2017 International Conference on Economics, Management Engineering and Marketing (EMEM 2017) ISBN:

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1 2017 International Conference on Economics, Management Engineering and Marketing (EMEM 2017) ISBN: Application of Richards Model on Hainan Population Growth Forecast Zhan-Ji GUI 1,a, Bin GUI 2,b,* and Fu-Sheng FENG 3,c 1 Department of Software Engineering, Hainan College of Software Technology, Qionghai, , P.R. China 2 School of Humanity and Law, Beijing University of Civil Engineering and Architecture, Beijing, P.R. China 3 School of Computer and Information Engineering, Heilongjiang University of Science and Technology, Haerbin, , P.R. China a zhanjigui@sohu.com, b guibin33@163.com, c ffs1974@163.com *Corresponding author Keywords: Population, Growth Model, Nonlinear Regression. Abstract. In this paper, the data on the Hainan population were used in the Chinese Statistical Yearbook and the Hainan Statistical Yearbook. The Richards growth model was used to predict trends in population growth in Hainan by regression analysis and Mathematica software. The peak of the population of Hainan was predicted using the Richards model. As a result of the two-child policy, the impact of population growth in Hainan was studied. Introduction Since June 1, 2014, Hainan Province introduced the two-children fertility policy for couples where either the husband or the wife is from a single-child family (hereinafter referred to as the two-children fertility policy). As of the end of December 2015, Hainan Province, a total of 4299 pairs of couples to apply for the birth of a second child, 1397 couples had children, 1279 women were pregnant. Since the implementation of the two-children fertility policy, the number of children born in Hainan Province is 1397 more than planned. The implementation of the two-children fertility policy, the population growth in Hainan Province is affected very small. Under this situation, The 5th Plenum of the 18th Central Committee of the Communist Party of China decided to fully implement the universal two-children policy.it is an important subject to the current macroeconomic policy research in Hainan that forecast the impact of full two-children policy on the Hainan population growth. The influence of the universal two-children policy on the newly-born population is divided into long-term effect and short-term effect. In the recent year, Hainan s full implementation of the universal two-children policy has obvious effects on childbirth encouragement. In 2016, the number of Hainan citizens applying for registration of birth increased significantly, and the number of births showed a significant growth trend. Based on Hainan population data at the end of the year in China Statistical Yearbook and Hainan Statistical Yearbook[1,2], using the Richards growth model, Mathematica software was used to simulate the development trend of population growth in Hainan by means of nonlinear regression analysis. And 85

2 predict the peak population of Hainan, the research method has a certain theoretical value and practical significance. The Establishment of the Model In the research on the population growth process, Malthus's exponential growth model is the pioneering work, and its major defect is an exponential growth rate hypothesis, which will lead to disastrous infinite population explosion and can never represent a sustainable process[3]. In fact, the population growth rule is that the initial growth amount in the growth process is relatively small, and it will reach a rapid growth period with time elapsing. Due to the regulation through the family planning policy, the growth rate will slow down, and the total growth amount will be stable. This process can be expressed by an S-shape curve. It is generally appropriate to use Logistic growth models to describe this growth process[4]. This paper describes the growth process by Logistic model and Richards model. Logistic model is compared with Richards model, Logistic model is a model of three parameters, and Richards model is four parameter model. The Richards model will have better flexibility for data fitting [5]. In this paper, the Richards growth model is used to study the population growth data in Hainan, and the Richards model can be described as [6,7] a d Nt ( ) 1- N( t) K rn( t), N0 N( t0) dt a (1) Where N (t) is population density, r is the intrinsic rate of increase, K (1) is the environment carrying capacity, and N 0 is the population density in time t 0. Equation (1) is solvable, and the solution of Richards equation (1) is K Nt ( ). a a rt 1 KN0 1e In order to calculate the parameter estimation of Richards model (2) (2), Ratkowsky (1983) introduced the re-parameterization method, which was utilized b ln ( K N ) a 1, c 1 a, then we to re-parameterize equation (2). We set 0 have (2) Nt () K 1/ c br t 1 e (3) (3) By virtue of the strong adaptability to data fitting, Richards growth model has been widely applied. However, as a nonlinear regression model with four parameters, the parameter estimation of Richards model is relatively complex. Our research results indicate that it re-parameterization is not carried out, and the process of calculating parameter estimation on Hainan population data through the Richards model (2) will not convergent. Parameters K, b, c, r of Richards 86

