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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Jurnal Fisika FLUX Jurnal Matematika Sains dan Teknologi Desimal: Jurnal Matematika MEDIA BINA ILMIAH BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Tropical Wetland Journal Bubungan Tinggi: Jurnal Pengabdian Masyarakat Jurnal Abdimas Prakasa Dakara

Yuni Yulida

Program Studi Matematika FMIPA Universitas Lambung Mangkurat

Author-ID : 425091

Agriculture, Biological Sciences & Forestry Arts Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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PEMBENTUKAN PERSAMAAN VAN DER POL DAN SOLUSI MENGGUNAKAN METODE MULTIPLE SCALE Farohatin Na'imah; Yuni Yulida; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 2 (2020): JURNAL EPSILON VOLUME 14 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Mathematical modeling is one of applied mathematics that explains everyday life in mathematical equations, one example is Van der Pol equation. The Van der Pol equation is an ordinary differential equation derived from the Resistor, Inductor, and Capacitor (RLC) circuit problem. The Van der Pol equation is a nonlinear ordinary differential equations that has a perturbation term. Perturbation is a problem in the system, denoted by ε which has a small value 0<E<1. The presence of perturbation tribe result in difficulty in solving the equation using anlytical methode. One method that can solve the Van der Pol equation is a multiple scale method. The purpose of this study is to explain the constructions process of Van der Pol equation, analyze dynamic equations around equilibrium, and determine the solution of Van der Pol equation uses a multiple scale method. From this study it was found that the Van der Pol equation system has one equilibrium. Through stability analysis, the Van der Pol equation system will be stable if E= 0 and -~<E<=-2. The solution of the Van der Pol equation with the multiple scale method is Keywords: Van der Pol equation, equilibrium, stability, multiple scale.

METODE DEKOMPOSISI LAPLACE UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL PARSIAL NONLINIER Sinar Ismaya; Yuni Yulida; Naimah Hijriati
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 10, No 1 (2016): JURNAL EPSILON VOLUME 10 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Partial differential equations are grouped into two parts: linear and nonlinear differential equations. Many natural phenomena are modeled in the form of nonlinear partial differential equations, such as K-dV and Burger equations. To be able to explain natural phenomena in the form of nonlinear partial differential equations required approach method which can then be applied to determine the solution of partial differential equation. One of the methods used to determine the solution of nonlinear differential equations is Laplace Decomposition Method which combines Laplace Transformation theory and Adomian Decomposition Method. This research is conducted by using literature method with the following procedure: Assessing Non-Linear Partial Differential Equation, Method Adomian Decomposition, Laplace Transformation and Laplace Decomposition Method; then determine the settlement of the non-linear differential equation with the Laplace Decomposition Method. The result of this research is obtained by solution of nonlinear partial differential equation of Order one by using Laplace decomposition method that is 0nnuu∞ == Σ with (????????, ????????) = ℒ-1????1????????ℒ {???????? (????????, ????????)} + 1????????ℎ (????????) ???? and ???????????????? + 1 (????????, ????????) = ℒ-1????-1????????ℒ {???????????? ???????? (????????, ????????) } -1????????ℒ {????????????????} ????; ????????≥0 and on the two-order nonlinear partial differential equation is 0nnuu = = Σ with ????????0 (????????, ????????) = ℒ-1????1????????2ℒ {???????? (????????, ????????)} + 1????????ℎ (????????) + 1????????2???????? (????????) ???? and ???????????????? + 1 (????????, ????????) = ℒ-1????-1????????2ℒ {???????????? ???????? (????????, ????????)} - 1????????2ℒ {????????????????} ????; ????????≥0

ANALISIS KESTABILAN MODEL SEIR UNTUK PENYEBARAN COVID-19 DENGAN PARAMETER VAKSINASI Miftahul Jannah; Muhammad Ahsar Karim; Yuni Yulida
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 3 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Covid-19 adalah penyakit menular yang disebabkan oleh coronavirus disease jenis baru, yaitu SARS-CoV-2. Oleh WHO, penyebaran Covid-19 telah ditetapkan sebagai pandemi global sejak 11 Maret 2020. Pada penelitian ini, penyebaran Covid-19 dimodelkan dengan menggunakan model matematika epidemik, yaitu model SEIR (Susceptible, Exposed, Infected, and Recovered) dengan memperhatikan faktor vaksinasi sebagai parameter. Selanjutnya, ditentukan titik ekuilibrium dan bilangan reproduksi dasar, serta diberikan analisis kestabilan pada model.

