POPULATION PROJECTION USING A DYNAMIC SYSTEM APPROACH: THE CASE OF POPULATION IN BANDA ACEH Saiful Mahdia, Munawara and Nurul Fajarb aSurvey and Policy Analysis Research Gruop (SPARG), Statistics Department, College of Mathematics and Sciens, Syiah Kuala University, Jl. Syech Abdurrauf 3, Banda Aceh, 23111, Aceh – Indonesia bMathematics Department, College of Mathematics and Sciens, Syiah Kuala University, [email protected]; [email protected]; [email protected], ABSTRACT Population growth is the change in the amount and composition of the population from year to year. It requires a method to project not only number of the population, but also the composition of the population in a region. In this study we apply dynamic system approach to simulate and project the number and composition of the population of Banda Aceh based on factors that influence population growth, that is, births, deaths, and migration. This simulation and projection is done by Vensim PLE 6.0.1c. Projecting population growth of Banda Aceh to year 2100 shows a positive trend with an average population growth of 0.88% every year with a ‘demographic bonus’ estimated to be around 2025-2035. Keywords: population, projection, simulation, dynamic system, vensim 1. INTRODUCTION Projections is an indication of future Residents have an important role in regional demographic changes that calculates births, development because it can influence policy deaths, and migration. There are several methods development, education, culture, and resources. of projection that are often used, one of which is a The population also has a contemporary and component method. The component method sustainable characteristic that are constantly allows as obtain the projections of population by changing every year. This population change cohort (based on the age group). The results of the caused by the fertility, mortality, and migration calculation method of these components can be (BPS, 2012). analyzed using simulation method with various Therefore, we need a method to estimate scenarios. the population and the composition of the Based on the description above, this population as an effort to meet the data needs research will be conducted to model and simulate of the population. One of the roles of the population growth factor in Banda Aceh. The demography science to estimate the number simulations will be performed by using the dynamical method systems in accordance with of population growth in the future is a the characteristics of the system being simulated. projection method. This study about population growth and the Department of Population and Civil projection and population structure in Banda Aceh Registration Banda Aceh 2008-2012. is based on population cohort that influenced 2.2. Basic modeling demographic factors by the component method. 2.2.1 Conceptual Model The projection then simulated with a number of The conceptual model is represented by scenarios on components: births, deaths, and causal diagram describing causal relationships migration. among variables. In this process each variables is connected with the an arrow line. The step of 2. METHODE conceptual modeling in this study begins with 2.1. Data classifying variable levels on the productive age The data used in this study is a secondary data including data of population, date of birth, and group (age 15-64 years) and non-productive age mortality data that all are grouped based on age group (age 0-14 years and 65 years and over). group, the data of life expectancy (AHH), and data Furthermore, associated with each variable rate, of migration. The source of in this research is auxiliary and constants variable. Here is a from the Central Statistics Agency (BPS) of Aceh conceptual model of the number and structure of population based cohort of four levels. Population Dependency ratio Imigration 0-14 Imigration 15-44 Imigration 45-64 Imigration 65+ P0. 15-44 P0. 45-64 P0. 65+ P0. 