3 model are all to be estimated. K is the limit value of population growth, or the largest population that can be accommodated in a country or region. b is the parameter associated with the initial population condition. r is the parameter describing the population growth rate. c determines the shape of the curve and the position of the inflexion point. The growth curve equation is S shape where the inflexion point changes with the parameter value. The parameters of Richard model have been widely applied based on its reasonable practical significant and strong description ability for the growth process. Forecast of Hainan Population Data According to the Hainan Provincial Statistical Yearbook[5] and the Chinese Statistical Yearbook[6], the data related to the population of Hainan, we listed the relevant data in Table 1. Table 1. Hainan Year-End Population Data Prediction. Unit: Million. Year Time t year-end population Year Time t year-end population Using Mathematica software to draw point diagram of the Hainan population growth data, the specific order format is as follows. data={{1,7.53},{2,7.62},{3,7.87},{4,7.96},{5,8.03},{6,8.178},{7,8.18},{8,8. 28},{9,8.36},{10,8.45},{11,8.54},{12,8.64},{13,8.69},{14,8.77},{15,8.87},{16,8.95},{17,9.03},{18,9.108},{19,9.171}}; d=listplot[data,plotstyle PointSize[0.012]] To execute the order format, we have Figure 1. Point Diagram of Hainan Population Growth Data. 87

4 Using the year-end population data of Hainan, the parameter estimation of K, b, c, r of equation (3) is given by Mathematica software order format HN=NonlinearModelFit[data,K/(1+Exp[b-r*x])^(1/c),{r,b,c,K},{x}] HN[{"ParameterTable","RSquared"}] Normal[HN] The result of the output is {K , b , c , r }. Correlation coefficient R 2 = The forecast equation of Hainan population is Nt () (4) (1 + Exp( x)) (4) The prediction curve of Richards prediction equation (4) and the point diagram of Figure 1 were drawn in Figure 2. Figure 2 shows that the Richards prediction equation (4) gives a good fit for the data of the Hainan population Figure 2. Prediction Curve and Point Diagram of Hainan Population Growth Data. Discussion Because of the cumulated influence of birth policy adjustments, and Chinese zodiac, it was predicted that there will be a certain accumulation of birth, there will be a jump up. According to statistics, the end of 2016 the province's resident population is million, the annual population birth rate of 14.57, the policy of more than 4.5%. Although the number of people born in Hainan did not produce the expected pulse mutation, there was no down and jump, but the universal two-children policy reversed the downward trend in Hainan's population. From the Richards prediction equation (4), it can be seen that the Hainan population is operating normally according to the prediction curve in Fig.2. According to the prediction equation (4), the peak population of Hainan can be predicted to be million, and its development space is sufficient. By the end of 2017, we can predict that the population of Hainan is million. 88

5 Comparing the Richards model with the Logistic model, since the Richards model is a four-parameter model, it has more flexibility in fitting the actual problem. The research method of this paper has a wide range of applications in solving practical problems. Acknowledgment This work is supported by the Philosophy and social sciences planning project of Hainan Province under Grant HNSK(YB)16-87 and the Nature Science Foundation of Hainan Province under Grant References [1] Haina Bureau of Statistics of China. Statistical Yearbook of Hainan, Beijing: China Statistics Press, [2] National Bureau of Statistics of China. Statistical Yearbook of the People's Republic of China, Beijing: China Statistics Press, [3] Z.J. Gui, Biological dynamic models and computer simulation. Science Press, Beijing, [4] Z.J. Gui, K.H. Wang, L.S. Chen, Mathematical Theory and Calculation of Pest Control. Science Press, Beijing, [5] D.A. Ratkowsky, Nonlinear regression modeling. New York: Marcel Dekker, [6] F.J. Richards, A flexible growth function for empirical use. J. Exp. Bot., 10(1959) [7] R.B. Banks, Growth and diffusion phenomena: mathematical frameworks and applications Berlin: Springer,