess program on June 20, 1995 [1]. Now naional finess has go remarkable achievemen. The survey shows ha he number of people who ofen paricipae in spors aciviies in 4 is more han 5.7% he number in 1997 and he counry has 28.2% of populaion who ofen ake par in physical exercise in 7 [1]. To beer implemen he naional finess program, he governmenakessomemeasuresmainlyonhreeaspecs. The firs one is conducing propaganda work, o make people aware of he imporance of spors finess and he implemenaion of he naional finess program and o arouse enhusiasm of he masses o paricipae in finess [1]. The second one is guidance, ha is, generally esablishing insiuions responsible for mass spors managemen work, such as social spors guidance cener, naional finess guidance cener, and social spors insrucors [1]. The purpose is o help guide people o exercise. The las one is improvemen of spors faciliies. China has buil and renovaed various spors sadiums and acively promoed open sadiums. These have grealy improved maerial condiions of naional finess [1]. In [1] General Adminisraion of Spor of China (GASC) also poined ou ha, alhough we have go many achievemensandexperience,hemasssporsinourcounry soverall developmen level is no high and he proporion of he populaion paricipaing in regular physical exercise is no high. We sill face many challenges [1]. According o he repor of GASC [2], populaion can be separaedinohreeclasses.thefirsoneispeoplewhonever ake par in physical exercise. We call i as never exercise for shor. The second one is people who occasionally ake par in physical exercise. We call i as occasionally exercise for shor. This class of people does weekly exercise aciviies of 1 o 2 imes. The hird one is people who ofen ake par in physical exercise. We call i as frequenly exercise for shor. This class of people does weekly exercise aciviies of no less han 3 imes, each ime no less han 30 minues and he exercise inensiy above he average of person. Of course, he social spors insrucors are included in he hird-class of people. So far, China has carried ou hree invesigaions of he curren siuaion of mass spors in 1997, 1, and 8. According o he hree surveys and he daa of Naional

2 2 Absrac and Applied Analysis Bureau of Saisics of China [3], he proporion of he hree classes of people is lised in Table 1.Based on hese daa,we can see ha he proporion of he hird-class of people is no high. In he naional finess program ( ), Chinese governmen pu forward he arge ha he proporion of he hird-classofpeopleshouldbemorehan32% [2]. I is a naural quesion wheher he goal can be aained. This is he firsproblemhawewanoprove. In addiion, all of hese programs cos an enormous sum of money every year, for example, over one year a oal invesmen of spors funds 191,450,000,000 RMB on consrucion of sie [1]. I is naural o ask how we can economically and quickly increase he number of frequenly exercise people. Based on he naional finess program [1], here are some measures including propagaion, guidance, and spors faciliies. There is no doub ha he hree measures ogeher can promoe naional finess. However, in order o save manpower and wealh of he counry, we wan o know which measure should be he bes one if only one measure can be chosen. This is he second problem ha we wan o prove. Currenly, alhough some lieraures repored he imporance of naional finess, hey only sae or compare he achievemen afer he implemenaion of he naional finess program [4, 5, 8, 9]. There are few lieraures discussing he bes sraegy o improve he naional finess program. There are no any mahemaical models o sudy how o improve he naional finess program. In his paper, based on a quesionnaire and he daa of GASC and he Naional Bureau of Saisics of China, we esablished a mahemaical model and incorporaed hree measures and hree classes of parameers. By numerical simulaion and analysis, he key parameersarefoundandusedodevelophebesmeasure. Hopefully, i could provide he heory reference for he mass spors policy basis. The paper is organied as follows. In Secion 2 we esablishamahemaicalmodelbasedonaquesionnaireandhe daa of he General Adminisraion of Spor of China and he Naional Bureau of Saisics of China. Secion 3 is devoed o parameer esimaion, numerical simulaions, and analysis of hesysem.thegoalisofindhekeyparameer.weendhe paper wih a brief discussion. r γ 2 Never exercise x α 2 x β 3 x γ 3 y α 1 x β 1 xy β 2 x Frequenly exercise μ Occasionally exercise y β 4 y Figure 1: The diagram of class ransformaion. The red line represens ransformaion by conac, he blue line represens auomaically ransformaion, and he green line represens reducion of he imes of exercise. x y γ Figure 2: The fiing beween he real number of hree classes of people and he soluion of he sysem. The red is real number and he blue line is he soluion. μy 2. Modeling Based on he surveys, he populaion can be separaed ino hree classes x, y,and [4 6]. x, y,and presen he number of individuals who never, occasionally, and frequenly paricipae in physical exercise a ime, respecively. Each class can be ransformed o oher classes. In order o beer undersand howodoransformaionbeweenhehree-classgroupsand in order o ge real daa, we conduced a quesionnaire survey. According o he quesionnaire, by conacing he people who occasionally paricipae in exercise, ha is, y, here is 10.57% of he firs-class of people x who become he second-class of people y. By conacing he people who frequenly paricipae in exercise, ha is,, hereare8.89% and11.2% ofhefirsclass of people x who become he second-class of people y and he hird-class of people,respecively;and hereis also 17.6% of he second-class of people y who become he hirdclass of people. Because of propaganda, here are 26.03% and 21.2% of he firs-class of people x who auomaically become he second-class of people y and he hird-class of people,respecively.ahesameime,somepeoplereduced he imes of exercise because of he lack of spor faciliies. For he hird-class of people,here are 24.52%and 15.93%of he class of people who become he second-class of people y and he firs-class of people x, respecively.andhereis15.04% of he second-class of people y who become he firs-class of

