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Optimal Prevention and Treatment Control on SVEIR Type Model Spread of COVID-19 Nainggolan, Jonner
CAUCHY Vol 7, No 1 (2021): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i1.12634

COVID-19 pandemic has disrupted the world's health and economy and has resulted in many deaths since the first case occurred in China at the end of 2019. Moreover, The COVID-19 disease spread throughout the world, including Indonesia on March 2, 2020.Â Coronavirus quickly spreads through droplets of phlegm through the throat to the lungs. Researchers in the medical field and the exact science are jointly examined the spread, prevention, and optimal control of COVID-19 disease. Due to the prevention of COVID-19, a vaccine has been foundÂ in early 2021, which at the time, the vaccination process was carried out worldwide against COVID-19. This paper examines the spread model of SVEIR-type COVID-19 by considering the vaccination subpopulation. In this study, control of prevention efforts ( Â and ) and healing efforts Â are given and being analyzed with the fourth-order Runge-Kutta approach. Based on numerical simulations, it can be seen that using the controls Â Â and Â can reduce the number of infected individuals in the subpopulation compared to those without control. The Â control can increase the number of recovered individual subpopulations.Keywords: COVID-19; SVEIR model; optimal control; treatment; vaccination.

ANALISIS MODEL PROBABILISTIK PUNAHNYA MUTAN PARASIT MALARIA YANG RESISTEN TERHADAP KLOROKUIN PLUS AMODIAKUIN Jonner Nainggolan
INTEGRAL Vol. 11 No. 1 (2013)
Publisher : INTEGRAL

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (266.471 KB)

In this paper probabilistic models are developed from a model of malaria parasite population dynamics proposed by Macdonald [1] based on Galton-Watson branching and generating Negative Binomial distribution with maximum likelihood estimation, to test a model of malaria parasite extinction. Values of the model parameters are calculated using a samples of patients treated at the Jayapura General Hospital. The response of malaria parasites to chloroquine plus amodiaquine was examined with in- vivo tests. Samples were taken from 40 people, with 17 sensitive samples, 9 samples of degree of RI, 8 samples of degree of RII, and 6 samples of degree RIII. The data sample used in the model must satisfy the Negative Binomial distribution. Model construction approach includes: the basic model, study models, and mathematical calculations. A goodness of fit test was used to test the feasibility of the model. The model was focused on predicting the probability of the extinction of mutant malaria parasites resistant to chloroquine plus amodiaquine in a local population. Data analysis revealed the point of the probability of the extinction of resistant malaria parasites using Galton-Watson theorem is s = 0.8814. The probability of the extinction of malaria parasites resistant to chloroquine plus amodiaquine is φNB =0,8902.Keywords: Probabilistic model, malaria, the point of the extinction of parasites,chloroquine plus amodiaquine.Model probabilistik dalam tulisan ini merupakan pengembangan model dinamika populasi parasit malaria yang dikaji oleh Macdonald [1] berbasiskan pencabangan Galton-Watson dan pembangkit distribusi Binomial Negatif dengan estimasi mak- simum likelihood. Kombinasi model pencabangan Galton-Watson dan pembangkit distribusi Binomial Negatif digunakan untuk mengkaji model peluang punahnya parasit malaria. Untuk menentukan nilai parameter-parameter model digunakan data pasien yang berobat di Rumah Sakit Umum Jayapura. Untuk melihat respon parasit malaria terhadap obat antimalaria, digunakan tes in-vivo. Jumlah sampel dalam penelitian ini sebanyak 40 orang, 17 sampel sensitif, 9 sampel derajat RI, 8 sampel derajat RII, dan 6 sampel derajat RIII. Data sampel yang digunakan pada kajian model harus memenuhi syarat distribusi Binomial Negatif. Kemudian dilakukan pengujian kelayakan model dengan menggunakan goodness of fit test. Kajian model tersebut difokuskan untuk memprediksi besarnya probabilitas punah- nya mutan parasit malaria yang resisten terhadap klorokuin plus amodiakuin. Dari hasil analisis data diperoleh titik punahnya parasit malaria dengan menggunakan teorema Galton-Watson s = 0,8814. Sedangkan peluang punahnya parasit malaria yang resisten terhadap klorokuin plus amodiakuin adalah φN B = 0, 8902.Kata Kunci: Model probabilistik, malaria, titik punahnya parasit, klorokuin plusamodiakuin.

