POPULATION Abdul Hamid, 2015), by 2043, The older

POPULATION AGEING IN MALAYSIA

1.0       INTRODUCTION

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Ageing
is the process of growing old. The terms ageing could be refers to human be
refers to human beings, animals, and fungi. In humans, ageing represents a
lifelong process from conception, birth, maturity to death. In this research,
chronological definition will be used and the United Nations’ and Ministry of
Health’s line which recommends “the
elderly or ageing population” will be the mean people aged 60 years or
older. In recent years, Malaysia has experienced spectacular economic growth
and social change. This is together with declining of fertility and mortality
rates that resulted in increasing survival of ageing population year by year as
shown in the data. This show that if the year increase, the population of ageing
will increase.

The
data shows that the ageing population has increased from 594,770 in 1986 to 1,895,030 in 2016.
Therefore, we know that from year 1986 until year 2016, the population is 32,773,225.
For the first decades, the population is 6,810,938 while in the third decades,
the population is 14,592,371. This shows that the population has increased from
first to third decades. Normally people are living longer
due to better health care and improved living conditions.  According to the Prof. Dr. Tengku Aizan
Tengku Abdul Hamid (Tengku Abdul Hamid, 2015), by 2043, The older population
aged 65 years or over will take only 23 years to double from 7 percent in 2020
to 14 percent, where one out of every five persons in the population will be an
elderly (UN, 2013).

Generally,
elderlies are less healthy than the young’s, hence an increase in the
proportion of the aged group is associated with an increase in the prevalence
of ill health. Malnutrition is also expected to be a major problem in the
elderly due to changes in dietary habits, poor dentition and types and amounts
of food consumed. Apart from that, the health care system in this country is
primarily geared towards short term care and hospitalization. This poses a
challenge to countries like Malaysia who have to cope with the ageing
phenomenon with limited medical and technological advances that are available.
Therefore, the calculation of the population ageing in Malaysia is needed to estimate
the increasing numbers of ageing population so that a solution to problems at
hand could be provide.

 

2.0       PROBLEM STATEMENT

Based
on data collected, the ageing population has continuously increases year by
year. However, the increases of ageing population for the next years are
unpredicted. The increases cause by the declining of fertility and mortality
rates. Although ageing population increasing as the rates of fertility and
mortality declining, elderlies are less healthy and Malaysia have limited
medical availability and technological advances. Thus, to know whether the
ageing population keeps increasing, the Discrete Malthusian Growth model to
calculate and predict the total of ageing population in future. 

 

3.0       OBJECTIVES

The
objectives of the project are:

       
i.           
To determine the ageing population for
the next years.

      ii.           
To choose the suitable model that fit
the data by calculating the root mean square error (RMSE).

    iii.           
To predict the total ageing population
in 2017 until 2022 with better model.

 

 

4.0       SIGNIFICANT
OF THE PROJECT

The
significant of the project is we will know the suitable model for the data by
calculating the root mean square error (RMSE) where the value is the smallest.
In addition, the ageing population can be verified whether it will increase for
the next year by conducting this project. This project also can let us predict
the total ageing population using Discrete Malthusian Growth model in 2017
until 2022. The lack of medical availability and technological advances led to
people awareness about the care of the elderly

 

 

5.0       SCOPE
OF THE PROJECT

This
project is about ageing population in Malaysia and the data for this project is
collected from 1986 until 2016. This project is focusing on Discrete Malthusian
Growths model. It consists of Autonomous and Non-Autonomous Discrete Malthusian
Growths model. One of these two models is chosen by finding the better model
using Root Means Square Error (RMSE) to calculate and predict the total urban
population in Malaysia in future from 2017 until 2022.

 

6.0       LITERATURE
REVIEW

Ageing
population changes are affected by fertility and mortality rates. Fertility
rates is the number of offspring born per mating pair while mortality rates
which also known as death rate is a measure of the number of deaths in a
particular population, scaled to the size of that population, per unit of time.
(Hamid, 2012) state that Malaysia is in the third stage of demographic
transition, where fertility rates are declining faster than mortality rates.
All of these changes have significant implication in the economy and society. This
is similar with the opinions of Bloom, Canning and Saville (2003) which said
that the population ageing issues influence the productivity and economic
growth of the nation.

Discrete
Malthusian Growth is a study about modification or changes. Specifically, it
demonstrates to make an interpretation of certifiable circumstances into the
mathematics language (James, 1990). Through the expansion in computational
capacity and the current attention in chaos, discrete dynamics has developed as
an imperative region of mathematical study and review. The Discrete Malthusian
Growth which are autonomous and non-autonomous have been used in this project.
Joseph (2008) state that autonomous do not have time dependence or sequential
and will figure out the population in one time, conversely to the
non-autonomous which need to figure out the population continuously by knowing
the time like years. As in the project, the autonomous and non-autonomous have
been used to know the ageing population. 

