-
State University of Makassar
INTERNATIONAL CONFERENCE ON MATHEMATICS,SCIENCES, TECHNOLOGY,
EDUCATION
AND THEIR APPLICATIONS
“Recent Research and Issues in Mathematics, Sciences,
Technology, Education
and their Applications”
ICMSTEA2014
53 rdUNM
ICMSTEA 2014PROCEEDINGS
Makassar, August 20-21, 2014
INTERNATIONAL CONFERENCE ON MATHEM
ATICS, SCIENCES, TECHNOLOGY, EDUCATION AND THEIR
APPLICATIONS
ICM
ST
EA
20
14M
akassar, August 20-21, 2014
ISBN: 979-604-151-0979- 604- 151- 0
PR
OC
EE
DIN
GS
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International Conference on Mathematics, Science, Technology,
Education and their Applications(ICMSTEA) 2014
i
Conference Proceeding
INTERNATIONAL CONFERENCE ON MATHEMATICS, SCIENCES,TECHNOLOGY,
EDUCATION AND THEIR APPLICATIONS
Makassar, 20th – 21st August 2014
RECENT RESEARCH AND ISSUES ON MATHEMATICS,SCIENCE, TECHNOLOGY,
EDUCATION AND THEIRAPPLICATIONS
ISBN 979-604-151-0
Faculty of Mathematics and Science
State University of Makassar
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International Conference on Mathematics, Science, Technology,
Education and their Applications(ICMSTEA) 2014
ii
ICMSTEA 2014: RECENT RESEARCH AND ISSUES ON MATHEMATICS,
SCIENCE, TECHNOLOGY, EDUCATION AND THEIR APPLICATIONS
Editorial Board:
Syafruddin SideIwan DiniRahmat SyamSumarlin MusAhmad FudhailAndi
Irma SuryaniAnsari Saleh AhmarMuh. Aqil RusliBustangMuh.
HijrahIrwanIswan Achlan SetiawanNur Wahidin AshariWahyuddin
BaraZulkifli RaisSitti Busyrah Muchsin
Reviewer Board:
Prof. Max Warshauer (Texas State University, USA)Prof. Susie
Groves (Deakin University, Australia)Prof. Peter Hubber (Deakin
University, Australia)Prof. Naoki Sato (Kyoto University,
Japan)Prof. Baharuddin bin Aris (UTM, Malaysia)Prof. Ismail bin
Kailani (UTM, Malaysia)Prof. Duangjai Nacapricha (Mahidol
University, Thailand)Prof. Muhammad Arif Tiro (State University of
Makassar, Indonesia)Prof. Suratman Woro Suprodjo (Gadjah Mada
University, Indonesia)Prof. Gufron D. Dirawan (State University of
Makassar, Indonesia)Dr. Frans van Galen (Utrecht University,
Netherlands)Dr. Siti Nuramaliati Prijono (The Indonesian Institute
of Sciences)Oslan Jumadi, Ph.D. (State University of Makassar,
Indonesia)Muhammad Abdy, Ph.D. (State University of Makassar,
Indonesia)Dr. Suarlin (State University of Makassar, Indonesia)Dr.
Ramlawaty (State University of Makassar, Indonesia)
©August 2014
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International Conference on Mathematics, Science, Technology,
Education and their Applications(ICMSTEA) 2014
iii
Preface
All praise to Allah SWT, because His mercy and blessings, the
proceedings of the"International Conference on Recent Research and
Issues in Mathematics, Sciences,Technology, Education and Their
Applications (ICMSTEA) 2014" is now finally in our hands.ICMSTEA
2014 was succesfully held at Phinisi Building, State University of
Makassar on 20th
– 21st August, 2014 and followed 149 parallel speakers and
around, around 450 participants intotal that registered and
participanted from many universities in Indonesia and abroad. It
isassigned to celebrate the 53rd commemoration of State University
of Makassar. The conferenceis organized by the Faculty of
Mathematics and Science in conjunction with several
committeemembers from the other faculties within State University
of Makassar.
These proceedings are divided into two volumes, the first volume
contains all the papers in thefield of mathematics education,
science education and its applications, and the second
volumecontains all the papers in the fields of mathematics, science
and its applications. We hope thateverything contained in these
proceedings will expand scientific insights while providing
newresearch ideas and innovations to the conference participants
and the reader.
We would like to thanks to the authors for contributing their
papers, and the reviewers whohave provided assessment and feedback
during the editing process. We also would like tothanks to those
who have helped the settlement of this proceedings.
We apologize if there are any mistakes in these proceedings. We
also would like to express myhighest appreciation to the sponsors
who have contributed to the successful implementation ofICMSTEA
2014 conference and the publication of these proceedings.
Editor Team
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International Conference on Mathematics, Science, Technology,
Education and their Applications(ICMSTEA) 2014
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Forewords from the Head of Committee
Assalamu’alaikum Warahmatullahi Wabarakatuh.Good morning and may
God’s blessings be upon us all.
Your Excellency the Rector of State University of Makassar
(UNM)Prof. Dr. H. Arismunandar, M.Pd. Ladies and gentlemen, on
behalf of the conferencecommittee, first, I would like to give our
welcome to all the delegates, keynote speakers,invited speakers,
parallel speakers and participants coming today. Welcome to the
conference,welcome to State University of Makassar, and welcome to
Makassar.
This conference entitled “International Conference on Recent
Research and Issues inMathematics, Sciences, Technology, Education
and Their Applications (ICMSTEA) 2014”. It isassigned to celebrate
the 53rd commemoration of State University of Makassar. The
conferenceis organized by the Faculty of Mathematics and Science in
conjunction with several committeemembers from other faculties
within State University of Makassar.
Ladies and gentlemen, the conference proudly invites eleven
keynote speakers coming fromseveral countries. Therefore, I would
like to express my sincere thanks to the keynote
speakers,including:
1. Professor Max Warshauer (Texas State University, USA)2.
Professor Naoki Sato (Kyoto University, Japan)3. Professor Peter
Hubber (Deakin University, Australia)4. Professor Susie Groves
(Deakin University, Australia)5. Dr. Frans van Galen (Utrecht
University, Netherlands)6. Professor Duangjai Nacapricha (Mahidol
University, Thailand)7. Professor Baharuddin bin Aris (Universiti
Teknologi Malaysia, Malaysia)8. Professor Suratman Woro Suprodjo
(Gadjah Mada University, Indonesia)9. Professor Ismail bin Kailani
(UniversitiTeknologi Malaysia, Malaysia)10. Professor Muhammad Arif
Tiro (State University of Makassar)11. Dr. Siti Nuramaliati Prijono
(The Indonesian Institute of Sciences)
I would like also to give sincere thanks and gratitude to the
invited speakers, including:
1. Prof. Dr. H. Arismunandar, M.Pd. (State University of
Makassar)
2. Prof. Kristian H. Sugiyarto, Ph.D. (State University of
Yogyakarta)
3. Prof. Dr. Sutarto Hadi (Lambung Mangkurat University)
4. Dr. Nurdin Noni, M.Hum. (State University of Makassar)
5. Dr. Yuni Sri Rahayu, M.Si. (State University of Surabaya)
6. Dr. Ayuddin M.T. (State University of Gorontalo)
7. Dr. Usman Pagalay (State Islamic University of Malang)
8. Dr. Suyanta, M.Si. (State University of Yogyakarta)
9. Dr. Elisa Sesa, M.Sc. (Tadulako University, Palu)
Next, I want to thanks and welcome to 149 parallel speakers and
totally, 450 participantsapproximately are registered to
participate from many universities in Indonesia from Aceh toPapua,
and other countries. All of them have shared their research and
theoretical paperspresented and discussed in the conference.