Analisis Kestabilan Lokal Titik Ekuilibrium Model Dinamik Kebiasaan Merokok Joko Harianto; Mira Aprilia Marcus; Jonner Nainggolan
KUBIK Vol 5, No 2 (2020): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v5i2.9348

Dinamika kebiasaan merokok dalam artikel ini dianalisis dengan pendekatan model epidemiologi. Lingkungan perokok dibagi menjadi empat populasi, yaitu populasi (Potential) menyatakan populasi dari individu-individu yang tidak merokok, populasi (Light) menyatakan populasi dari perokok ringan, populasi (Smokers) menyatakan populasi dari perokok berat, populasi menyatakan populasi dari individu-individu yang berhenti merokok sementara dan populasi menyatakan populasi dari individu-individu yang berhenti merokok secara permanen. Model tersebut dimodifikasi kemudian dianalisis titik ekuilibriumnya. Langkah pertama, ditentukan titik ekuilibrium bebas rokok. Langkah kedua, ditentukan titik ekuilibrium kebiasaan merokok. Langkah ketiga, ditentukan the Smoking Generation Number (R0 ) dengan menggunakan next generation matrix yang melibatkan radius spektral. Langkah terakhir, kestabilan lokal setiap titik ekuilibrium pada modelnya dianalisis. Hasil analisis menunjukkan bahwa titik ekuilibrium bebas rokok stabil asimtotik lokal saat nilai the Smoking Generation Number kurang dari satu. Sebaliknya, jika nilai the Smoking Generation Number lebih dari satu dan b1(m+g) lebih dari b2(b1-m), maka titik ekuilibrium perokok ringan stabil asimtotik lokal. Sedangkan titik ekuilibrium perokok berat stabil asimtotik lokal jika nilai the Heavy Smoking Generation Number lebih dari satu. Kemudian dilakukan simulasi numerik menggunakan Software Maple untuk mengecek hasil analisis kestabilan lokal titik ekuilibrium tersebut.

KONTROL PENGOBATAN OPTIMAL PADA MODEL PENYEBARAN TUBERKULOSIS TIPE SEIT JONNER NAINGGOLAN
E-Jurnal Matematika Vol 6 No 2 (2017)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2017.v06.i02.p158

A tuberculosis model of SEIT type which incorporates treatment of infectives is considered. The population is divided into four compartments, that is: S are individuals in the susceptible compartment, E are individuals in the exposed compartments, I are individuals in the infected compartment, and T are individuals in the treatment compartments. For this model, controls on treatment is incorporated to reduce the actively infected individual compartments, via application of the Pontryagins Maximum Principle of optimal control theory. Numerical calculations with the approach of the Runge-Kutta method of fourth order can be seen that, the influence of the control treatment to more effectively reduce the number of individuals in the infected compartment compared with no controls. The basic reproduction ratio with control less compared with no controls.

UPAYA MENINGKATKAN HASIL BELAJAR PESERTA DIDIK DENGAN DENGGUNAKAN MODEL PEMBELAJARAN VAN HIELE PADA TOPIK EGIEMPAT DI KELAS XI RPL (REKAYASA PERANGKAT LUNAK) SMK NEGERI 9 JAYAPURA TAHUN AJARAN 2017/2018 Suzana Weyai; Bettisari Napitupulu; Jonner Nainggolan
Jurnal Inovasi Penelitian Vol 1 No 11: April 2021
Publisher : Sekolah Tinggi Pariwisata Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47492/jip.v1i11.504