 

 

 

7.0
METHODOLOGY

There are two models
that being used in this project to predict the number of ageing population in
Malaysia. The first model is Discrete Malthusian Growth Model. It consists of
autonomous and non-autonomous. In order to determine the better model, Root
Means Square Error (RMSE) is also being used in this project.

There are the steps
that have been conducted during completing the project:

Step
1: Finding the data

The data has been shown
in the appendix 1.

 

Step
2: Study the collection data and determine the model

Study the data and determine which are the best
model should be used in this project.

 

Step
3: Calculate the Autonomous Discrete Malthusian Growth Model

Calculate the predicted value of total population by
using general formula of autonomous.

Step 4: Calculate the
Non-Autonomous Discrete
Malthusian Growth Model

Find the predicted value of total population by
using general formula of non-autonomous.

,

where
 is the linear growth rate
equation,

Find  by plotting the scatter chart of the
relationship between growth rate and years.

Step
5:
Calculate the error of each data for all
model

Find
the error of the ageing population by using the formula:

Error
=

 

Step
6: Calculate the Sum Square Error (SSE) and Root Means Square Error (RMSE) for
all model.

Sum
Square Error (SSE) and Root Means Square Error (RMSE) are used in this project
to find out the better model to predict the ageing population for the year 2017
until 2022. The formula for SSE and RMSE are stated as below:

Sum
Square Error (SSE) =

Root
Means Square Error (RMSE) =

Step 7: Record the result of the
project

Record all of the calculated data by tabulation and
show the better model for this project.

 

 

 

 

 

 

 

8.0       RESULT

8.1       Autonomous Discrete Malthusian Growth Model

n

Year

Ageing Population

Growth rate, r

Predicted Population

Error square

0

1986

594770

0

594770

0

1

1987

612035

0.0290

617490

0.0001

2

1988

628939

0.0276

641078

0.0004

3

1989

646065

0.0272

665568

0.0009

4

1990

664116

0.0279

690992

0.0015

5

1991

686517

0.0337

717388

0.0019

6

1992

709808

0.0339

744792

0.0022

7

1993

733374

0.0332

773243

0.0027

8

1994

756418

0.0314

802781

0.0033

9

1995

778896

0.0297

833448

0.0043

10

1996

803412

0.0315

865285

0.0051

11

1997

826281

0.0285

898339

0.0064

12

1998

849422

0.0280

932656

0.0080

13

1999

875621

0.0308

968283

0.0092

14

2000

906498

0.0353

1005272

0.0097

15

2001

953186

0.0515

1043673

0.0075

16

2002

1000484

0.0496

1083541

0.0059

17

2003

1044492

0.0440

1124933

0.0051

18

2004

1085718

0.0395

1167905

0.0050

19

2005

1129772

0.0406

1212519

0.0047

20

2006

1188262

0.0518

1258837

0.0031

21

2007

1244643

0.0474

1306925

0.0023

22

2008

1295158

0.0406

1356849

0.0021

23

2009

1341005

0.0354

1408681

0.0023

24

2010

1387690

0.0348

1462492

0.0026

25

2011

1459590

0.0518

1518360

0.0015

26

2012

1538906

0.0543

1576361

0.0006

27

2013

1623986

0.0553

1636578

0.0001

28

2014

1711956

0.0542

1699095

0.0001

29

2015

1801175

0.0521

1764001

0.0004

30

2016

1895030

0.0521

1831386

0.0012

 

Figure 8.1: Predicted value of
ageing population and error square of autonomous.

From the table above, we obtain the growth rate and
the average growth rate by using formula

Growth
rate, r =

Average
growth rate =
= 0.0382

 

Then,
predicted of ageing population is calculated as follows:

when n = 0

= 617490

Find
Sum Square Error (SSE)

SSE = 0.0998

Thus,
we get the Root Means Square Error for autonomous Discrete Malthusian Growth
Model with formula:

RMSE
=
= 0.056745

8.1.2
Non-Autonomous Discrete Malthusian Growth Model

 

