Garuda - Garba Rujukan Digital

Perilaku Solusi Sistem Persamaan Diferensial Waktu Tunda Dinamika Virus HIV Dalam Sel Tubuh Tambunan, Lidia Veronika; Sinaga, Lasker Pangarapen
Jurnal Sains Indonesia Vol 42, No 1 (2018): Jurnal Sains Indonesia
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar

The dynamics model of the HIV-virus without delay in the cells of the human body has a critical point in two conditions, namely virus-free conditions and endemic conditions. Based on stability analysis with eigenvalues and Routh Hurwitz criteria, these two critical points are asymptotically stable. With a graph of the behavior of the HIV-virus model dynamics solution with time delay shows asymptotic stable behavior. Observations were made with numerical simulations (Forward Euler method) based on the selection of parameter values randomly and the delay time randomly. Graph behavior of infected cell solutions and increased plasma viruses causes a graph of healthy cell solutions to decrease and vice versa. Based on the analysis and simulation conducted, it appears that the solution modeled the dynamics of the HIV-virus without delay and with the delay time moving towards the equilibrium point or called asymptotically stable. The provision of greater delay causes the number of infected cells and plasma viruses to decrease significantly and on this occasion, the number of healthy cells can increase.

KONVERGENSI DAN KONTINUITAS DERET KUASA SOLUSI PERSAMAAN LAPLACE PADA DIMENSI N Sinagai, Lasker P
JURNAL PENELITIAN SAINTIKA Vol 12, No 2 (2012): SEPTEMBER 2012
Publisher : JURNAL PENELITIAN SAINTIKA

Show Abstract | Download Original | Original Source | Check in Google Scholar

Persamaan Laplace adalah salah saiu bentuk persamaan differensialparsial yang banyak diteliti karena sangat berguna untuk menuelesaikan kasusÂ kasus maiemaiika ierapan. Tulisan ini menunjukkan deret kuasa solusi daripersamaan Laplace pada dimensi n serta menunjukkan kekonvergenan dankekontinuannya. Untuk mencapai tujuan ini, persamaan Laplace akan diubahmenjadi beberapa persamaan differensial biasa oleh metode pemisahan variabel danselanjutnya metode deret kuasa solusi akan menyelesaikan persamaanÂpersamaanbarn tersebut. Solusi persamaan adalah perkalian atas deretÂderei kuasa denganvariabel terpisah. Deret kuasa solusi persamaan Laplace adalah konvergen absolutdan kontinu.

Perilaku Solusi Sistem Persamaan Diferensial Waktu Tunda Dinamika Virus HIV Dalam Sel Tubuh Tambunan, Lidia Veronika; Sinaga, Lasker Pangarapen
Jurnal Sains Indonesia Vol 42, No 1 (2018): Edisi Januari - Juni
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jsi.v42i1.12242

The dynamics model of the HIV-virus without delay in the cells of the human body has a critical point in two conditions, namely virus-free conditions and endemic conditions. Based on stability analysis with eigenvalues and Routh Hurwitz criteria, these two critical points are asymptotically stable. With a graph of the behavior of the HIV-virus model dynamics solution with time delay shows asymptotic stable behavior. Observations were made with numerical simulations (Forward Euler method) based on the selection of parameter values randomly and the delay time randomly. Graph behavior of infected cell solutions and increased plasma viruses causes a graph of healthy cell solutions to decrease and vice versa. Based on the analysis and simulation conducted, it appears that the solution modeled the dynamics of the HIV-virus without delay and with the delay time moving towards the equilibrium point or called asymptotically stable. The provision of greater delay causes the number of infected cells and plasma viruses to decrease significantly and on this occasion, the number of healthy cells can increase. [BEHAVIOR OF SOLUTION OF DIFFERENTIAL EQUATION SYSTEM TIME DELAYING THE DYNAMICS OF HIV VIRUSES IN BODY CELLS] (J. Sains Indon., 42(1): 12-16, 2018)Keywords:HIV-Virus, Dynamic System, Equilibrium Point, Stability Criteria, Forward Euler Method

Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR Willyam Daniel Sihotang; Ceria Clara Simbolon; July Hartiny; Desrinawati Tindaon; Lasker Pangarapan Sinaga
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 1 (2019): JMSK, July, 2019
Publisher : Department of Mathematics, Hasanuddin University