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International Conference on Mathematics, Science, Technology,
Education and their Applications(ICMSTEA) 2014
v
In this occasion, I would like to thanks to Deputy of Governor
of South Sulawesi Province(Ir. H. Agus Arifin Nu’mang, M.Si), Mayor
of Makassar City (Ir. H. Ramdhan DhanyPomanto), Rector of UNM
(Prof. Dr. H. Arismunandar, M.Pd.), and Director of Post
GraduateProgram of UNM (Prof. H. Jasruddin Daud Malago), who are
very kind to be the host ofwelcoming dinner and lunch during the
conference.
I want to thanks also to Kalla Group, KIA Kalla, Erlangga Press,
Opti Lab, and e-BimbelYogyakarta for their contribution as the
sponsors of this conference.
Finally, it is my privilege to thanks to all organizing
committee members who have beenshowing good work and determination
for the accomplishment of this conference. I would liketo apologize
to all of you when there are some inconvenience things during the
implementationof this conference.
Thank you and wish you have a meaningful conference.
Assalamu’alaikum Warahmatullahi Wabarakatuh.
Head of Committee,
Suwardi Annas, Ph.D.
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International Conference on Mathematics, Science, Technology,
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Forewords from the Dean of Faculty of Mathematics and
Science,State University of Makassar
BismillahirrahmanirrahimAssalamu’alaikum Warahmatullahi
Wabarakatuh
First of all, let us praise to the Almighty, Allah SWT, because
of his Blessings and Helps, weare able to gather here to attend the
International Conference on Recent Research and Issues
inMathematics, Sciences, Technology, Education and Their
Applications (ICMSTEA) 2014.
The development of education and technology in recent decades
grows very rapidly. Inaddition, they have been specialized into
many specific topics. Indeed, for researchers andlecturers, being
qualified of a specific field as well as being aware of the
contemporarydevelopment of other fields are two crucial things. One
of the reasons why we undertake theconference is to fulfill those
two things. By attending the conference, researchers and
lecturershave a good opportunity to share their research findings
and to obtain broader descriptions ofthe development of other
general knowledge.
We convey our deep appreciation and gratitude to all of the
committees that work from thebeginning to support and organize the
conference. We also strongly expect the participants ofthe
conference to be continually productive, increase the capacity in
conducting a research, andcarry out both national and international
scientific publications.
Finally, let me again recite thank you to the all participants
of the conference who are receptiveto spend their time to be
present and entirely involved at this events. I wish the
conferenceadvantageous for all of us.Billahitaufiqwalhidayah,
Wassalamu’alaikum Warahmatullahi Wabarakatuh.
Dean of Faculty of Mathematics and ScienceState University of
Makassar
Prof. Dr. H. Hamzah Upu, M.Ed.
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International Conference on Mathematics, Science, Technology,
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Forewords from Rector of UNM
BismillahirrahmanirrahimAssalamu’alaikum Warahmatullahi
Wabarakatuh
Your respectable, the high officials of State University of
Makassar, the committee, thespeakers, and the participants of
conference.
It gives me a great pleasure to extend to you all a very warm
welcome, especially to ourkeynote speakers who have accepted our
invitation to attend the conference.It is an opportune time to
convey to you that UNM is celebrating the 53rd Dies Natalis and
itcommends the faculty of Mathematics and Science (FMIPA) to be in
charge of all activitysequences in the Dies Natalis. However, the
support of other faculties is also really influentialand gives
valuable contribution to the success of the event.
In that celebration, we undertake several agendas including
educational and sport activities.The conference, ICMSTEA, is one of
our educational activities that covers a wide range ofvery
interesting items relating to mathematics, sciences, education,
technology and theirapplications.
By taking participation of this seminar, it is highly expected
to all of us to share our researchfindings to society and
continuously develop new ideas and knowledge. Those things are
twosignificant steps in improving the quality of nations around the
world, increasing ourfamiliarity to each other, and even avoiding
underdevelopment.
On this good occasion, let me quote what Obama said about the
education related to thisconference and I wish fruitful for all of
us:
Every single one of you has something you’re good at. Every
single one of you has somethingto offer. And you have a
responsibility to yourself to discover what that is. That is
theopportunity an education can provide.
Furthermore, I would like to take this opportunity to express my
heartfelt gratitude to allorganizing committee especially for the
Faculty of Mathematics and Science that primarilyhosts this
conference particularly and other Dies Natalis events
generally.
Finally, this is a great time for me to declare the official
opening of the InternationalConference on Recent Research and
Issues in Mathematics, Sciences, Technology, Educationand Their
Applications (ICMSTEA) 2014.
I wish you a very enjoyable stay in Makassar, I warmly welcome
you again, as in Makassar,we say “salamakki battu ri
mangkasara”.
Wassalamu’alaikumwarahmatullahiwabarakatuh.
Rector of State University of Makassar
Prof. Dr. H. Arismunandar, M.Pd.
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TABLE OF CONTENTS
Preface iii
Forewords from the Head of Committee iv
Forewords from the Dean v
Forewords from the Rector vii
Table of Contents viii
Designing and Design Research 1Frans van Galen, Utrecht
University
Mathworks, Math Problems and Math Education Research 2Max, Texas
State University
Job Orientation of Undergraduate Statistics Students of FMIPA
UniversitasNegeri Makassar 3Muhammad Arif Tiro, State University of
Makassar
Membraneless Vaporization Devices: Effective On-line Tools for
Separation ofVolatile Compounds in Flow-Based Analysis 4Nacapricha,
D, Uraisin, K, Choengchan, N, Ratanawimarnwong, N. andWilairat, P,
Mahidol University
Correlation between Structures and Electronic Properties of
OrganicSemiconductor Thin Films 5Naoki Sato, Kyoto University
STEM and OER to Stimulate Student Engagement 6Baharuddin Aris,
Universiti Teknologi Malaysia
Representation Construction: A Research Developed Inquiry
Pedagogy forScience Education 7Peter Hubber, Deakin University
Improving Mathematics Teaching through Lesson Study 8Susie
Groves, Deakin University
Introduction to Modeling for Geographical Resources Management
9Suratman, Gajah Mada University
Role of Biological Sciences in Developing the Scientific Basis
for SustainableDevelopment 10Siti Nuramaliati Prijono, The
Indonesian Institute of Sciences (LIPI)
Mathematics Leadership 11Ismail Kailani, Universiti Teknologi
Malaysia
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Developing of School-Based Management Training Model for
Principals 12Arismunandar, Nurhikmah H., Widya Karmilasari Ahmad,
State Universityof Makassar
Analysis of Complex Building Structures through Cooperative
Learning: AnApproach to Understand Complex Subjects
18Ayuddin,Gorontalo State University
Learning Number Pattern Using The Arrangement of Planting Palm
Tree 25Sutarto Hadi, Agni Danaryanti, Kamaliyah, Lambung Mangkurat
University
Analysis of Dynamic Behavior CD4+T Cellsand CD8+T
CellstomycobacteriumTuberculosis Infections 33Usman Pagalay, Alfi
Nur Rochmatin,Islamic State University of Malang
Review on Misconception in Chemistry Textbooks, Teachers and
Students ofSenior High School as Users: Case Study on the Concepts
of Quantum Numbersand Electronic Configurations 40Kristian H.