PEMODELAN MATEMATIKA PENYEBARAN COVID-19 DENGAN MODEL SVEIR Gian Septiansyah; Muhammad Ahsar Karim; Yuni Yulida
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(2), 2022
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v16i2.6496

Coronavirus disease 2019 or also known as Covid-19 is a disease caused by a type of coronavirus called Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) or better known as the corona virus. Covid-19 become a pandemic since 2020 and has been widely studied, one of which is in mathematical modeling. In this study, the spread of Covid-19 is modeled using the SVEIR (Susceptible, Vaccination, Exposed, Infected, and Recovered) model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, determines the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The purpose of this study explains the formation of the Covid-19 SVEIR model, determines the equilibrium point, the basic reproduction number, and analyzes the stability of the Covid-19 SVEIR model. The result of this study is to explain the formation of the Covid-19 SVEIR model and obtained two equilibrium points, the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number is obtained through the Next Generation Matrix method. The results of the stability analysis at the disease-free equilibrium point were locally asymptotically stable with conditions while at the endemic equilibrium point local asymptotically stable with conditions . The natural death rate is greater than the effective contact rate. A numerical simulation is presented to show a comparison spread of Covid-19 by providing different levels of vaccine effectiveness using the Runge-Kutta Order method.

MODEL EPIDEMIK PENYAKIT DIARE DENGAN FUNGSI INSIDENSI HOLLING TIPE DUA Yuni Yulida; Aprida Siska Lestia; Riska Fitria; Azkia Khairal Jamil
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(2), 2022
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v16i2.6642

Model epidemik merupakan salah satu bentuk model matematika di bidang epidemologi. Penyakit diare adalah salah satu penyakit menular yang dapat dicegah melalui treatment. Tujuan penelitian ini adalah untuk menjelaskan terbentuknya model epidemik penyebaran penyakit diare, menganalisis kestabilan model, dan membuat simulasi numerik. Penelitian ini menggunakan metode linierisasi untuk melinierkan model nonlinier. Metode matriks next generation untuk menentukan Basic reproduction number dan metode runge kutta orde empat untuk melakukan simulasi model. Hasil dari penelitian ini, diperoleh model epidemik penyakit diare berbentuk Model SIRT (Susceptible, Infected, Treatment, Recovered) dengan fungsi insidensi Holling Tipe 2. Selanjutnya, diperoleh dua titik ekulibrium dan diperlihatkan bahwa berperan penting dalam proses penyebaran penyakit. Jika maka titik ekuilibrium bebas penyakit stabil asimtotik sehingga populasi akan terbebas dari wabah penyakit. Sebaliknya jika maka titik ekuilibrium endemik stabil asimtotik sehingga penyakit akan selalu ada dalam populasi. Berdasarkan nilai indeks sensitivitas menunjukkan bahwa parameter laju kontak efektif dan laju kelahiran adalah parameter yang paling sensitif (berbanding lurus) terhadap perubahan nilai . Selanjutnya, simulasi model diberikan untuk memperlihatkan ilustrasi terhadap analisa kestabilan model

Pelatihan Calon Pembina Olimpiade Sains Nasional Bidang Matematika bagi MGMP Matematika SMA Kabupaten Hulu Sungai Tengah Muhammad Ahsar Karim; Yuni Yulida; Azkia Khairal Jamil; Riska Fitria; Gabriel Henokh Gultom; Raihan Nooriman; Rizky Purnama Wulandari
Bubungan Tinggi: Jurnal Pengabdian Masyarakat Vol 4, No 4 (2022)
Publisher : Universitas Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/btjpm.v4i4.6245

