State University of Makassar - Universitas Negeri Medandigilib.unimed.ac.id/6050/1/Fulltext.pdf · Iwan Dini Rahmat Syam Sumarlin Mus Ahmad Fudhail Andi Irma Suryani Ansari Saleh

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

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


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


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


iv

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.


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.


vi

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.


vii

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


xv

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

Evolution Equation of Homogeneous Semi-Markov Processes in HealthInsurance Additional Premiums Calculation for Outpatient Respiratory Disease 565Faihatuz Zuhairoh, STKIP YPUP Makassar

Survival Analysis and Its Application in Public 574Aswi, State University of Makassar

Optimal Control of the Forest Arealogistic Growth Model Preservingthe StableInteraction of Temperature, Pressure and Atmospheric CO2 582Agus Indra Jaya, Rina Ratianingsih, Affandi,TadulakoUniversity

Measurability of the Henstock Integrable Function of Vector Valued Functionon a Locally Compact Metric 588Manuharawati, Surabaya State University

Application of SIR Mathematical Model for Transmission of Dengue Feverthrough Collaboration Counseling with Health Center Staff in Lanrisang,Pinrang 593Syafruddin Side, State University of Makassar

Lattices as Ordered Sets 596Fitriani, Bahar, UIN Alauddin Makassar, State University of Makassar

Contemporary Correlation 599Sukarna, State University of Makassar


xvi

Screening of Tembelekang Plant (Lantanacamaralinn) Active CompoundsForprevention of Infectious 605Muharram, Iwan Dini, Pince Salempa, Sitti Faika, Ahmad Fudhail,State University of Makassar

Performance of the Diffusive Gradients in Thin Films (DGT) Technique forMeasurement of Labile Cu in Environmental 611Khairuddin, Abd Wahid Wahab, Buchari, Indah Raya, Tadulako University,Hasanuddin University, Bandung Institute of Technology

Cadmium: A Micronutrient for Diatom Marine Phytoplankton 618Arifin, M. Sjahrul, Ahyar Ahmad, Indah Raya, Halu Oleo University

Antibiotic Activity Test Cellulolytic Bacteria Isolates CC1 And CC2 of theLarvae of the Butterflies (Cossuscossus) 627Maswati Baharuddin, Abd. Rauf Patong, Ahyar Ahmad, Nursiah La nafie,University of Hasanuddin

Synthesis and Characterization of Coke from Charcoal Obtained from Pyrolysisof Coconut Shell 632Meytij Jeanne Rampe, Vistarani Arini Tiwow, State University of Manado,State University of Makassar

Isolation and Structure Elucidation of Β-Sitosterol Compound from the N-Hexane Fraction of Root Wood of Pterospermum Subpeltatum C.B. 638Pince Salempa, State University of Makassar

Synthesis of Pesticides Organic of Kirinyuh (Chromolaena Odonata) forArmyworm and Caterpillar Soil Pest on Cabbage and Scallion 644Ignatius R.S. Santoso, Henny L. Rampe, Manado State University, SamRatulangi University

Synthesis Molecular Imprinted Polymer Methacrylic Acid (MIP_MAA) UsingMolecular Imprinting 647St. Fauziah, Nunuk Hariani, Muh. Bachri Amran, Paulina Taba, HasanuddinUniversity, Technology Institute of Bandung

Structure-Activity Relationship for Larvacidal Activity of Non-phenolicCompounds from the Stem Bark of Red Mangrove (Rhizophora Stylosa) 653Suyatno, Nurul Hidajati, Surabaya State University

The Influence of Variation in the Amount of Starch Adhesive on the CalorificValue of Coconut Shell Charcoal 658Sudding, State University of Makassar

Design of Bentonite Acid Modified Electrodes in Cyanide Biosensors 666Catherina Bijang, Abd. Wahid Wahab, Maming, Ahyar Ahmad, Paulina Taba,Pattimura University, Hasanuddin University

Analyse of Water Flow, Rainfall and Evaporation in Maros Karst Areas and


xvii

Sustainable Use in Agriculture 674Muhammad Arsyad, State University of Makassar

Immunohistochemical Study on The Distribution of Adenohypophysial CellTypes in The Pituitary Gland of Bungo Fish (Glossogobius Cf. Aureus) fromTempe Lake, South Sulawesi 682Dwi Kesuma Sari, Andi Tamsil, Kazuhide Adachi, Yasuhiro Tsukamoto,Hasanuddin University, Indonesian Moslem University, Kyoto PrefectureUniversity

A Study on the Topographical of Syrinx in Laughting Chicken (Ayam Gaga)from South Sulawesi 686Andhika Yudha Prawira, Novi Susanty, Farida Nur Yuliaty, Dini KurniaIkliptikawati, Dwi Kesuma Sari, Hasanuddin University

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Computation Model for the FEB/FE2B Layer Growth Diffusion Kinetic duringthe ST41 Low Carbon Steel Powder Pack Boriding 695Sutrisno, State Islamic University Syarif Hidayatullah Jakarta

Level Relations in the Field of Health Services Clinic Sanitation by the NumbersDisease Occurrence Environment Based on Work Area Community HealthCenter Makassar 701Zaenab, Mawaddah, Ministry of Health Polytechnic Makassar