Sugiyarto,Yogyakarta State University
Separation of Ca (II) and Mg (II) Metal Ion Underground River
Water in Baronwith Activated and Inactivated Zeolite by Fixed Bed
Column AdsorptionMethod 51Suyanta, Susila K, Annisa F, Hendarti and
Rr. Putri F, Yogyakarta StateUniversity
Developing Equivalent Electrical Circuit Model for Organic
Photovoltaic Cells 57Elisa Sesa, Darmawati Darwis, M. Syahrul Ulum,
Abdullah, Warwick Belcher,Paul Dastoor, Tadulako University and
Newcastle University
Isolation and Identification of Hydrocarbon Degradation Bacteria
and PhosphateSoluble Bacteria in Lapindo Mud Sidoarjo–East Java
70Yuni Sri Rahayu, Yuliani, Guntur Trimulyo,Surabaya State
University
The Construction Process of Students’ Mathematics Knowledge
Based onCognitive Style in A Learning 80Abdul Rahman, Ansari Saleh
Ahmar, State University of Makassar
Influence of Self-Concept and Learning Interest on Mathematic
Achievementsof 8th Grade Students through Activities and Creative
Thinking Ability at JuniorHigh School in Alla Subdistrict at
Enrekang District 91Djadir, State University of Makassar
What Is the Ability of Geosense? 99Feny Rita Fiantika, Surabaya
State University
Mathematics Learning Based Mathematical Communication Cultured
andCharacter of Indonesia 103Izwita Dewi, Tiur Malasari Siregar,
Nurhasanah Siregar, Medan StateUniversity
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Hipnoteaching as A Teaching Model 109Ja’faruddin, State
University of Makassar
Student Understanding of Symbols in Math Algebra 114Dian Septi
Nur Afifah, Surabaya State University
Analysis of Concept Understanding of Trigonometric Ratio’s From
Student’sInitial Ability on Class X.1 SMA Negeri 11 Makassar
118Andi Fauziah Mustafa, Suwardi Annas, Alimuddin, State University
of Makassar
Improving College Students’ Understanding on Mathematical
Finance Coursethrough The Use of Post-Hypnotic Suggestion of
Hypnotherapy 124Hamzah Upu, Bustang, State University of
Makassar
Designing Learning Continuum as A Basis for Constructing
Diagnostic Test(Its Implementation for Algebra Expression)
129Kusaeri, Universitas Islam Negeri Sunan Ampel Surabaya
The Development of Internet-Based Assessment of Math Learning
Evaluation 135Marwati Abd. Malik, Mas’ud B, University of
Muhmmadiyah Parepare
The Influence of the Implementation of Unconscious Mind Program
to Students’Mathematics Learning Achievement 142Muh. Hijrah, Sabri,
Ja’faruddin, State University of Makassar
Development of Teacher Competence Instrument Based on Rating by
Studentsat SMA in Pangkep District 149Muhammad Ilham Rauf, Baso
Intang Sappaile, Ruslan, State Universityof Makassar
Learning from Misconception to Re-educate Students in Solving
Problemsof Mathematics 152Nasrullah, Usman Mulbar, State University
of Makassar
Exploration of Mathematics Representation in Solving Mathematics
ProblemBased on the Level of Metacognitive Awareness of Grade X-IPA
atSMAN 1 Majene 160Nurdin Arsyad, Rezki Amaliyah A. R, State
University of Makassar
Problem Based Learning (PBL) to Enhance Mathematical Analysis
andEvaluation Skills of Junior High School Students 167Nur Wahidin
Ashari, Dadan Dasari, Stanley Dewanto, University of Educationand
Padjajaran University
Pre-service Teachers’ Perspective to Identify Evidence of
Teachers’ Effort onDeveloping Democratic Classroom through Video
174Rahmah Johar, Cut Khairunnisak, M. Ikhsan, Cut Morina Zubainur,
SyiahKuala University
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The Profile of Thinking in Solving Algebra Based on SOLO
Taxonomy Viewedfrom The Level of Self-efficacy at Students of SMP
Al-Azhar Palu 181Rio Fabrika Pasandaran, Ilham Minggi, Alimuddin,
State University ofMakassar
Is Reforming School Mathematics Curriculum Urgent in Indonesia?
187Sabri, Ilham Minggi,State University of Makassar
Mathematics Learning at Non-RME Classroom 192Syahrullah Asyari,
Ikhbariaty Kautsar Qadry, State University of Makassar
andMuhammadiyah University of Makassar
Effect of Cooperative Learning on Mathematics Achievement of
Sixth GradeStudents of Mendrelgang Primary School in Bhutan
202Tulashi Devi Pradhan, Naresuan University, Thailand.
The Description of Mathematical Problem Solving on SPLDV
Material Basedon Student’s Personalities 213Muhammad Zainal Abidin,
Ilham Minggi, Muh. Jufri, State Universityof Makassar
Rigorous Mathematical Thinking in Geometry Course 220Mega Teguh
Budiarto, Pradnyowijayanti, Ikakurniasari, Surabaya
StateUniversity
Cooperative Interaction in Learning Mathematics 229Suradi, State
University of Makassar
The Application of the Pigeonhole Principle, Modular Arithmetic,
andPermutation in Playing Magical Trick of A Card Game 236Fajar
Arwadi, State University of Makassar
Influence Theoretical Problem Based Learning Model Cooperative
Setting(PBMSK) against Intelligence Personal Development 242Ahmad
Talib,Ismail Kailani. Universiti Teknologi Malaysia
The Effect of Student’s Learning Style on Student Resistant
Misconception inChemistry Concept 243Septyadi David Eka Aryungga,
Suyono, State University of Surabaya
The Design of Instruction Model Based on the Metacognitive Skill
forEstablishing Problem Solving Ability and the Understanding of
ChemicalConcept 250Ijirana, Tadulako University
Preliminary Analyzes of Metacognition Awareness and Learning
Outcome ofBasic Chemistry for Biology’ Students FMIPA UNM
258Muhammad Danial, Nurlaela, State University of Makassar
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The Relationship between Prior Knowledge and Creative Thinking
Ability inChemistry of Students in Grade XI Science at Public High
School of Takalar 264Ramlawati, Dewi Satria Ahmar, Melati Masri,
State University of Makassar
Characterization of Polyblend of Kelor Seed (Moringa Oliefera)
with Eggshellas Adsorben for Water Treatment 273Suherman, Sitti
Aminah, Solfarina, Tasrik, UIN Makassar
Effect of Learning Model Cycle Learning through Contextual
Approach toLearning Chemistry Class VIII IPA SMP 30 Makassar
(Studies in the SubjectMatter of the Chemical) 281Ni Luh
Asriniasih, Sugiarti, State University of Makassar
Higher-Order Thinking (HOT) Skills in UN, TIMSS, and PISA Items
294Wasis, Sukarmin, Muji Sri Prastiwi, Surabaya State
University
The Changing of Student Healthy Eating Behavior during Study
Food ChemistryBased on Social Cognitive Theory 301Halimah Husain,
Alimuddin, Jasruddin, Sudding, State University of Makassar
Development of Science Practical Courses to Improve the Inquiry
Ability ofProspective Teacher 309Rosnita,Universitas Tanjungpura
Pontianak
Multiple-Choice Exams with Pictorial-to-Pictorial Format
Representation ofDensity of Liquid and Aspect Cognitive Measured
318Helmi Abdullah, Jasruddin, D.Malago, Patta Bundu, Syamsul Bachri
Thalib,State University of Makassar
Developing of Physics Teaching Materials on Based Environmental
325Jasruddin, D. Malago, Helmi Abdullah,State University of
Makassar
The Influence of Learning Strategies and Cognitive Learning
Styles on LearningOutcomes in Physics of Students at SMAN 5
Bulukumba 330Kaharuddin Arafah, Kasmiati, State University of
Makassar
Development of Web Based Physics Learning Media for 10th Grade
Senior HighSchool in Dynamic Electricity Topic 337Kiar Vansa
Febrianti, Fakhrizal Arsi,State University of Jakarta