n

Year

Ageing Population

k(t) = 0.0011t – 2.1234

Predicted Population

Error square

0

1986

594770

0

594770

0

1

1987

612035

0.0623

631824

0.0010

2

1988

628939

0.0645

651511

0.0013

3

1989

646065

0.0667

670889

0.0015

4

1990

664116

0.0689

690579

0.0016

5

1991

686517

0.0711

711335

0.0013

6

1992

709808

0.0733

736839

0.0015

7

1993

733374

0.0755

763399

0.0017

8

1994

756418

0.0777

790357

0.0020

9

1995

778896

0.0799

816856

0.0024

10

1996

803412

0.0821

842843

0.0024

11

1997

826281

0.0843

871140

0.0029

12

1998

849422

0.0865

897754

0.0032

13

1999

875621

0.0887

924766

0.0032

14

2000

906498

0.0909

955215

0.0029

15

2001

953186

0.0931

990893

0.0016

16

2002

1000484

0.0953

1044025

0.0019

17

2003

1044492

0.0975

1098031

0.0026

18

2004

1085718

0.0997

1148628

0.0034

19

2005

1129772

0.1019

1196353

0.0035

20

2006

1188262

0.1041

1247381

0.0025

21

2007

1244643

0.1063

1314574

0.0032

22

2008

1295158

0.1085

1379687

0.0043

23

2009

1341005

0.1107

1438532

0.0053

24

2010

1387690

0.1129

1492404

0.0057

25

2011

1459590

0.1151

1547413

0.0036

26

2012

1538906

0.1173

1630800

0.0036

27

2013

1623986

0.1195

1722805

0.0037

28

2014

1711956

0.1217

1821625

0.0041

29

2015

1801175

0.1239

1924067

0.0047

30

2016

1895030

0.1261

2028303

0.0049

 

Figure 8.2: Predicted value of
ageing population and error square of non-autonomous.

 

Graph
8.1: Scatter plot of the relationship between growth rate and year.

 

The linear equation of growth rate is obtained from
the graph:

k(t)
= 0.0011t – 2.1234

Value
of  and has been found
 = (+ n)

 

When
 = 1987, n = 0

k(t)
= 0.0011t – 2.1234
= 0.0623

 

The predicted population has been calculated by using formula

= 631824

 

Sum
Square Error (SSE) is computed

SSE = 0.0872

 

Thus,
we get the Root Means Square Error for autonomous Discrete Malthusian Growth
Model with formula:

RMSE
=
= 0.053048

 

Since we have calculated the Root Means Square Error (RMSE) of
the two models above, we can see that RMSE Non-Autonomous Discrete Growth
Malthusian Model is smaller than Autonomous Discrete Malthusian Growth Model.
So, we can conclude that Non-Autonomous Discrete Malthusian Growth Model is the
best model. Therefore, the model has been chosen in this project to calculate
the predicted total ageing population from 2017 to 2022.

n

Year

Growth rate, r

Predicted population

31

2017

0.1283

2138162

32

2018

0.1305

2417192

33

2019

0.1327

2737953

34

2020

0.1349

3107303

35

2021

0.1371

3533314

36

2022

0.1393

4025505

 

Figure 8.3: Predicted value of
ageing population from 2017 to 2022

 

 

9.0       CONCLUSION

Based on the project, the Autonomous Discrete
Malthusian Growth and Non-Autonomous Discrete Malthusian Growth were used.
There is strong relationship on the ageing population according to year by
years. As for the Autonomous Discrete Malthusian Growth model, the total for
root mean square error (RMSE) is 0.056745. Meanwhile, the RMSE
for the non-autonomous is 0.053048.

In conclusion, the best
model in calculating the ageing population in Malaysia is Non-Autonomous
Discrete Malthusian Growth. This is because, the RMSE for this model shows the
lowest value of error compares to the Autonomous Discrete Malthusian Growth.
Hence, the Non-Autonomous Discrete Malthusian Growth is chosen as the best
model to predict the total of ageing population for the year 2017 to 2022.

 

10.0     REFERENCES

Arokiasamy, J. T. (1997). Social problems and
care of the elderly. The Medical journal of Malaysia, 52(3),
231..

Hamid, T. A. T. A. (2015). Population
Ageing in Malaysia: A mosaic of Issues, challenges and prospects.

Joseph, M. M. (2008). Math 121 ¬ Calculus for Biology I Spring Semester. San Diego.

Karim, H. A. (1997). The elderly in Malaysia:
demographic trends. Medical Journal of Malaysia, 52,
206-212.

Mafauzy, M. (2000). The problems and challenges
of the aging population of Malaysia. The Malaysian journal of medical
sciences: MJMS, 7(1), 1.

Sandefur, J. T. (1990). Discrete Dynamical System:
Theory and applications.

 

 

 

Appendix
A

 

n

Year

Population

0

1986

594770

1

1987

612035

2

1988

628939

3

1989

646065

4

1990

664116

5

1991

686517

6

1992

709808

7

1993

733374

8

1994

756418

9

1995

778896

10

1996

803412

11

1997

826281

12

1998

849422

13

1999

875621

14

2000

906498

15

2001

953186

16

2002

1000484

17

2003

1044492

18

2004

1085718

19

2005

1129772

20

2006

1188262

21

2007

1244643

22

2008

1295158

23

2009

1341005

24

2010

1387690

25

2011

1459590

26

2012

1538906

27

2013

1623986

28

2014

1711956

29

2015

1801175

30

2016

1895030