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

ANALISIS KESTABILAN MODEL MATEMATIKA JUMLAH PEROKOK PENGARUH KENAIKAN HARGA ROKOK DENGAN DINAMIKA AKAR KUADRAT FIDELIS NOFERTINUS ZAI; ARYL ZULDAUS SEMBIRING; ARDINAL VANBASTEN; ANGGI NOVITA NASUTION; LASKER PANGARAPAN SINAGA
E-Jurnal Matematika Vol 9 No 4 (2020)
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.2020.v09.i04.p310

Consumption of cigarettes in large quantities by the public is one of the main concerns in every country because cigarettes contain harmful ingredients that can trigger various diseases. This journal will explain the mathematical model of the number of smokers affected by rising prices of cigarettes with square root dynamics. The population is divided into four, composed of potential smokers, occasionally smokers, heavy smokers, and ex-smokers. The results of the model analysis are that there is a single point of smoker’s endemic equilibrium. If conditions are met, then the endemic equilibrium point of smokers will be asymptotically stable, and over a long period of time there will always be a spread of smokers.

OPTIMASI PRODUKSI ULOS BATAK DENGAN PROGRAM INTEGER MELALUI METODE BRANCH AND BOUND DI UD. PARNA ULOS Kristin Natalia Panjaitan; Lasker Sinaga .
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 8, No 1 (2022): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v8i1.34059

Program Integer adalah model matematis yang mana hasil penyelesaian pemrograman liniernya berupa bilangan bulat. Salah satu metode untuk menyelesaikan persoalan Program Integer adalah Metode Branch and bound. Tujuan dari penulisan ini adalah untuk menentukan jumlah masing-masing jenis ulos yang akan diproduksi oleh UD. Parna Ulos. Adapun jenis Ulos yang menjadi variabel keputusan dalam penulisan ini ialah Ulos ragi hotang biasa, Ulos Angkola Raja, Ulos Mangiring, Ulos Bintang Maratur, Ulos pinuncaan, dan Ulos sibolang. Penelitian ini menggunakan program integer metode Branch and Bound dengan bantuan Sofware for Windows V5. Pada penelitian ini terdapat 6 variabel dan 5 kendala.Variabel keputusan yang digunaan adalah jenis Ulos yang diproduksi oleh UD.Parna Ulos. Adapun kendala pada penelitian ini adalah bahan baku benang katun, lem Ulos (Kanji), waktu produksi, permintaan dan kuota persediaan. Dari hasil perhi- tungan program integer dengan metode Branch and bound dalam menyelesaikan permasalahan produksi harian Ulos adalah 14 lembar Ulos ragi hotang biasa, 10 lembar Ulos angkola raja, 8 lembar Ulos mangiring, 8 lembar Ulos bintang maratur, 7 lembar Ulos pinuncaan dan 10 lembar Ulos sibolang. Jadi, jumlah Ulos optimal yang bisa diproduksi dalam sehari dari bahan baku yang tersedia, waktu produksi dan permintaan pasar adalah 57 lembar dengan pendapatan maksimal Rp7.079.000, 00. Abstract The Integer Program is a mathematical model in which the result of the linear programming solution is an integer. One method to solve Integer Program problems is the Branch and bound method. The purpose of this paper is to determine the number of each type of ulos that will be produced by UD. Parna Ulos. The types of Ulos that became the decision variables in this paper were Ulos Hotang Biasa, Ulos Angkola Raja, Ulos Mangiring, Ulos Bintang Maratur, Ulos Pinuncaan, and Ulos sibolang. This research uses an integer program with themethod Branch and Bound with the help of Software for Windows V5. In this study, there are 6 variables and 5 constraints. The decision variable used is the type of Ulos produced by UD. Parna Ulos. The obstacles in this research are the raw material of cotton yarn, Ulos glue (Kanji), production time, demand and supply quota. From the calculation results of the integer program using the Branch and bound method in solving the daily production problems of Ulos, there are 14 sheets of ordinary Ulos Ragi Hotang Biasa, 10 pieces of Ulos Angkola Raja, 8 pieces of Ulos mangiring, 8 pieces of Ulos

ANALISIS SENSITIVITAS DAN KONTROL OPTIMAL MODEL SEIR PENYEBARAN COVID-19 DI INDONESIA Nailan Ni'mah Nasution; Lasker P Sinaga
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 7, No 3 (2021): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v7i3.32461