Innovative Learning Development Model for Improving High Level
ThinkingSkills and Student Learning Culture 345Raharjo, Wahono
Widodo,Wasis, Surabaya State University
National Test Quality (UN) at 2012/2013 School Year of Subjects
PhysicsLesson Is Evaluated from Difficult Level and Different Power
Item in LevelSMA/MA Study Program Sciences (IPA) In Makassar City
352S. Salmiah Sari, State University of Makassar
The Influence of Cooperative Learning Strategies Think Pair
Share (TPS)
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toward Capability in Probelm Solving of Ecology with Different
Cognitive Style 360Amiruddin Kasim, Tadulako University
Correlation Student Activity of Creating Concept Map and Concept
MapProduct that Created by Student with Learning Outcomes on the
NervousSystem Material in SMA Negeri 10 Bulukumba 368Asmayani,
State University of Makassar
Study on Learning Process (Project Based Learning) in
Environment ScienceCourse 376Baiq Fatmawati, STKIP
Hamzanwadi-Selong
The Development of Chart-Based Instructional Media of Biology as
Biocompassfor Protists Subject Grade X Semester I 380Engka Rukmana,
Nurhayati B, Andi Rahmat Saleh, State University of Makassar
Scientific Inquiry Skills of Preserved Biology Teacher in
Laboratory Activity 389Fenny Roshayanti, Sumarno, Muhammad Syaipul
Hayat, PGRI University ofSemarang
Utilization of Simple Microscope as Alternative Media at Basic
Competency 6.3Describe the Diversity of Life Organizational System
from Cells to Organism atClass VII MTSN Turikale Kabupaten Maros
396Kasmiatang Kadir, MTSN Turikale Kabupaten Maros
Item Test Analyzing for Odd Semester Examination of Biology
Matter in ClassXI Senior High Schools in Tamalanrea District at
Makassar City for AcademicYears 2013/2014 402Muhammad Takwin
Machmud, Hardiyanti M, Yusminah Hala, A. MushawwirTaiyeb, State
University of Makassar
The Different of Science Cognitive Learning Outcome on The
RespiratorySystem by Using Problem Based Instruction Model with
Demonstration Methodand without Demonstration Method in Class VIII
MTSN Kelara 412Nurul Fatimah Syukri, Firdaus Daud, A. Asmawati
Azis, State Universityof Makassar
Implementation of Representation Visuospatial (Vs) Teaching in
Cell BiologyConcept for Undergraduate Students Mathematics and
Biology Education 420Purwati Kuswarini Suprapto, Universitas
Siliwangi
RelationshipAnalysis of Sport in Creating Fasting with the
Student HealthAspects Science Foundation Islamic School Foundation
Sciences of The Qur’anAl-Muzahwirah Makassar 425Muhammadong,
Arifuddin Usman, State University of Makassar
Evaluation on Managerial Supervision Program Secondary Education
Unit ofSupervisors in Poso District 432Yunita Timbani, Makassar
State University
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Knowledge and Attitude of Primary School Teacher Candidates the
PortofolioAssessment 438Andi Makkasau, Patta Bundu, State
University of Makassar
Correlation Islamic Values against Sport in Creating Emotional
Intelligence inStudents Aliyah Islamic School An-Nahdlah Makassar
447Arifuddin, U, Muhammadong, State University of Makassar
Analysis of the Roles of School Supervisors in Guiding Teachers
to ConductClassroom Action Research at Senior High School in
Bulukumba District 456Erny, State University of Makassar
Using Laboratory Simulation in Vocational High School to Model
Real WorldProblems 460Hendra Jaya, Sapto Haryoko, State University
of Makassar
Vocational Education Reform in a Global Era 466Muhammad Yahya,
Muhammad Farid, State University of Makassar
The Readiness of Students, Vocational High School Building
EngineeringDepartment, and Construction Industry in Applying
Internship Program inMakassar City 476Onesimus Sampebua, Anas
Arfandi, State University of Makassar
Rearranging Free Education Policy in Indonesia (Case Study: Free
EducationPolicy in Makassar) 482Suarlin, State University of
Makassar
Utilizing Audio Visual (VCD) to Improve Repruduction Written
Skill in EnglishLearning of Teacher Training of Elementary School
Program (PGSD) 492Rohana, State University of Makassar
The Impact of Policy on Region Expansion to Office
Administrative Services inBarombong Subdistrict of Gowa District
505Rudi Salam, Rosdiana, Suarlin, Haedar Akib, State University of
Makassar
Procedures of Constructing Tests by the High School English
Teachers inMakassar 513Suhartina A. Busrah, Baso Jabu, Muhammad
Nasiruddin Sainu, StateUniversity of Makassar
The Development of Science and Technology through the
Professionalism ofLecturers 521Syamsidah, State University of
Makassar
Positive Expectation Model Development Education Improvement
Efforts as AStress Self-management Skills Student Vocational High
School (SMK)Makassar 527Abd Saman, Muh Jufri, State University of
Makassar
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Application of Structural Equation Modeling (SEM) with Analysis
of MomentStructures (AMOS) 534Suwardi Annas, Irwan, State
University of Makassar
Developing Students Books with Topics Matrix Based on
RigorousMathematical Thinking (RMT) in Curriculum 2013 541Ika
Kurniasari, Pradnyo Wijayanti, Mega Teguh Budiarto, State
University ofSurabaya
Homomorphisms and Isomorphisms in the Fuzzy Subgroup
545Sukmawati, Fitriani, STKIP YPUP Makassar
Approximate Analytical Solution for SIR Model of Dengue Disease
in SouthSulawesi Using Homotopy Analysis and Iteration Variation
548Syafruddin S., Yulita Molliq Rangkuti, MakassarState University,
Medan StateUniversity
Stability Analysis of System of 1 Prey – 2 Predator with Holling
Type IIFunctional Response 557Abadi, Surabaya State University
Portfolio Optimization Analysis of Stock Using Markkowitz Model
561Ansari Saleh Ahmar, State University of Makassar
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International Conference on Mathematics, Science, Technology,
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State University of Makassar
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548
APPROXIMATE ANALYTICAL SOLUTION FOR SIR MODEL OFDENGUE DISEASE
IN SOUTH SULAWESI USING HOMOTOPY
ANALYSIS AND ITERATION VARIATION METHOD
Syafruddin S1 & Yulita Molliq Rangkuti21Department of
mathematics, Faculty of Mathematics and Natural Sciences,
Universitas Negeri
Makasar, UNM, Daeng Tata street, Makasar, Sulawesi Selatan,
Indonesia.2Department of mathematics, Faculty of Mathematics and
Natural Sciences, Universitas Negeri Medan,
UNIMED, Willem Iskandar street, Pasar V Medan Estate, 2022,
Medan, Sumatera Utara, Indonesiaemail: [email protected]
Abstract
Model Susceptible-Infected-Recovered (SIR) of the dengue disease
are considered in thisarticle. Analytical methods for the numerical
iteration method namely variations (MIV) and thehomotopy analysis
method (MAH) is applied to solve the SIR model of dengue
disease.Lagrange coefficients sought then used in MIV and
additional parameters in homotopy theory inMAH. Schema of these
methods is very easy to use and also produces a convergent series
sothat near to actual solution when compared to traditional
methods. The results obtained, MIVmore accurate representation of
MAH for a time interval t ≤ 9 when compared with actual data and
RK4 method. MIV can be an alternative method for the answers SIR
model or othernonlinear systems.