3 Absrac and Applied Analysis 3 Table1:Daaofsurveyforheproporionofhehreeclassesofpeople. Year Firs-class (%) Second-class (%) Third-class (%) The oal number of populaions (million) References [3 5] [3 5] [3, 6] Table 2: Parameers. Parameers r K α 1 α 2 β 1 β 2 β 3 β 4 γ 1 γ 2 γ 3 μ Descripion Inrinsicraeofincreaseofhuman Carrying capaciy of populaion Auomaic ransformaion rae of individual from he class x o he class y because of propaganda Auomaic ransformaion rae of individual from he class x o he class because of propaganda Transformaion rae of individual from he class x o he class y by conacing individuals a he class y Transformaion rae of individual from he class x o he class y by conacing individuals a he class Transformaion rae of individual from he class x o he class by conacing individuals a he class Transformaion rae of individual from he class y o he class by conacing individuals a he class Auomaic ransformaion rae of individual from he class o he class y because of he lack of spors faciliies Auomaic ransformaion rae of individual from he class o he class x because of he lack of spors faciliies Auomaic ransformaion rae of individual from he class y o he class x because of he lack of spors faciliies Deah rae of human Table 3: Birh rae and deah rae. Year Birh rae (per year) Deah rae (per year) Mean Table 4: Value of parameers. Parameers Values (per year) Reference r [3] K [7] α Esimaed β Esimaed γ Esimaed μ [3] people x. ThediagramofclassransformaionisinFigure 1. Then we obain he following sysem: dx d =rx(1 x K ) β 1xy β 2 x β 3 x α 1 x +γ 2 +γ 3 y α 2 x, dy d =β 1xy + β 2 x + α 1 x+γ 1 γ 3 y β 4 y μy, d d = γ 1 γ 2 +β 3 x + β 4 y + α 2 x μ. (1) x y Figure3:Thesysemapproachesasableposiiveequilibrium sae. The number of people who frequenly paricipae in physical exercise is increased. All he parameers are lised in Table 2.Theaimisosudy he impac of lead/guidance, conduc propaganda, and spors faciliies on naional finess developmen. In deail, i is o sudy he effec of hese parameers α, β, andγ on he dynamicsofhenaionalfinessmodelandofindhekey parameer. 3. Simulaion and Analysis Since he sysem is very complex, heoreical analysis is very difficul and we use numerical simulaion o analye

