Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
Population Projection Using a Dynamic System Approach: the Case of
Population in Banda Aceh
a
a
Saiful Mahdi , Munawa and Nurul Fajar
b
a
Survey and Policy Analysis Research Gruop (SPARG), Statistics Department, College of Mathematics and Sciens, Syiah Kuala
b
University, Jl. Syech Abdurrauf 3, Banda Aceh, 23111, Aceh – Indonesia, Mathematics Department, College of Mathematics and
Sciens, Syiah Kuala University, Saiful.mahdi@fmipa.unsyiah.ac.id; munawar@stat.unsyiah.ac.id; fnurul23@gmail.com,
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
INTRODUCTION
Residents have an important role in regional development because it can influence policy development, education,
culture, and resources. The population also has a contemporary and sustainable characteristic that are constantly
changing every year. This population change caused by the fertility, mortality, and migration [3]. Therefore, we
need a method to estimate the population and the composition of the population as an effort to meet the data
needs of the population. One of the roles of demography science to estimate the number of population growth in
the future is a projection method. Projection is an indication of future demographic changes that calculates births,
deaths, and migration. There are several methods of projection that are often used, one of which is a component
method. The component method allows as obtain the projections of population by cohort (based on the age
group). The results of the calculation method of these components can be analyzed using simulation method with
various scenarios.
Based on the description above, this research will be conducted to model and simulate the population growth
factor in Banda Aceh. The simulations will be performed by using the dynamical method systems in accordance
with the characteristics of the system being simulated. This study about population growth projection and
population structure in Banda Aceh is based on population cohort that influenced demographic factors by the
component method. The projection then simulated with a number of scenarios on components: births, deaths,
and migration.
METHOD
The data used in this study is a secondary data including data of population, date of birth, and mortality data that
all are grouped based on age group, the data of life expectancy (AHH), and data of migration. The source of in this
research is from the Central Statistics Agency (BPS) of Aceh and the Department of Population and Civil
Registration Banda Aceh 2008-2012.
Conceptual Model. The conceptual model is represented by causal diagram describing causal relationships among
variables. In this process each variables is connected with the an arrow line. The step of conceptual modeling in
this study begins with classifying variable levels on the productive age group (age 15-64 years) and non-productive
age group (age 0-14 years and 65 years and over). Furthermore, associated with each variable rate, auxiliary and
constants variable. Here is a conceptual model of the number and structure of population based cohort of four
levels..
190
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
Population
Imigration 15-44
Imigration 0-14
Birth
Surv. 14-15
Population
15-44
Surv. 44-45
Imigration 65+
P0. 65+
Emigration 45-64
Emigration 15-44
Emigration 0-14
Population
0-14
Imigration 45-64
P0. 45-64
P0. 15-44
P0. 0-14
Dependency ratio
Population
45-64
Emigration 65+
Surv. 64-65
Death 0-14
Death 15-44
Death 45-64
Mortality 0-14
Mortality 15-44
Mortality 45-64
Life tabel 15-44
Life tabel 45-64
Population
65+
Death 65+
Total of Fertility
<one year>
Life tabel 0-14
<Life expectancy>
Mortality 65+
one year
Life expectancy
Life tabel 65+
Deaths
<Time>
FIGURE 1. Conceptual model for population projections
Based on Figure 1 seen that the total population is affected by the components of population consist of births,
deaths, and migration.
TFR
Birth. Birth is one of the factors increasing the number of residents. Birth can also affect the number of deaths in
that cohort and the number who survive to get into the next cohort. The birth also affects the dependency ratio of
the population. The number of births is determined by the level of fertility (TFR) in a certain region, the higher the
total fertility rate, the more likelihood the number of births. Here is a chart TFR Banda Aceh in 2008-2012 as shown
in the following graph:
3
2,5
2
1,5
1
0,5
0
2006
2,85
1,17
2008
1,53
2,52
1,95
2010
2012
2014
Years
FIGURE 2. The total fertility rate of Banda Aceh Year 2008-2012
Based on Figure 2 seen that the TFR Banda Aceh continues to increase every year. In 2011 occurred a significant
increase on the TFR to 2.85. This means that every woman in the Banda Aceh bore three children during the fertile
period. The increase is due much to the birth of this year, but declined again in 2012. Decline of this TFR could
have been caused by one of the government programs is family planning programs. From the graph, average of
TFR of Banda Aceh from 2008-2012 of 2.01, which means there are 2 births per population of women of
childbearing age in each year from 2008 to 2012.