Keywords: Variation iteration method, homotopy perturbation
method, SIR Model,Lagrange coefficients.
1. IntroductionVariation iteration method (MIV) wasintroduced by
He, 1997. Legendremultiplication algorithm sought to carryMIV. He
has completed a variety ofdifferential equations using MIV
(He,1998,2007). His research has shown thatHIV is a powerful method
to obtainapproximate solutions. Yildirim andCherruault, 2009 have
solved the SIRmodel with constant vaccanasi strategy.Abu Bakar et
al, 2013 obtain anapproximate solution of the SIR modelinfected
with the disease using HPM.Gothbi et al, 2011 obtain an
approximatesolution of the general SIR model usingMIV and HPM.
Haemorrhagic fever is a diseasecaused by a virus of the
Togaviridae genus,subgenus Flavivirus. The virus in question
is transmitted into the human body throughthe bite of mosquitoes
that act as vectors.In Southeast Asia in general and Indonesiain
particular the mosquito Aedes aegypti isa major vector of dengue
viruses that causeoutbreaks. There is no specific vaccine forthe
treatment of dengue fever, MohdRizam et all, 2008.
Interesting phenomenon in thespread of dengue in this period is
thedisplacement of the age of the patient.Dengue fever is common
earlier in childrenof primary school age, but now there is alot of
attacking humans in all agesSyafruddin and Noorani 2013.
Themortality rate of this virus could reach 40percent of patients,
then this is a dangerousthreat to about 2.5 billion people in
theentire world, especially people in thetropical and subtropical
countries.
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549
Mathematical modeling andnonlinear dynamic method used
incomparing, designing, implementing andoptimizing assess various
identification,prevention, treatment, control andprogram.
Therefore, the mathematicalmodel can be a useful tool to
betterunderstand the mechanisms that justify theoutbreak of dengue
fever and controlstrategies to improve the speed of themosquito
(vector).
In this paper, a model Susceptible-Infected-Removed (SIR) to be
considered,which is expected to be able to know thenumber of hosts
infected with theepidemic, the number of hosts recovered,the number
of mosquitoes that causedengue fever was suspected. This modelhas
been modified by Side and Noorani,2013 becomes:
1 ( ) ( ) ( )hdx
x t x t z tdt
(1)
( ) ( ) ( )dy
x t z t y tdt
(2)
1 ( ) ( ) ( )dz
z t y t z tdt
(3)
where ߤ is human life span, the shape ofthe number suspectable
rate ,ܣ ܾߚ is thenumber of the host population, ௩ߤ is thelife span
of mosquitoes, ܰ is the number
of the host population, ߙ =ఉ
ఓೡே, ߚ =
ߛ + ߤ , =ߛ ௩ܾߚ and =ߜ ௩ߤinhomogeneous form.
2. Variation Iteration Method (MIV)
Variation iteration method (MIV)was introduced by He in 1997.
MIVdeveloped from common Lagrangecoefficients method with
iteratively run.The virtue of this method is assumingcompletion
linearization mathematicallyused as an initial approximation,
theapproximation is appropriate for someparticular point can be
obtained.
To understand the basic concepts ofMIV, first consider the
differentialequation form as follows:
)(tgNuLu , (4)
where L is a linear operator, the operatorN is not linear and
)(tg is nothomogeneous term. According MIV, couldin the form of a
justification function asfollows:
dstguNLusuut
nininini 0
,,,1,)(~)( ,
Where mi ,,2,1 , is Lagrangecoefficient (Inokuti, 1978), which
can beidentified using the theory of variation,
denoted as an approximation to- n and u~
be considered as a discontinuous variation
(Inokuti, 1978), as .0~,
niu The iteration
scheme in equation (5) will be close to thatexact completion for
n as follow:
)(lim
)( , tun
tu nii
(6)
3. Homotopi Analysis Method (MAH)
Consider the following differentialequation:
ܰ[ݖ(ݐ)] = 0, ݅= 1,2, ⋯ , ,݊ (7)Where ܰ is linear operator which
showedthe entire equality, ݔ and areݐ independentvariables and (ݐ)ݖ
is an unknownfunction. With the traditional general senseHomotopi
method, Liao, 1992 to build theso-called zero-order deformation
equation:
(1 − ൣܮ(ݍ ߶(ݍ;ݐ) − ൧(ݐ),ݖ
= ℏܰݍ [߶(ݍ;ݐ)],
(8)
Where ݍ ∈ [0,1] is a embedded parameter,ℏ is an additional
parameter, L is a linearoperator addition, is(ݐ),ݖ the initial
guessof (ݐ)ݖ and ߶(ݍ;ݐ) is a unknownfunction. It is important to
note that aperson's bias freely choose additionalobjects such as
ℏand L in MAH. Clearly,if both =ݍ 0 and =ݍ 1 then߶(ݐ; 0) = (ݐ),ݖ
and ߶(ݐ; 1) =
,(ݐ)ݖ
(9)
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550
Satisfied. So q ascending from 0 to 1, thecompletion of various
߶(ݍ;ݐ) of the initialassessment ,ݖ to completion .(ݐ)ݖExpantion
߶(ݍ;ݐ) by a Taylor seriesagainst q, obtained :
߶(ݍ;ݐ) = (ݐ),ݖ + ,ݖ ݍ(ݐ)
ା∞
ୀଵ
, (10)
where
,ݖ =1
݉ !
߲ ߶(ݍ;ݐ)
ݍ߲ฬୀ
.(11)
If additional linear operator, the initialguess of additional
parameters ℏ,, andadditional function is selected, then theequation
of the series (10) converges toq = 1 and
߶(ݐ; 1) = (ݐ),ݖ + ,ݖ ,(ݐ)
ା∞
ୀଵ
(12)
This became the settlement of non linearequations of origin, as
proved by Liao. Aswith ℏ = −1, equation (8) becomes:
(1 − ൣܮ(ݍ ߶(ݍ;ݐ) − ൧(ݐ),ݖ
+ ܰݍ ൣ ߶(ݍ;ݐ)
− =൧(ݐ),ݖ 0,
(13)
Which method mostly used in the HPM.(He, 1999).
From (13), the construction of theequation can be deduced from
the zero-order deformation equation. Defined vector
,̅ݖ = ,(ݐ),ଵݖ,(ݐ),ൣݖ ⋯ ൧(ݐ),ݖ, (14)
Differentiation (25) m times as much onthe setting of parameters
q and then let q =0 and finally divided them by m!, We callto-order
deformation equation m.