— Covid-19 (Coronavirus Disease) merupakan penyakit yang menyerang sistem pernafasan akibat infeksi SARS-CoV-2 (Severe Acute Respiratory Syndrome 2). Wabah ini ditemukan pertama kali di Wuhan, provinsi Hubei, Cina pada Desember 2019 dan menyebar dengan cepat ke berbagai negara sehingga dinyatakan sebagai pandemi pada Maret 2020. Sebagai upaya mengatasi pandemi Covid-19, ilmuwan matematika mengembangkan berbagai model matematika untuk mempelajari karakteristik epidemi wabah, memprediksi penyebaran virus serta menawarkan berbagai langkah intervensi. Penelitian ini bertujuan untuk menganalisis sensitvitas dan kontrol optimal dari model SEIR penyebaran Covid-19 dengan menerapkan strategi kontrol berupa vaksinasi individu rentan dan pengobatan individu terinfeksi. Hasil analisis sensitivitas menunjukkan bahwa parameter terkait penambahan jumlah individu rentan dan kematian individu rentan merupakan parameter paling berpengaruh terhadap nilai bilangan reproduksi dasar, jumlah individu terpapar dan terinfeksi. Penerapan strategi kontrol pada model berupa vaksinasi dan pengobatan penting untuk dilakukan karena efektif untuk menurunkan jumlah individu terinfeksi hingga 99%. Covid-19 (Coronavirus Disease) is an acute respiratory system disease caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome 2). This outbreak was first discovered in Wuhan, Hubei province, China in December 2019 and has spread rapidly to various countries and was declared as a pandemic in March 2020. To overcome the Covid-19 pandemic, mathematicians develop mathematical model to study the spread of viruses and offer various intervention measures. This study aims to analyze the sensitivity and optimal control of the SEIR model for the Covid-19 dynamic in Indonesia by implementing control strategies. The control strategy used is vaccination of susceptible individuals and treatment of infected individuals. The sensitivity analysis shows that the rate of increase in the number of susceptible individuals and the mortality of susceptible individuals is the parameter that most influences the value of the basic reproduction number, the number of exposed and infected individuals. The control strategy used was effective in reducing the number of infected individuals to aroud 99%.

ANALISIS PERILAKU SOLUSI MODEL GERAK AYUNAN YANG DIPENGARUHI GAYA GESEKAN YANG BERBANDING LURUS DENGAN KECEPATAN SUDUT Lasker P Sinaga
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 4, No 1 (2018): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v4i1.11016

ABSTRAKModel gerak ayunan yang dipengaruhi gaya gesekan yang berbanding lurus dengan kecepatan sudut merupakan suatu persamaan diferensial nonlinear. Model ini diubah menjadi sistem persamaan diferensial nonlinear yang lebih sederhana dan memiliki solusi bersifat periodik dengan titik kritis dengan n bilangan bulat. Titik-titik kritis akan stabil jika n adalah bilangan genap dan sebaliknya, tidak stabil jika n adalah bilangan ganjil. Bentuk kestabilan (simpul, pelana atau spiral) dari titik kritis bergantung pada nilai-nilai parameter model tersebut.Kata kunci: persamaan diferensial, sistem dinamik, gerak ayunan, titik kritis, kestabilan ABSTRACTThe pendulum motion model influenced by friction force that is directly proportional to the angular velocity. This model is converted into a simpler nonlinear differential equation system and has a periodic solution with critical point where n is an integer. The critical points will be stable if n is an even numbers and vice versa, will be unstable if n is an odd number. The stability form (node, saddle or spiral) of critical points depends on the value of the model’s parameter.Key words: differential equation, dynamic system, pendulum motion, critical points, stability

BIFURKASI HOPF PADA MODEL DINAMIKA SEIR PENYEBARAN COVID-19 DI INDONESIA Chi-Chi Monalisa Hutabarat; Lasker P Sinaga
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 8, No 2 (2022): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v8i2.34204