0-14 Emigration 0-14 Emigration 15-44 Emigration 45-64 Emigration 65+ Population Population Population Population 0-14 15-44 45-64 65+ Birth Surv. 14-15 Surv. 44-45 Surv. 64-65 Death 65+ Death 0-14 Death 15-44 Death 45-64 Total of Fertility Mortality 0-14 Mortality 15-44 Mortality 45-64 Mortality 65+ one year <one year> Life expectancy Life tabel 0-14 Life tabel 15-44 Life tabel 45-64 Life tabel 65+ <Life expectancy> Deaths <Time> Figure 2.1. Conceptual model for population projections Based on Figure 2.1 seen that the total population population of women of childbearing age in each is affected by the components of population year from 2008 to 2012. consist of births, deaths, and migration. B. Deaths A. Birth Death is one of the factors causing a Birth is one of the factors increasing the reduction in the amount of and changes in number of residents. Birth can also affect the population structure. The number of deaths is number of deaths in that cohort and the number determined by the high mortality rate. The death who survive to get into the next cohort. The birth rate is obtained from the table of death and life also affects the dependency ratio of the expectancy. Mortality rate is calculated based on population. the chance of dying in each population cohort. The number of births is determined by the Number of deaths each cohort is level of fertility (TFR) in a certain region, the influenced by the number of inhabitants and the higher the total fertility rate, the more likelihood mortality rate in the cohort in question. the number of births. Here is a chart TFR Banda Furthermore, the number of deaths in each cohort Aceh in 2008-2012 as shown in the following into factors that affect the total number of deaths. graph: While the life expectancy can be seen in the following graph: 3 2,5 2,85 71,5 71,42 2 2,52 71,15 1,5 70,88 TFR 1,95 71 1 1,53 70,56 1,17 AHH 0,5 70,24 0 70,5 2006 2008 2010 2012 2014 70 Years 2006 2008 2010 2012 2014 Tahun Figure 2.2. The total fertility rate of Banda Aceh Year 2008-2012 Figure 2.3. Life ecpextancy of Banda Aceh Year 2008-2012 Based on Figure 2.2. seen that the TFR Banda Aceh continues to increase every year. In Based Figure 2.3. seen that the life 2011 occurred a significant increase on the TFR to expectancy Banda Aceh from 2008-2012 tended 2.85. This means that every woman in the Banda to have a positive trend with an average 70.85. Aceh bore three children during the fertile period. This means that babies born in the year 2008-2012 The increase is due much to the birth of this year, will be able to live up to 70 to 71 years. but declined again in 2012. Decline of this TFR could have been caused by one of the government C. Migration programs is family planning programs. From the Migration of the population is one other graph, average of TFR of Banda Aceh from 2008- factor that determines population growth that can 2012 of 2.01, which means there are 2 births per reduce or increase the number of residents. Migration caused by the push factor of the area of b. Amplitude variations comparison origin and pull factors in destination areas. |푆푠 − 푆푎 | 퐸1 = 2.2.2. Computation Model 푆푎 The formulation of the model is done after a structured conceptual model composed. The Where: formulation of this model is done by inserting 푆푠 = standard deviation of model mathematical formulas and relationships between 푆푎 = standard deviation of data variables so that the model created can be Model is considered valid if 퐸2 ≤ 30% simulated. Validation of the model is obtained as in the following table: 2.3. Verification and Validation Model 1. Verification Tabel 2.1. Validation of model Stages to ascertain whether of that model (%) (%) create in accordance with the modeler perception Validasi model E1 E2 E1 E2 called verification. Verification is done by software Vensim, namely by looking at the model Cohort 1 (age 0-14) 0.047 4.7 0.557 55.7 check and check unit. If checking the unit on Cohort 2 (age 15-44) 0.007 0.7 0.273 27.3 software models and appears OK, the models and Cohort 3 (age 45-64) 0.004 0.4 0.830 83.0 the overall unit of variable compliance. Cohort 4 (age 65+) 0.040 4 0.577 57.7 Total of Population 0.009 0.9 0.687 68.7 2. Validation Model Births 0.285 28.5 0.773 77.3 Validation is the testing of the model Deaths 0.647 64.7 0.983 98.3 whether the model is correct and made in accordance with the real system. Validation of the Based on the table above, it appears that the model is done by comparing the average value and validity of using means comparison test (E1) variance amplitude difference between the actual shows the results considered valid, because the data and simulation data. According to (Suryani, value of E1 <5%. It's just for the birth data and 2006) there are two ways of testing the validation death data is not valid because the actual data is that is mean comparison and amplitude variance not recorded completely. comparison. To test the validity of using Amplitude Variations Comparison (E2) the data looks not a. Error rate (mean comparison) valid, because the results of the validation> 30%, yet for the second cohort of the data is seen valid |푆 − 퐴 | 퐸 = because the result of the validation <30%.