ൣܮ ,ݖ (ݐ) − ߯ ,ݖ ൧(ݐ)
= ℏܴ , ൫̅ݖ, ିଵ൯,
(15)
where
ܴ, ൫̅ݖ, ିଵ൯
=1
(݉ − 1)!
߲ ିଵ߶(ݍ;ݐ)
ݍ߲ ିଵቤୀ
,
(16)
and
߯ = ቄ0, ݉ ≤ 1,1, ݉ > 1.
(17)
It is emphasized that ,ݖ (ݐ) ݉ ≥constructed by the linear
equation (15)with linear boundary conditions that comefrom original
problem, which can be easilysolved with a computer symbol
crateMAPLE or MATHEMATICA.
3.1. MIV application for Sir Modelsfrom Spread of Dengue Fever
Disease
Variation iteration method is a method ofsemi analytic powerful
and widely used tosolve differential equations. The basictheory for
using MIV, first, rewritten SIRmodel of dengue fever as
follows:
1 ( ) ( ) ( )hdx
x t x t z tdt
( ) ( ) ( )dy
x t z t y tdt
1 ( ) ( ) ( )dz
z t y t z tdt
where ߤ is human life span, the shape ofthe number susceptible
rate ,ܣ ܾߚ is thenumber of the host population, ௩ߤ is thelife span
of mosquitoes, ܰ is the number
of the host population, ߙ =ఉ
ఓೡே, ߚ
ߛ + ߤ , =ߛ ௩ܾߚ and =ߜ ߤinhomogeneous formTo use the SIR model
MIV, built functionsjustification as follows:
(ݐ)ାଵݔ = ݔ + න (ݏ)ଵߣݔ݀ݏ݀
௧
− (1ߤ − (ݔ
+ ෧ݖݔߙ ൨݀ݏ,
(18)
(ݐ)ାଵݕ = ݕ + න (ݏ)ଶߣݕ݀ݏ݀
௧
− ෧ݖݔߙ + ൨ݕߚ ,ݏ݀
(19)
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551
(ݐ)ାଵݖ = ݖ + න (ݏ)ଷߣݖ݀ݏ݀
௧
− ݕߛ + ෧ݖݕߛ
+ ൨ݖଵߜ ,ݏ݀
(20)
Where ,ߣ ݅= 1,2,3 is a general Lagrangecoefficient which can be
identifiedoptimally by theory of variation and thesubscript n
denotes to-n. To obtain (ݏ)ߣ isoptimal, do the following:
ାଵݔߜ = ݔߜ + න (ݏ)ଵߣߜݔ݀ݏ݀
௧
− (1ߤ − (ݔ
+ ෧ݖݔߙ ൨݀ݏ,
(21)
ାଵݕߜ = ݕ + න (ݏ)ଶߣߜݕ݀ݏ݀
௧
− ߙ ෦ݕܿߚ ൨ ,ݏ݀
(22)
ାଵݖ = ݖ + න (ݏ)ଷߣݖ݀ݏ݀
− ෦ݕߛ௧
+ ෧ݖݕߛ
+ ෦ݖଵߜ ൨ ,ݏ݀
(23)
where ,ݕ,ݔ ෧ݖݕ ෧ݖݔ, , and ǁݖconsidered as a discontinuous
variationi,ݔ,ݕ = 0 and ǁݖ = 0. Then, we have
ାଵݔߜ = ݔߜ + න (ݏ)ଵߣߜݔ݀ݏ݀
௧
+ ,ݏ൨݀ݔߤ
(24)
ାଵݕߜ = ݕ + න (ݏ)ଶߣߜݕ݀ݏ݀
௧
+ ൨ݕߚ ,ݏ݀
(25)
ାଵݖߜ = ݖߜ + න (ݏ)ଷߣߜݖ݀ݏ݀
௧
+ ൨ݖଵߜ ,ݏ݀
(26)
or
ାଵݔߜ = ݔߜ + න ߣߜଵݔ݀ݏ݀
௧
+ ݏ൨݀ݔߤଵߣߜ
(27)
ାଵݕߜ = ݕߜ + න ߣߜଶ(ݏ)ݕ݀ݏ݀
௧
+ ൨ݕߚଶߣߜ ݏ݀
(28)
ାଵݖߜ = ݖߜ + න ߣߜଷݖ݀ݏ݀
௧
+ ൨ݖଷߣଵߜߜ ݏ݀
(29)
thenାଵݔߜ = 1)ߜ + ݔ(ଵߣ
+ න ଵ′ߣ]ߜ
௧
+ ݔ[ߤଵߣ ,ݏ݀
(30)
ାଵݕߜ = 1)ߜ + ݕ(ଶߣ
+ න ଶ′ߣ]ߜ
௧
+ ݕ[ߚଶߣ ,ݏ݀
(31)
ାଵݖߜ = 1)ߜ + ݖ(ଷߣ
+ න ଷ′ߣ]ߜ
௧
+ ݖ[ଷߣଵߜߜ ,ݏ݀
(32)
Thus, the following stationary conditionobtained:
ݔߜ : (1 − ௦ୀ௧|((ݐ)ଵߣ = 0,
ݕߜ : (1 − ௦ୀ௧|((ݐ)ଶߣ = 0,
ݖߜ : (1 − ௦ୀ௧|((ݐ)ଷߣ = 0,
ݔߜ′ : ଵߣ
(ݏ)′ + ห௦ୀ௧(ݏ)ଵߣߤ = 0,
ݕߜ′ : (ݏ)ଶߣ + ௦ୀ௧|(ݏ)ଶߣߚ = 0,
ݖߜ′ : (ݏ)ଷߣ + ௦ୀ௧|(ݏ)ଷߣଵߜ = 0,
Solution of the system of equationsobtained:
(ݏ)ଵߣ = −݁ఓ(௦ି ௧),
(ݏ)ଶߣ = −݁ఉ(௦ି ௧),
(ݏ)ଷߣ = −݁ఋభ(௦ି ௧),
(33)
Here, the general Lagrange coefficients(33) is described by the
Taylor series andselected for only one term in thecalculation
easier, general Lagrangecoefficients can be written as follows:
(ݏ)ଵߣ = −1,
(ݏ)ଶߣ = −1,
(ݏ)ଷߣ = −1,
(34)
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552
Substitution of the general Lagrangemultipliers in (34) to
equation (18)-(20)yields the following iteration formula:
(ݐ)ାଵݔ = ݔ
− න ݔ݀ݏ݀
௧
− (1ߤ − (ݔ
+ ൨ݖݔߙ ,݀ݏ
(35)
(ݐ)ାଵݕ = ݕ − න ݕ݀݀ݏ
− ݖݔߙ
௧
+ ൨ݕߚ ,ݏ݀
(36)
(ݐ)ାଵݖ= ݖ
− න ݖ݀ݏ݀
௧
− ݕߛ+ ݖݕߛ
+ ൨ݖଵߜ .ݏ݀
(37)
Iteration begins with the initialapproximation as obtained from
the data ofthe Indonesian health minister (2007),
ଵܿ =ହସ
ହ଼ଽଷ, ଶܿ =
ସ଼
ହ଼ଽଷ, ଷܿ = 0.056,
ߙ = ߚ,0.232198 = =ߛ,0.3288790.375, and ଵߜ = 0.0323. The
iterationformulas (87) - (89) are obtained:ଵݔ=
0.9999365546− 0.0130022687 ,ݐ
(38)
ଵݕ=
0.00006344538675+ 0.01298140513 ݐ
(39)
ଵݖ=
0.056 − 0.001786340333 ,ݐ (40)
ଶݔ=
0.9999365546− 0.0130022687 ݐ+ 2.922132174 × 10ିସݐଶ
−1.797714851 × 10ିݐଷ, (41)ଶݕ=
0.00006344538675+ 0.01298140513 ݐ+ 0.1797714851 × 10ିହݐଷ
−0.002426569924 ,ଶݐ (42)ଶݖ=
0.056 − 0.001786340333 ݐ+ 0.002326579355 ଶݐ
+0.2898650945 × 10ିହݐଷ, (43)
ଷݔ=
0.9999365546− ݐ0.01300226807− ଷݐ0.0001831331308
ଶݐ0.0002922132174+
+ 0.1728532016 × 10ିଵଶݐ
+0.1290829001 × 10ିଽݐ
− 0.2997118573 × 10ିݐହ
+0.1623956764 × 10ିହݐସ, (44)ଷݕ=
0.00006344538675+ 0.01298140513 ݐ+ 0.000449144614 ଷݐ
−0.00242656993 ଶݐ
− 0.1728532016 × 10ିଵଶݐ
−0.1290829001 × 10ିଽݐ
+ 0.2997118573 × 10ିݐହ
−0.1771743755 × 10ିହݐସ, (45)=ଷݖ 0.056 − 0.00178634033 ݐ
− 0.000308504557 ଷݐ
+0.002326579355 ଶݐ
− 0.2791579206 × 10ିଵଶݐ
+0.1782033109 × 10ିଽݐ
+ 0.4208392710 × 10ିݐଷ
−0.3102165044 × 10ିହݐସ,and so on.