Temperature Trend Analisis in Jakarta City: 1981-2010 711Rosmini Maru, State University of Makassar

Petrography of Pyrite Minerals from Mineral Deposits Kecamatan BontocaniKabupaten Bone 719Nurhayati, State University of Makassar

The Diversity of Anopheles Sppmosquitos Species in Traditional Mining AreasOndistrict of Rarowatu Utara, Bombana 724Amirullah, Nasaruddin, Waode Harlis, Husnaeni, Halu Oleo University,Open University Makassar

Phosphate-solubilizing Actinomycetes Isolated from Rhizosphere of ManihotUtilisima in South Sulawesi 734Alimuddin Ali, Nurlaela Alydrus, Moh. Sahrul Tamsil, Andi Asrini Nurani Ulfa,Muslimin,State University of Makassar

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xviii

Development of Biology Instructional Media Based E-Learning Using Joomlaand Wondershare Quiz Creator for Skeletal and Muscular System Concept 745Anshar Mansabadi, Asmawati Azis,State University of Makassar

Identification of Physical and Social Ecotourism Potential in Ramma Valley atBawakaraeng Mountain South Sulawesi 753Mohamad Padri, Surianto, Andi Andriana, Aji Maulana, A. Nurul Virninda,State University of Makassar

Diversity and Indicator Species of Herbaceous Understory Vegetation at ForestDominated with Vitex Cofassus on Mount 760Muhammad Wiharto, Hamka L, Fatma H, Syamsiah, Abdul Hamid,Satriani,State University of Makassar

Developing Students’ Leader Character through Sekolah Alam (A Case Study InSekolah Alam Bogor Middle School Level) 770Nurhikmah Tenripada,State University of Makassar

The Effect of Different Grains on Oyster Mushroom (Pleurotus ostreatus)Spawn Growth 776Rukman Muslimin, A. Mu’nisa, Alimuddin Ali, Hartono, Oslan Jumadi,State University of Makassar

Content of Flavonoid Compounds of Ageratum Conyzoides Leaves Extract fromSome Altitude Habitats 780Yuliani, Soemarno, Bagyo Yanuwiadi, Amin Setyo Leksono, BrawijayaUniversity

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xix

Development of Model-Based Learning Visual Media through The ModelFour-D Thiagarajan for Expository Writing in Junior High School 837Akmal Hamsa, Ihramsari Akidah, State University of Makassar

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xx

Enhanced Fatigue Characteristics of Copper Microstructures due to EqualChannel Angular Pressing (ECAP) Process 959Kusno Kamil, Indonesian Moslem University

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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.

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)

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)

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)

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)

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)

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)

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).

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.

References

1. He, J.H., (1997), Variationaliteration method for delaydifferential equations,Communications in NonlinearScience and NumericalSimulation,:2 (4) pp.235–236.

2. He, J.H., (1998), Approximateanalytical solution for seepageflow with fractional derivatives inporous media, Computer Methodsin Applied Mechanics andEngineering: 167 (1-2) pp. 57–68.

3. He, J.H., (2007), The variationaliteration method for eighth-orderinitial-boundary value problems,”Physica Scripta:76 (6), pp. 680–682.

4. Yildirim, A. and Cherruault, Y.(2009), Analytical approximatesolution of a SIR epidemic modelwith constant vaccation strategyby homotopy perturbation method,: 38 (9) pp.1566-1575.

5. Abubakar, S., Akinwande, N.I.,Jimoh, O.R., Oguntolu, F.A, andOgwumu, O.D., (2013).

Approximate solution of SIRinfectious disease model usinghomoopy perturbation method(HPM), The pacific journal ofscience and technology: 14 (2)pp.163-169.

6. Ghotbi A. R., Barari, A., Omidvar,M. and Domairryk, G., (2011),Application of HomotopyPerturbation and VariationalIteration Methods to SIR EpidemicModel, Journal of Mechanics inMedichine and Biology.: 11, pp.149-161.

7. Mohd.Rizam,A.B.,Salisu,G.M.,Noor Akma,I. and Mansor,M.(2008). Deterministic models indengue transmission dynamics.Research Bulletin of Institute forMedical Research 2(1) pp.21-33

8. Syafruddin, S & M.S.M Noorani(2013). A SIR model for spread ofdengue fever disease (simulationfor south sulawesi Indonesia andselangor Malaysia). World journalof modeling and simulation. 9(2),pp.96-105.

9. Side, S. and. Noorani, M.S.M,(2013), A SIR Model for Spread ofDengue Fever Disease (Simulationfor South Sulawesi, Indonesia andSelangor, Malaysia)", WorldJournal of Modelling andSimulation: 9(2) pp. 96—105.

10. Inokuti M., Sekine H., Mura T.:General use of the Lagrangemultiplier in nonlinear mathematicalphysics, in: S. Nemat-Nasser (Ed.),Variational Method in Mechanics ofSolids, Pergamon Press, Oxford,156–162 1978.

11. Liao, S.J. (1992) The homotopyanalysis method and its applicationsin mechanics, PhD desertation,Shanghai Jiaotong University.

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