4 4 Absrac and Applied Analysis α = α = α = β = β = β = (a) Changing he value of α (b) Changing he value of β 1 1 γ = γ = γ = (c) Changing he value of γ Figure 4: Increasing he value of α and β and reducing he value of γ can all increase he number of.theimpacofβ on he sysem is he bigges. The impac of γ on he sysem is lile bigger han he impac of α. he dynamical behaviors based on he real daa. According o he daa of he Naional Bureau of Saisics of China [3], he birh rae and he deah rae of populaion in China are lised in he Table 3. In 1991, China Academy of Sciences published a repor abou he produciviy and populaion carryingcapaciyofhelandresourceinchina.thecarrying capaciy is [7]. To obain he value of oher parameers, we performed some esimaions based on he daa of GASC and he Naional Bureau of Saisics of China. For convenience, we assume ha α 1 = α 2 = α, β 1 = β 2 = β 3 = β 4 = β,andγ 1 = γ 2 = γ 3 = γ.then, we esimae he hree parameers based on he minimal error mehod and obain he fiing figure (Figure 2). Finally, hevalueofallparameersislisedintable 4.Basedonhese values of parameers, he sysem approaches a sable posiive equilibrium sae (Figure 3). From Figure 3, wecanseeha henumberofpeoplewhofrequenlyparicipaeinexercise will increase. Hence, he goal of Chinese governmen in he naional finess program ( ) can be aained. Nowwewanosolvehesecondquesion.Bychanging he value of hree parameers α, β, and γ, we invesigae he impac of hese hree measures on he number of hree classes of people x, y, and (Figure 4). From Figure 4(a), wecan see ha α canno infec he dynamics of he sysem. This meanshainensifyingpropagandaisnoobviousoincrease he number of people who frequenly paricipae in spor

5 Absrac and Applied Analysis β 1 = β 1 = β 1 = β 2 = β 2 = β 2 = (a) Changing he value of β 1 (b) Changing he value of β β 3 = β 3 = β 3 = β 4 = β 4 = β 4 = (c) Changing he value of β 3 (d) Changing he value of β 4 Figure 5: The impac of four differen β on he sysem. exercise. However, Figure 4(b) displays he fac ha β can srongly infec he dynamics of he sysem. In oher words, by providing guidance for he firs- and second-class of people, more and more people will frequenly paricipae in spor exercises. A las, improving spor faciliy can increase he numberofhepeoplewhofrequenlyparicipaeinspor exercise, which can be seen from Figure 4(c). Now we wan o know which class of people provided guidancehacanleadohebeseffec.bychanginghefour differen parameers β 1,β 2,β 3,andβ 4 in he original sysem (1), we find ha β 3 and β 4 have sronger effec in he sysem (Figure 5). This means ha only he hird- class of people guiding he oher classes of people x and y canleadobeer effec. Nex, by changing he values of β 3 and β 4,wecompare he effec of guiding beween he firs- and he second-class of people (Figure 6) and we can obain he following resuls. Firs, from he black line we can see ha guiding boh he firs- and second-class of people will increase he number of he hird-class of people quickly, which means he effec by guiding he firs wo classes of people is he bes one. Second, if we wan o increase he number of people who frequenly paricipae in spor exercise in a shor period of ime, guiding hefirs-classofpeoplewillbehebesmeasure.lasly,ifwe

