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Mathematical Modeling of Kelantan’s Population Growth

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alif yusof

on 22 December 2013

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Transcript of Mathematical Modeling of Kelantan’s Population Growth

Group members :
AHMAD AIZAT BIN MOHAMMAD ZAMRI (2012243402)
MOHAMAD AFIQ BIN SHAHRIMAN (2012835282)
MUHAMMAD ALIF BIN YUSOF (2012857764)

Content outline
Introduction
Problem statement
Objective
Literature review
Methodology
Implementation
Result
Discussion
Recommendation

Introduction

The population projection has become one of the most important problems in the world.
Population sizes and growth in a country directly influence the situation of economy, policy, culture, education and environment of that country and determine exploring and cost of natural resources.
No one wants to wait until those resources are exhausted because of population explosion.
Methodology
Discussion
Based on the graph 1, as you can see that in 1970 population of Pahang was 523 800 and continued to increase year by year until it reach its carrying capacity.
There had been major differences between actual population and estimated population started in the year 1980.
The factors of increasing in population are the improvement in education, agricultural productivity and health services.
In the figure 2, the graph is keep increasing until it reach its carrying capacity which is 4793.242478. The growth rate of Pahang population is estimated 5% per year.


Mathematical Modeling of Pahang’s Population Growth
Problem statement
the population growth of Pahang is modelled using logistic growth model by Pierre Francois Verhulst.
Objective
The objective of this study is to :

To study a standard model of population growth in a constrained environment.
To estimate the population of Pahang’s citizen for the future year.

Literature review
According to Augustus Wali (2012), the data for Uganda population
-International Data Base (IDB) online - MATLAB software.
-used least square method
-population growth rate, the carrying capacity and the year
-approximately a half of the value of its carrying capacity.
-Population growth of any country depends on the vital coefficients.
According to Larsen (2011),
-logistic growth model
-forecasting mean dry grain weight per plant for corn at the state level.
-describe the performance of a constrained logistic growth model in forecasting mean dry grain weight per plant at harvest for corn.

Implementation
Recommendation
Obtain the data from the appropriate sources
Use another better model to estimate the population
Technological development, pollution,social trends and disaster has significant influence on the estimation of the population in some area, therefore they must be reevaluate every few years to enhance to improve the determination of variation in the population growth rate
Result
Methodology
Result
Result
Pahang
Pahang is the third largest state in Malaysia, after Sarawak and Sabah, and the largest in Peninsular Malaysia. Its state capital is Kuantan, and the royal seat is at Pekan.
Pahang is an agrarian economy and the state is driven by the tropical timber production. Fishery products are also a main source of income especially for the communities on the long coastline of the state
t=0:41;
>>N=4793.242478./(1+(8.15090202)*(0.9496388204).^t);
>>format long
>>N
>>plot(t,N)
Methodology
Methodology
Result
Graph of predicted the population values against time
It has a total area of 36,137 square kilometres and is administratively divided into 11 districts: Bera, Bentong, Cameron Highlands, Jerantut, Kuantan, Kuala Lipis, Maran, Pekan, Raub, Rompin and Temerloh.
Literature review
According to Wang (2012),
1)Thomas R. Malthus’s model 2)logistic model 3)coalition model
are examined in study of Mathematical Models for Population Projection. First of all, the explicit solutions for each model are exactly reached via using mathematical techniques of differentiation and integration. Then the tests of practical data and analysis for these models are done based on the explicit solutions; the comparisons of predicted data and actual data of population growth for the models are given by chart, tables and figures. They prove the efficiency of these models

Literature review
Literature review
According to Rusliza Ahmad (2012),
-effect of time delay on stability of mutualism population model with limited resources for both species.
First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. She analyzes the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Even though tilapia fish farming has been commercialized, the use of mathematical models in determining harvesting strategies has not been widely applied in Malaysia. Logistic growth model is appropriate for population growth of animal when overcrowding and competition resources are taken into consideration. The best harvesting strategy for the selected fish farm is periodic harvesting. These findings can assist fish farmers to increase the supply to meet the demand for tilapia fish.

According to Mohamed Faris Laham(2012),
- harvesting strategies for tilapia fish farming.
- Two logistic growth models have been used namely
a) constant harvesting
b) periodic harvesting.

To determine the graph plot using Matlab and Microsoft Excel
Full transcript