Deaths. Death is one of the factors causing a reduction in the amount of and changes in population structure. The
number of deaths is determined by the high mortality rate. The death rate is obtained from the table of death and
life expectancy. Mortality rate is calculated based on the chance of dying in each population cohort. Number of
deaths each cohort is influenced by the number of inhabitants and the mortality rate in the cohort in question.
191
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
Furthermore, the number of deaths in each cohort into factors that affect the total number of deaths. While the
life expectancy can be seen in the following graph:
AHH
71,5
71
70,5
71,42
71,15
70,88
70,56
70,24
70
2006
2008
2010
2012
2014
Tahun
FIGURE 3. Life expectancy of Banda Aceh Year 2008-2012
Based on Figure 3 seen that the life expectancy Banda Aceh from 2008-2012 tended to have a positive trend with
an average 70.85. This means that babies born in the year 2008-2012 will be able to live up to 70 to 71 years.
Migration. Migration of the population is one other factor that determines population growth that can reduce or
increase the number of residents. Migration caused by the push factor of the area of origin and pull factors in
destination areas.
Computation Model. The formulation of the model is done after a structured conceptual model composed. The
formulation of this model is done by inserting mathematical formulas and relationships between variables so that
the model created can be simulated.
Verification and Validation Model. Stages to ascertain whether of that model create in accordance with the
modeler perception called verification. Verification is done by software Vensim, namely by looking at the model
check and check unit. If checking the unit on software models and appears OK, the models and the overall unit of
variable compliance.
Validation Model. Validation is the testing of the model whether the model is correct and made in accordance with
the real system. Validation of the model is done by comparing the average value and variance amplitude
difference between the actual data and simulation data. According to [10] there are two ways of testing the
validation that is mean comparison and amplitude variance comparison.
a.
Error rate (mean comparison)
=
| ̅ − ̅|
̅
where:
̅ = the average of simulation
̅ = the average of data
Model is considered valid if ≤ 5%
b.
Amplitude variations comparison
=
| ̅ − ̅ |
̅
192
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
where:
̅ = standard deviation of model
̅ = standard deviation of data
Model is considered valid if
≤ 30%
Validation of the model is obtained as in the following table:
TABEL 1. Validation of model
(%)
Validasi model
E1
E2
E1
(%)
E2
Cohort 1 (age 0-14)
0.047
4.7
0.557
55.7
Cohort 2 (age 15-44)
0.007
0.7
0.273
27.3
Cohort 3 (age 45-64)
0.004
0.4
0.830
83.0
Cohort 4 (age 65+)
0.040
4
0.577
57.7
Total of Population
0.009
0.9
0.687
68.7
Births
0.285
28.5
0.773
77.3
Deaths
0.647
64.7
0.983
98.3
Based on the table above, it appears that the validity of using means comparison test (E1) shows the results
considered valid, because the value of E1 <5%. It's just for the birth data and death data is not valid because the
actual data is not recorded completely. To test the validity of using Amplitude Variations Comparison (E2) the data
looks not valid, because the results of the validation> 30%, yet for the second cohort of the data is seen valid
because the result of the validation <30%. In this study the testing of validity of using Amplitude Variations
Comparison visible is invalid, and then tested the paired-t test for the actual data with simulated data. This test is
done to see whether there is any difference in the actual data with simulated data. Confidence interval used in this
test was 95% with the following hypotheses:
H0 : µ = µ0 there is no difference between the actual data with simulated data
H1 : µ ≠ µ 0
there is difference between the actual data with simulated data
Data will reject H0 if the value of α <P-value. Testing paired-t test was performed using SPSS software version 22.Results of testing paired t test are shown in Table 2.