Corona Virus Disease 2019 (Covid-19) adalah penyakit yang menyerang sistem pernafasan akibat infeksi SARS-CoV-2 (Severe Acute Respiratory Syndrome). Pada Desember 2019, virus corona pertama kali muncul di Wuhan, provinsi Hubei, China yang berubah menjadi wabah pandemi yang menyebar ke seluruh dunia, termasuk Indonesia. Untuk mengatasi pandemi Covid-19, peneliti dari berbagai bidang memberikan kontribusinya. Ilmuwan matematika mempelajari karakteristik epidemi wabah, memprediksi penyebaran virus serta menawarkan berbagai langkah intervensi melalui pengembangan model matematika sehingga dapat mengendalikan penyebaran penyakit. Penelitian ini bertujuan untuk menganalisis stabilitas dan bifurkasi hopf dengan melihat perubahan struktur orbit pada sistem seiring dengan perubahan nilai parameter. Analisis kestabilan menunjukkan bahwa dinamika Covid-19 di Indonesia akan mencapai titik stabil untuk waktu yang lama, yaitu setelah mencapai 500 bulan. Berdasarkan analisis sensitivitas pada refrensi sebelumnya, parameter  dan  disebut parameter bifurkasi. Hasil analisis menunjukkan bifurkasi Hopf terjadi pada simulasi exposed terhadap infected yang ditandai dengan munculnya limit cycle p AbstractCoronavirus Disease 2019 (Covid-19) is an acute respiratory system disease caused by SARS-CoV-2 (Severe Acute Respiratoryiscovered Syndrome 2). In December 2019, coronavirus was first discovered in Wuhan, Hubei province, China which turned into a pandemic outbreak and has been spreading in whole the world, including Indonesia. Research from various disciplines is carried out to overcome the Covid-19 pandemic. Mathematicians develop mathematical models to study the characteristics of epidemic, predict the spread of viruses and offer various intervention measures. This study aims to analyze the stability and hopf bifurcation of the SEIR model for the Covid-19 dynamic in Indonesia by looking at changes in the orbit structure of the system along with changes in parameter values. Stability analysis shows that the dynamics of Covid-19 in Indonesia will stable to occur for a long term, after reaching 500 months. Based on the sensitivity analysis in the previous reference, parameters  dan  are bifurcation parameters. The results of the analysis show that the Hopf bifurcation occurs in the exposed to infected simulation which is indicated by the appearance of a limit cycle in the orbit.

OPTIMASI VEHICLE ROUTING PROBLEM DENGAN MENGGUNAKAN ALGORITMA GENETIKA UNTUK MEMINIMASI BIAYA PENGIRIMAN BARANG DI PT GLOBAL TRANS NUSA Edwin Prasetya Tamba; Lasker Sinaga .
KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi Vol 8, No 2 (2022): Karismatika
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jmk.v8i2.36289

Vehicele Routing Problem (VRP) merupakan merupakan salah satu masalah optimasi dalam menentukan rute optimal kendaraan. Algoritma Genetika merupakan salah satu metode yang cukup baik digunakan untuk optimasi rute terutama untuk permasalahan distribusi yang menggunakan dua atau lebih kendaraan. Pencarian solusi direpresentasikan dengan kromosom yang diproses algoritma genetika melalui inisialisasi individu, nilai fitness, seleksi, crossover, dan mutasi. Hasil dari penerapan algoritma tersebut dapat mengoptimalkan rute pengiriman dan mengurangi jarak tempuh transportasi sebesar 106,7 km di bulan Januari, 100,4 km dibulan Februari, 164,6 km di bulan Maret, 64,4 di bulan April, 136,5 km di bulan Mei dan 57,1 km di bulan Juni. Dan mengurangi total biaya pengiriman sebesar 29,98% di bulan Januari, 31,84 di bulan Februari, 41,85% di bulan Maret, 20,03% di bulan April, 26,4% di bulan Mei, dan 26,4% di bulan Mei dan 26,4 % di bulan Juni dengan parameter algoritma yang digunakan adalah Probabilitas Crossove r= 0,9, Probabilitas Mutasi = 0,05, Maximum Generasi = 100 dan Jumlah Populasi = 60. Abstrak. Vehicle Routing Problem (VRP) is one the optimization problems in determining the optimal vehicle route. Genetic Algrithm is a method that is quite good for route optimization, especialy for distribution problems that use two or more vehicles. The search for solutions is represented by chromoshomes which are processed by genetic algorithm through individual initialization, fitness values, selection, crossover and mutation. The results of the application of the algorithm can optimize delivery routes and reduce transportation mileage by 106,7 km in Januari, 100,4 km in February, 164,4 km in March, 64,4 in April, 136,5 km in May and 57,1 km in June. And reduce the total shipping cost by 229,98% in January, 31,84% in February, 26,4% in March, 20,03% in April, 26,4% in May and 26,4 in June ith the algorithm parameters used are Crossover Probability =0,9, Mutation Probability=0,05, Maximum Generation=100 and Total Population=60.

Title

Found 17 Documents
Search

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Title Search

Found 17 Documents Search

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Title

Found 17 Documents
Search