Weyai, Suzana 2018. “The Efforts of Improving the results of Learning Using a Learning Model Van Hiele on the topic Quadrilateral in class XI RPL (Software engineering) SMK Negeri 9 Jayapura Academic year 2017/2018”. Thesis. Master of Mathematics Education Study Program of the Faculty of Teacher Training and Educational Sciences of the University of Cenderawasih. Supervisor (1) Dr. Bettisari Napitupulu, M. Sc. (2) Dr. Jonner Nainggolan, M. Si. This research approach was qualitative research with this type of class action research, data collected in the form of test result pre Cycle, the research was done in two cycles and at each end of the cycle is evaluations and test. The result of the study participants in the measure through final test cycle I and cycle II. The study was conducted in this research is a study based on the stage of the van Hiele thinking method that began with stage 0 (visualization), stage I (analysis), to stage II (informal deduction) through the phase information, orientation, explanation, free orientation, and the phase of integration on a sub chapter of parallelogram, rectangle, square, rhombus, quadrilateral, and trapezoid. Learning is conducted in the form of group discussions using LKK and media of instructions. There are two LKK used, namely: (1) LKK 1 contains definitions and properties of rectangles and LKK 2 contains the circumference and area of a quadrilateral. With the application of the learning model based on the stage of the van Hiele method, average value and yiels learning learners increased. From the result of the implementation of the material with the cycle 1 data obtained 20 learners (100%) reach the complete study with an average rating of 84.1 and classes of implementation material B cycle 1 retrieved 12 people (75%) reach the complete study with and a average rating of class 85.75.

Analisis Kestabilan Lokal Titik Ekuilibrium Model Dinamik Kebiasaan Merokok Joko Harianto; Mira Aprilia Marcus; Jonner Nainggolan
KUBIK Vol 5, No 2 (2020): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v5i2.9348

Dinamika kebiasaan merokok dalam artikel ini dianalisis dengan pendekatan model epidemiologi. Lingkungan perokok dibagi menjadi empat populasi, yaitu populasi (Potential) menyatakan populasi dari individu-individu yang tidak merokok, populasi (Light) menyatakan populasi dari perokok ringan, populasi (Smokers) menyatakan populasi dari perokok berat, populasi menyatakan populasi dari individu-individu yang berhenti merokok sementara dan populasi menyatakan populasi dari individu-individu yang berhenti merokok secara permanen. Model tersebut dimodifikasi kemudian dianalisis titik ekuilibriumnya. Langkah pertama, ditentukan titik ekuilibrium bebas rokok. Langkah kedua, ditentukan titik ekuilibrium kebiasaan merokok. Langkah ketiga, ditentukan the Smoking Generation Number (R0 ) dengan menggunakan next generation matrix yang melibatkan radius spektral. Langkah terakhir, kestabilan lokal setiap titik ekuilibrium pada modelnya dianalisis. Hasil analisis menunjukkan bahwa titik ekuilibrium bebas rokok stabil asimtotik lokal saat nilai the Smoking Generation Number kurang dari satu. Sebaliknya, jika nilai the Smoking Generation Number lebih dari satu dan b1(m+g) lebih dari b2(b1-m), maka titik ekuilibrium perokok ringan stabil asimtotik lokal. Sedangkan titik ekuilibrium perokok berat stabil asimtotik lokal jika nilai the Heavy Smoking Generation Number lebih dari satu. Kemudian dilakukan simulasi numerik menggunakan Software Maple untuk mengecek hasil analisis kestabilan lokal titik ekuilibrium tersebut.

Exploration of Ethnomathematics of House and Traditional Music Tools Biak-Papua Cultural Alvian M Sroyer; Jonner Nainggolan; Ida M Hutabarat
Formatif: Jurnal Ilmiah Pendidikan MIPA Vol 8, No 3 (2018): Formatif: Jurnal Ilmiah Pendidikan MIPA
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat Universitas Indraprasta PGRI

This research is an ethnomathematics study of the Biak Papuan community. The ethnomathematics studied are houses and traditional musical instruments. The shape and style of the traditional Biak house still remain to this day. The purpose of this study was to examine and reveal the relationship between mathematics and the traditional home culture of the Biak community, namely rum Som, rum Sram and Sram Mankubui and traditional musical instruments namely Tifa. The research method used is an exploratory survey method with a qualitative approach. The results showed that the shape of the roof of rum Som, rum Sram, Sram Mankubui was rectangular, half elliptical and triangular trapezoid. Whereas Tifa's musical instruments look like the two most belted cones combined.