TABEL 2. Paired-t test models
Validasi model
Cohort 1 (age0-14 )
Cohort 2 (age 15-44)
Cohort 2 (age 45-64)
Cohort 4 (age 65+)
Total of Population
Births
Deaths
α
P-value
0.05
0.807
0.794
0.909
0.740
0.887
0.140
0.172
Selisih
data
-2206
869
-126
-314
-1777
955
18929
Based on Table 2 it appears that the value of the P-value of each model > 0:05, which means not enough evidence
to reject H0. We can conclude there is no difference between the actual data with simulated data, so that the
model is quite feasible to use.
193
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
SKENARIO OF MODEL AND DISCUSSION
The scenario is done by changing the parameter values of the model and the structure of the model to estimate
the other results are in accordance with the wishes. There are two types of scenarios in the simulation of
dynamical systems, namely the structure scenario and the parameters scenario. Structure scenario is used to
change the structure of the model by adding or reducing the number of variables. While the parameters scenario
are used to change the value of a variable parameters that affect the model. In this study, researchers developed a
scenario parameters only for projecting the population of the Banda Aceh. Parameter values are changed is the
value of the variable total fertility rate and life expectancy by considering the condition optimistic.
In the optimistic scenario, the number of births and deaths appear comparable population that continues to
increase every year, estimated birth and death of Banda Aceh will be stable in the year 2054. Along with the birth
and death of the population, the population of the Banda Aceh has also continued to increase in every year, an
average increase of Banda Aceh population at 0.0088 or 0.88%. It is estimated that the city of Banda Aceh will have
a demographic dividend in 2027 with a dependency ratio of 0.18714. Means that every 100 working age
population (considered productive) has dependents as much as 18 to 19 people who are not productive. Banda
Aceh dependency ratio is expected to hold steady in 2045 is equal to 0.2. Here is a graphic simulation model
scenario:
Birth
7,000
Jiwa/Year
5,250
3,500
1,750
0
2008
2031
2054
Time (Year)
Birth : Skenario 2
Birth : Skenario 1
2077
2100
Birth : model
FIGURE 4. The graph projection of the total birth population of Banda Aceh Year 2008-2100
Based on Figure 4 number of born in Banda Aceh population both in scenario 1, scenario 2, as well as the
optimistic scenario (model) looks comparable to that continues to increase every year. Total fertility is expected to
be stable in the year 2054. In scenario 1 the number of births estimated population of Banda Aceh about 7,000
births in 2100, in scenario 2 range 4,000 births, while the optimistic scenario (models) of approximately 5,000
births.
Deaths
30,000
Jiwa/Year
22,500
15,000
7,500
0
2008
2031
2054
Time (Year)
Deaths : Skenario 2
Deaths : Skenario 1
Deaths : model
194
2077
2100
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
FIGURE 5. The graph projection of the total death population of Banda Aceh Year 2008-2100
Based on Figure 4 number of deaths in Banda Aceh residents both in scenario 1, scenario 2, as well as the
optimistic scenario (model) looks comparable to that continues to increase every year. The number of deaths is
expected to be stable population in the year 2054. In scenario 1 the number of deaths estimated population of
Banda Aceh before 2100 about 22,000 deaths, in scenario 2 around 19,000 deaths, while the optimistic scenario
(models) of approximately 20,500 deaths.
Population
500,000
Jiwa
375,000
250,000
125,000
0
2008
2031
2054
Time (Year)
Population : Skenario 2
Population : Skenario 1
2077
2100
Population : model
FIGURE 6. The graph projection of the total population of the Banda Aceh Year 2008-2100
Based on Figure 5. The total populations in Banda Aceh residents both in scenario 1, scenario 2, as well as the
optimistic scenario (model) looks comparable to that continues to increase every year. The total population is
expected to be stable in the year 2054. In scenario 1 the estimated total population of the Banda Aceh before 2100
around 450,000 people with an average population increase of 1%, in scenario 2 of about 380,000 inhabitants with
an average population increase of 0.84%, while the optimistic scenario (model) around 400,000 residents with an
average population increase of 0.88%.