6 6 Absrac and Applied Analysis 1 1 β 3 = , β 4 = β 3 = β 4 = β 3 = , β 4 = Figure 6: Comparing he effec of guiding for differen classes of people. wanoincreasehenumberofhehird-classofpeopleover a long period of ime, guiding he second-class of people will be he bes measure. 4. Discussion As we know, naional finess can improve naional physical qualiy. Naional finess is promoed all over he world. Furhermore, Chinese governmen pu forward he arge ha he proporion of he hird-class of people should be more han 32% [2]. I is needed o consider wheher he goal can be aained and how o beer and faser achieve he anicipaed goal. In previous lieraures and repors, all conclusions are from repors or experiences. However, here arenoanyresulsbasedonmahemaicalheory.inhis paper,basedonaquesionnaireandhedaaofhegeneral Adminisraion of Spor of China and he Naional Bureau of Saisics of China, we esablished a mahemaical model for hree classes of people and represened hree measures by hree classes of parameers. By numerical simulaion and analysis, he key parameer β is found. Furhermore, he wo previous problems can be answered. By simulaion and analysis based on our mahemaical model, he following conclusions can be obained. Firs, he number of people who frequenly paricipae in spor exercises will increase definiely and hen he goal can be aained. Second, we found ha conducing propaganda canno increase obviously he number of people who frequenly paricipae in spor exercises. In realiy, people can be impressed by much propaganda. However, i is always difficuloacdueovariousreasons.third,sporsfaciliies are no so imporan as people imagine. From he figures we can see ha he effec of reducing he value of γ is no sronger. In fac, here are many ways o paricipae in physical exercise wihou spors faciliies. Lasly, i is very imporan o provide guidance for all people.from he simulaion of he model, we can see ha he effec of parameer β is he bigges. Furhermore, increasing he value of β byfiveimescanobainbeer effec han increasing he value by en imes. Hence, proper guidance will enable more people o paricipae in physical exercise frequenly. Currenly, here are many ways o provide guidance, for example, esablishing naional finess guidance cenerandprovidingsocialsporsinsrucor.thereporof he General Adminisraion of Spor of China in 9 [10] also fully affirmed ha social spors insrucors play a very imporan role in naional finess. In addiion, by comparing he effec beween β 3 and β 4, we found some differen resuls. If we wan o increase he number of people who frequenly paricipae in spor exercise in a shor period of ime, guiding hefirs-classofpeoplewillbehebesmeasure.ifwewan oincreasehenumberofhehird-classofpeopleinalong period of ime, guiding he second- class of people will be he bes measure. Hence, we can provide more and more social spors insrucors only for he firs- and he second-class of people in he fuure. In summary, hese conclusions are also consisen wih he acual siuaion. Furhermore, based on he mahemaical modeling and he real daa, we hink ha guidance is he bes measure for naional finess. Hopefully, hese conclusions could provide he heory reference for he mass spors policy basis. Conflic of Ineress The auhors declare ha here is no conflic of ineress regarding he publicaion of his paper. Acknowledgmens ThisresearchissupporedbySporsandSocialScienceFoundaion of Spors Bureau of Anhui Province (ASS ). The auhors would like o specially hank Professor Huaiping Zhu, York Universiy of Canada, for his guidance and help. Also, hey would like o hank anonymous reviewers for he very helpful suggesions which improved grealy his paper. References [1] General Adminisraion of Spor of China, Ouline of he naional finess program (The implemenaion of fifeen years), pp. 1 66, [2] General Adminisraion of Spor of China, The naional finess program ( ), 2011, hp:// ne/ardeail.aspx?aid=6537. [3] Naional Bureau of Saisics of China, hp:// [4] Z.J.ZhangandC.Liu, Commenaryonhedevelopmenof Chinese spors populaion since reform and opening, Journal of Physical Educaion Insiue of Shanxi Normal Universiy,vol. 22, no. 1, pp , 7.

7 Absrac and Applied Analysis 7 [5] X. R. Zhou and M. Y. Tan, Comparaive research on our mass spors condiion during wo imes invesigaion, Spor Science, vol.24,no.7,pp.12 15,4. [6] General Adminisraion of Spor of China, In 7 China urban and rural residens o paricipae in physical exercise siuaion survey bullein, 2012, hp:// es/ /19/conen hm. [7] China Academy of Sciences, Populaion carrying capaciy of China, 1991, hp://h.wikipedia.org. [8] X. P. Lin, The research on China mass spors developing endency oward 2010, China Spor Science and Technology,vol. 37, no. 11, pp , 1. [9] P. Tang, Analysis of he characerisics of he naional spors meeing, Spors Culure Guide,vol.12,pp.9 11,2010. [10] General Adminisraion of Spor of China, Acive in he mass spors, social spors insrucor was generally recognied, 9, hp://

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