(46)
3.2. MAH Applications for SIR Modelof the Spread of Dengue
FeverDisease
In this section, we use the MAH to resolvethe SIR model of
dengue disease. To solvethe SIR model, we defined not
linearoperator as:
[(;ݐ)߶]ܰ = (ݐ)ݖ(ݐ)ݔߙ (47)[(;ݐ)߶]ܰ = (ݐ)ݖ(ݐ)ݔߙ (48)[(;ݐ)߶]ܰ =
(ݐ)ݕ(ݐ)ݔߛ (49)
and linier operator as:
[(;ݐ)߶]ܮ =(ݐ)ݔ݀
ݐ݀+ (ݐ)ݔߤ
(50)
[(;ݐ)߶]ܮ =(ݐ)ݕ݀
ݐ݀+ (ݐ)ݕߚ (51)
[(;ݐ)߶]ܮ =(ݐ)ݖ݀
݀ݐ+ (ݐ)ݖߜ (52)
With nature ]ܮ ଵܿ] = 0 (53)
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553
Where ଵܿ is a constant Integration. Use theabove definition, we
built zero-orderdeformation equation:.
(1 − (;ݐ)߶]ܮ( − [(ݐ)ݔ = ܰ ℏ߶(;ݐ) (54)(1 − (;ݐ)߶]ܮ( − [(ݐ)ݕ = ܰ
ℏ߶(;ݐ) (55)(1 − (;ݐ)߶]ܮ( − [(ݐ)ݖ = ܰ ℏ߶(;ݐ) (56)
Obviously, when = 0 and = 1;ݐ)߶ 0) = (ݐ)ݔ and ;ݐ)߶ 1) = (ݐ)ݔ
(57);ݐ)߶ 0) = (ݐ)ݕ and ;ݐ)߶ 1) = (ݐ)ݕ (58);ݐ)߶ 0) = (ݐ)ݖ and ;ݐ)߶
1) = (ݐ)ݖ (59)Therefore, the parameter p is embedded up from 0 to
1, (;ݐ)߶ of the initialguess ,,(ݐ)ݔ (ݐ)ݕ and (ݐ)ݖ to thesolution
,(ݐ)ݔ (ݐ)ݕ dan .(ݐ)ݖ Then wegenerate the equations of
deformationorder to mݔ]ܮ (ݐ) − ߯ ݔ ିଵ(ݐ)]
= ℏܴ ⃗ݔ] ିଵ(ݐ)],(60)
ݕ]ܮ (ݐ) − ߯ ݕ ିଵ(ݐ)]= ℏܴ ⃗ݕ] ିଵ(ݐ)],
(61)
ݖ]ܮ (ݐ) − ߯ ݖ ିଵ(ݐ)]= ℏܴ ⃗ݖ] ିଵ(ݐ)],
(62)
With natureݔ (0) = 0, ݕ (0) = 0 dan
ݖ (0) = 0,(63)
whereܴ ⃗ݔ ିଵ
=ݔ݀ ିଵݐ݀
− (1ߤ − ݔ ିଵ)+ݔߙ ିଵݖ ିଵ
(64)
ܴ ⃗ݕ ିଵ =ݕ݀ ିଵݐ݀
− ݔߙ ିଵݖ ିଵ
+ ݕߚ ିଵ
(65)
ܴ ⃗ݖ ିଵ =ݖ݀ ିଵݐ݀− 1)ߛ − ݖ ିଵ)ݕ ିଵ+ ݖߜ ିଵ
(66)
Now, the solution to-m order deformationequation (60)-(62) for m
≥ 1 be ݔ (ݐ) = ߯ ݔ ିଵ(ݐ)
+ ℏିܮଵ[ܴ ⃗ݔ) ିଵ)](67)
ݕ (ݐ) = ߯ ݕ ିଵ(ݐ)+ ℏିܮଵ[ܴ ⃗ݕ) ିଵ)]
(68)
ݖ (ݐ) = ߯ ݖ ିଵ(ݐ)+ ℏିܮଵ[ܴ ⃗ݖ) ିଵ)]
(69)
From (188)-(189), we obtained
(ݐ)ଵݔ = .ܜܐ (70)(ݐ)ଵݕ = −.ૢૡܜܐ (71)(ݐ)ଵݖ = .ૠૡܜܐ (72)
(ݐ)ଶݔ = ܐ (.+ ܐ (.+ .ૢܜ)) ܜ
(73)
(ݐ)ଶݕ = ܐ (−.ૢૡ+ ܐ (−.ૢૡ− .ૠܜ)) ܜ
(74)
(ݐ)ଶݖ = ܐ (.ૠૡ+ ܐ (.ૠૡ+ .ૡܜ)) ܜ
(75)
⋮(ݐ)ଽݔ
= .)ܜܐ+ ܐ (.ૡ+ .ૢૡૢܜ)− .ૢܐ (−.ૡ+ (ܜ (ૠ. + (ܜ− .ૡૢૡܐ (−.ૢૢૡ+ (ܜ
(.ૡૡ + (ܜ (.ૠૢ+ (ܜ − .× − ܐ (−.ૠૢૡ+ (ܜ (.+ (ܜ (.ૢ + (ܜ (ૡ.ૢ+ ૠ.ૠૡܜ+
(ܜ− .ૠૢܐ (−.ૡૡૡ+ (ܜ (.ૡૡ + (ܜ (ૢૡ.ૡ+ .ૡܜ+ (ܜ − .ૢ× − ૠ (−.ૡૡܐૢ+ (ܜ
(.ૡૢ + (ܜ (.ૢૠ+ (ܜ (ૡ.ૡ + ૠ.ૡૡܜ+ (ܜ (ૡૡ. + .ૡܜ+ (ܜ− .ૠૠૡ× − ૠܐ
(−.ૡૢ+ (ܜ (.ૠૠ+ (ܜ (.ૡૡ + .ܜ+ (ܜ (.ૠ + .ૢૡܜ+ (ܜ − .ૡૡ× − ܐૡ (−.ૢ+
(ܜ (. + (ܜ (ૠ.ૡૡ+ .ૢܜ+ (ܜ (ૡ.ૡૢ+ .ૢܜ+ (ܜ (ૠ .ૢ+ ૠ.ૠܜ+ ((ܜ
(76)
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554
(ݐ)ଽݕ= .ૡૢ)ܜܐ+ ܐ (.ૡ + .ૠܜ)+ ܐ (.ૡ + .ૠܜ+ .ૢܜ)+ .ૠૢܐ (ૡ.ૡૡ+ (ܜ
(.ૠ + .ܜ+ (ܜ+ .ૠૠܐ (.ૠ+ (ܜ (.ૠ + .ૢܜ+ (ܜ (ૢ.ૡ + .ૠૠૢܜ+ (ܜ+ .ૠܐ
(ૡ.ૢ+ .ૡૠૡૡܜ+ (ܜ (ૠ.ૢ+ .ૠܜ+ (ܜ + ૡ.ૢૡૢ× − ૠܐૢ (ૠ.ૢ + (ܜ (.ૢૢ+ .ૢૠܜ+
(ܜ (ૡ.+ .ܜ+ (ܜ (ૢૠ.ૡ+ .ૡૡܜ+ (ܜ + .ૢ× − ૠܐ (. + .ૢૡܜ+ (ܜ (.ૢૠૠ +
ૡ.ܜ+ (ܜ (ૢૠ.ૠ + ૠ.ૢૢܜ+ (ܜ+ ૠ.ૡ× − ܐૡ (.ૢ+ .ܜ+ (ܜ (.ૡૠૡ+ .ܜ+ (ܜ
(ૡ.ૡ+ .ૢૡૡܜ+ (ܜ (ૢ.+ .ૢૠܜ+ ((ܜ
(77)
(ݐ)ଽݖ= .ૠૡૡ)ܜܐ+ ܐ (. − .ૡૠܜ)− .ૡૢܐ (−.ૡ+ (ܜ (ૡ.ૡૢ + (ܜ− .ૠૢܐ
(−.ૡૡૠૠ+ (ܜ (ૠ. + (ܜ (ૢ.+ .ૢܜ+ (ܜ− .ૢܐ (−.+ (ܜ (ૢ.ૢ + .ܜ+ (ܜ−
.ૢૢૢૢ× − ૠܐ (−.+ (ܜ ( .ૢૢ + (ܜ (.ૠ+ .ૢܜ+ (ܜ (ૡ.+ .ૢૢૢܜ+ (ܜ − .ૢ× −
ܐૡ (−.ૢૡૢૠ+ (ܜ (.ૠૠૠ + (ܜ (ૠ.ૠ+ .ૡܜ+ (ܜ (.ૢૠ+ ૡ.ૡܜ+ (ܜ (.ૡૡ+
.ૢૠૠૡܜ+ (ܜ− .ܐ (−.ૠ+ (ܜ (. + ૠ.ܜ+ (ܜ (ૢ .ૢૢ + .ܜ+ (ܜ − .ૠ× − ૡܐૠ
(−.ૠૢ+ (ܜ (.ૠ+ .ૡܜ+ (ܜ (ૢ.ૢૠ+ .ૡૡૠܜ+ (ܜ (ૢ.ૢ+ .ૠૢܜ+ ((ܜ
(78)
In the end, we use nine terms to get thefollowing approximation