PROBABILISTIK PUNAHNYA MYCOBACTERIUM TUBERCULOSA YANG RESISTEN TERHADAP OBAT ANTI TUBERKULOSIS RESISTENSI PRIMER, RESISTENSI TERHADAP ISONIAZID, DAN TB–MDR DI PUSKESMAS KOTA MEDAN Jonner Nainggolan
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 9 No 2 (2017): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2017.9.2.2862

In this paper, probabilistic models are developed from a dynamical model of tuberculosis transmission based on a Galton-Watson branching and Negative Binomialdistribution generation with weighted probability estimation used to test an extinction model of mycobacterium germ. The values of model parameters were obtained from the medical record data at Puskesmas Kota Medan : 31 tuberculosis patients treated during February-August 2015, with 25 sensitive samples, 3 samples of RI degree, 2 samples of RII degree, and 3 samples of RIII degree. Data analysis using Galton-Watson theorem revealed the extinction point of resistant malaria parasites, that is s = 1. The successful transmission of mycobacterium bacteria is 36 people per year. The extinction probability of mycobacterium bacteria that is resistant to anti-tuberculosis drugs is ϕNB = 1.

PENGEMBANGAN MODUL IPA TERPADU BERBASIS KEARIFAN LOKAL PAPUA MATERI INTERAKSI MAHLUK HIDUP TERHADAP LINGKUNGAN SRI LESTARI; TIURLINA SIREGAR; JONNER NAINGGOLAN
Jurnal Ilmu Pendidikan Indonesia Vol 7, No 3 (2019)
Publisher : Program Magister Pendidikan IPA, Program Pascasarjana Universitas Cenderawasih

Papua's local wisdom module is really needed to improve learning outcomes with contextual and tangible control where so far there has been lack of teaching materials based on local wisdom. This research is a research and development (Research & Development) that aims to find out how to develop integrated science modules based on local Papuan wisdom materials on the interaction of living things with the environment in class VII students of Nurul Huda Yapis Jayapura in knowing improvement in learning outcomes after using the module. The development model used is the ADDIE model (Analyze, Design, Development, Implementation, Evaluation) with an experimental design using a pre test post test one group design, which uses one research class with a sample of 37 students. The results showed. (1) The results of the feasibility test for the prepared learning modules, based on material validation, obtained an average of 90.6%, media validation with an average of 92%, educator responses 96.25% and mean responses of students by 90.7%. In general the average for the module feasibility test is 92.10% which means the module is very suitable for use in learning. (2) There is an increase in students' learning outcomes after using a module based on local Papuan wisdom, based on the n-Gain results in RPP 1 is 0.57, RPP 2 is 0.71 and RPP 3 is 0.75. The n-Gain average for the three RPPs is 0.68 with a moderate category which means the use of science modules based on local Papuan wisdom is quite effective in improving student learning outcomes.

PENINGKATAN PEMBELAJARAN ETNOMATEMATIKA NOKEN PADA KELAS V SD INPRES VIM II KOTARAJA JAYAPURA PAPUA Jonner Nainggolan; Abraham Abraham
JURNAL PENGABDIAN PAPUA Vol 2, No 3 (2018)
Publisher : LPPM Uncen

The curriculum 2013, demands the concept of science-based learning that is associated with local culture. Mathematical concepts related to the local culture of Papua one of them is noken etnomatematics. The purpose of community service is to introduce the concept of noken etnomatematics to the students of class V SD Inpres Vim II Kota Raja Abepura Jayapura as many as 35 students. The method of implementation is to socialize the material, time and object before the implementation of activities to teachers and Headmaster. In the implementation of community service learning is used lecture method, discussion, and props. The results obtained in the pre-test with an average value of = 26.42 including low, the lowest value of 7 and the highest value of 50. Results obtained on the post-test with an average value of = 41.54 including moderate, the lowest value of 17 and the highest value of 70. Improved learning outcomes obtained after the activities of community service for N-Gain = 0.38 including the moderate category.Keywords: Learning, etnomatematics, noken, N-gain.

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