Dependency ratio
0.6
Dmnl
0.45
0.3
0.15
0
2008
2031
2054
Time (Year)
2077
2100
Dependency ratio : Skenario 2
Dependency ratio : Skenario 1
Dependency ratio : model
FIGURE 7. The graph dependency ratio projected population of Banda Aceh Year 2008-2100
Based on Figure 6 seen that the dependency ratio of Banda Aceh continued to decline from 2008 to 2030, then
rose to the landless stable until the year 2045 In scenario 1 is estimated lowest dependency ratio in 2025 was
0,216, scenario 2 in 2029 amounted to 0,164, while the scenario optimistic (models) in 2027 amounted to 0.187.
This means, in scenario 1 for every 4.6 people bear the productive age population aged 1 person unproductive. In
195
Proceedings of the 2nd International Conference on Natural and Environmental Sciences (ICONES)
September 9-11, 2014, Banda Aceh, Indonesia
ISSN 2407-2389
scenario 2, for every 6 people bear the productive age population aged 1 person unproductive. In the optimistic
scenario (model), for every 5.3 working age people aged bear 1 unproductive. Banda Aceh Dependency ratio will
stabilize in 2045 is equal to 0.2, in other words, by the year 2045 every 5 people of childbearing age would have
dependency 1 person productive age population. This could be due to the population growth of Banda Aceh, the
better, the higher the per capita income so the ability to save residents of Banda Aceh higher.
CONCLUTION
1.
2.
3.
4.
Total of the births, deaths, and a total population of Banda Aceh continues to increase every year with
different levels. The increase is highest between now and the year 2030 continued to show a positive
trend growth but the rate continues to decline towards a steady growth after 2050.
Projected population of the city of Banda Aceh has a positive trend with an average population increase
of 0.88% every year.
Under the optimistic scenario, the estimated population of Banda Aceh will have a demographic dividend
in 2027 with the lowest dependency ratio in 0187 or 18.7. This means, every 5.3 people of productive age
care on population aged unproductive.
Migration of Banda Aceh residents assumed the same for each year up to 2100.
REFERENCE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Borshchev, A., & Filippov, A. 2004. From system dynamics and discrete event to practical agent based modeling:
reasons, techniques, tools. In Proceedings of the 22nd international conference of the system dynamics society. Rev.22
BPS. 2013. Analisis Spasial Angka Harapan Hidup Penduduk Indonesia Hasil Ssnsus 2010. BPS-Jakarta, Indonesia.
BPS. 2012. Pengembangan Model Life Table Indonesia. BPS-Jakarta, Indonesia.
Close, M.c., Newell, C.J. dan Frederick, K.D. 2002. Modeling and Analysis of Dynamic Systems. United States of
America.
Munifah, L. 2006. Proyeksi Penduduk Kota Surakarta Berdasarkan Metode Langsung dan Metode Tidak Langsung.
Skripsi. Universitas Sebelas Maret, Surakarta.
Rahman, I. 2012. Pengembangan Model Dinamis untuk Mendapatkan Gambaran Interaksi Aspek Ekonomi dan
Lingkungan Hidup Secara Timbal Balik dari Model Pembangunan Kota Terintegrasi. Skripsi. Universitas Indonesia.
Jakarta.
Statistics Indonesia. 2013. Demografi. http://www.datastatistikindonesia.com
/portal/index.php?option=com_content&task=view&id=83&Itemid=905. ( 28 Oktober 2013).
Sterman, J. 2000. Busines Dynamics: System Thinkng and Modeling for A Complex World. Boston: The McGrau Hill
Companies, Inc.
Suryani, E. dan Rosiana, Y. 2012. Simulasi Sistem Dinamik Analisis Pengaruh Performa Ekonomi Makro Terhadap
Angka Kemiskinan. Jurnal Teknik POMITS. Vol. 1(1) : 1-6
Suryani, E. 2006. Pemodelan & Simulasi. Graha Ilmu. Yogyakarta.
Ventana Systems Inc. 2010. Vensim Reverence Manual.
Ventana Systems Inc. 2003. Vensim 5 Modeling Guide.
Wang, J. et al. 2008. System Dynamics Model of Urban Transportation System and Its Application. Journal of
Transportation Systems Engineering and Information Technology. Vol. 8, Issue 3.
196