solution:
(ݐ)ݔ = ݔ
ଽ
ୀଽ
(79)
(ݐ)ݔ = ݕ
ଽ
ୀଽ
(80)
(ݐ)ݔ = ݖ
ଽ
ୀଽ
(81)
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555
4. Result and DiscussionFrom the data obtained by the
researcher(KKM, 2007-2008), rate of infection forhumans to be cured
is ,)=0.3288330ߛ) theeffective contact rate, humans tomosquitoes is
(bβv)=0.3750000, theeffective contact rate, humans tomosquitoes
is(bβh)=0.7500000, human life span(µ
)=0.0000460, the life span of
mosquitoes (µ௩)=0.0323000. Iteration
and the term has been preceded by
7675893
76754060 x , ,
7675893
4870 y and
.056.00 z Iteration of the SIR modelsuperbly encoded using MAPLE
and
MATHEMATICA package USING digits16. MIV iterations to 10, MAH
term to 10,RK4 at =ݐ∆ 0.001 is used to get asettlement from SIR
models of denguefever then shown a comparison betweenthe results of
the MAH, MIV and real datain Table 1. From table 1 it can be
seenMIV more accurate than the MAH. MAHwill be divergent for the
interval ≤ݐwhereas MIV intervals will be divergent≤ݐ 9.
Table 1. Absolute error of MAH solutions and MV compared to
RK4with h = 0:001 and ℏ = -1
tMIV MAH
∆ ∆ ∆ ࢠ ∆ ∆ ࢠ∆1 2.401 E-11 3.934E-10 2.852E-10 1.759 E-08
3.553e-09 3.624e-082 7.439 E-11 7.198E-11 6.156E-12 2.136 E-06
7.740e-07 4.457e-063 1.514 E-08 4.335E-08 3.289E-08 3.456 E-05
1.869e-05 7.341e-054 3.386E-07 9.813E-07 7.455E-07 2.463 E-04 1.759
E-04 5.376 E-045 3.704 E-06 1.082E-05 8.220E-06 1.124 E-03 9.864
E-04 2.548 E-036 2.579 E-05 7.602E-05 5.772E-05 3.877 E-03 1.149
E-03 2.928 E-037 1.313 E-04 3.912 E-04 2.968 E-04 1.105 E-02 3.986
E-03 2.799 E-028 5.306 E-04 1.602 E-03 1.215 E-03 2.746 E-02 3.501
E-02 7.467 E-029 1.791 E-03 5.506 E-03 4.188 E-04 6.156 E-02 8.397
E-02 0.181110 5.218 E-03 1.645 E-02 1.263 E-02 0.1274 0.1819
0.407611 1.335 E-02 4.379 E-02 3.44 E-02 0.2476 0.3625 0.863612
3.008 E-02 0.1055 8.677 E-02 0.4574 0.6736 1.739
5. Conclusion
1. The number of infected humanswill reach the peak in the 12th
andthen will decline until eventuallyno man no infected humans
(thishappens if we anticipate thesymptoms of dengue fever as
earlyas possible).
2. The more people who suspectthe less infected and vice
versa.
3. The number of infectedmosquitoes is directlyproportional to
the number ofinfected humans.
4. The use of semi- numericalanalytic method has been aconcern
for researchers.Variation iteration method(MIV) and the method
ofanalysis Homotopi (MAH).
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556
5. The results of the use of semi-numerical method is analytical
,accurate MIV for the time intervalt ≤ 9, MAH is accurate for the
time interval t ≤ 7. In addition, the calculation of the scheme,
MIVeasier in the calculation comparedwith MAH. From the
resultsobtained MIV could be analternative method to penyelesianSIR
model or other nonlinearsystems .
AcknowledgementsWe would like to thank DIPA StateUniversity of
Makassar(No.156/UN36.9/PL/2014) forfinancial support.
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