Olimpiade Sains Nasional bidang Matematika tingkat SMA merupakan kompetisi bergengsi bagi siswa SMA/MA di seluruh Indonesia yang memerlukan strategi dan teknik penyelesaian soal-soal yang cenderung tidak standar, pemahaman konsep yang mendalam, dan ide kreatif. Melalui kegiatan PDWM ULM Tahun 2022, tim dosen Program Studi Matematika FMIPA ULM sebagai pelaksana dan MGMP Matematika SMA HST sebagai mitra bekerja sama menyelenggarakan kegiatan pelatihan Olimpiade Sains Nasional bidang Matematika bagi anggota MGMP Matematika SMA Kabupaten Hulu Sungai Tengah. Kegiatan ini bertujuan untuk menambah pengetahuan dan meningkatkan kemampuan anggota MGMP Matematika SMA HST agar dapat melaksanakan pembinaan Olimpiade Sains Nasional bidang Matematika bagi siswa di sekolah masing-masing. Metode yang digunakan dalam kegiatan ini adalah ceramah, diskusi, dan latihan mandiri. Kegiatan dilaksanakan selama dua hari, yaitu hari pertama yang berlangsung secara offline di sekretariat MGMP Matematika SMA HST dan hari kedua yang berlangsung secara online. Hasil evaluasi kegiatan melalui pree-test dan post-test menunjukkan adanya peningkatan signifikan dari pengetahuan dan kemampuan peserta, dengan rata-rata nilai hasil test dari peserta meningkat sebesar 41 poin pada post-test dibandingkan pada pree-test. Maksimum perubahan nilai dari pree test ke post-test adalah 90 poin, sedangkan minimum perubahan nilai dari pree test ke post-test adalah 5 poin. Melalui survey di akhir kegiatan, peserta menyampaikan harapan agar kegiatan pengabdian ini dapat berlanjut, diadakan secara berkala, dan dilaksanakan full offline.The National Science Olympiad in Mathematics at the Senior High School level is a prestigious competition for high school students throughout Indonesia who require strategies and techniques for solving questions that tend to be non-standard, in-depth understanding of concepts and creative ideas. Through the PDWM ULM 2022 program, a team of lecturers from the Program Studi Matematika FMIPA ULM as implementers and the association of MGMP Matematika SMA in Hulu Sungai Tengah Regency as partners collaborated in organizing training for the National Science Olympiad in Mathematics for members of the association. This activity aims to increase knowledge and improve the members' ability so that they can coach the National Science Olympiad in Mathematics for students in their respective schools. The methods used in this activity are lectures, discussions, and independent exercises. The activity was carried out for two days, the first day, which took offline at the MGMP Matematika SMA secretariat, and the second day, which took online. The results of the evaluation of activities through the pre-test and post-test showed a significant increase in the knowledge and abilities of the participants, with the average test score of the participants increasing by 41 points in the post-test compared to the pre-test. The maximum change in value from the pre-test to the post-test is 90 points, while the minimum change in value from the pre-test to the post-test is 5 points. Through a survey at the end of the activity, participants expressed their hope that this training could continue, be held regularly, and be carried out fully offline.

ANALISIS KESTABILAN DAN SOLUSI NUMERIK PADA MODEL SEIR UNTUK PENYAKIT TUBERKULOSIS Azkia Khairal Jamil; Yuni Yulida; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 1 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i1.6403

One of the infectious diseases that can be modelled into the SEIR model is Tuberculosis (TB), this is because TB has a bacterial incubation period, so it is at this time that a person enters the exposed subpopulation. TB is divided into two types, namely latent TB and active TB. This study aims to explain the formation of the SEIR Model for the Spread of Tuberculosis, determine the equilibrium point and Basic Reproductive Numbers on the SEIR Model for the Spread of Tuberculosis, analyze the stability of the SEIR Model for the spread of Tuberculosis at the equilibrium point, and make numerical simulations. The result of this research is the formation of a mathematical model on the spread of Tuberculosis, and from the model obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Then the basic reproduction number ( ) was found through the Next Generation Matrix. Furthermore, the stability analysis was carried out at the disease-free equilibrium point and it was found that the local asymptotic stable model with , while at the endemic equilibrium point it was found that the local asymptotic stable model with . Numerical simulations are presented to show numerical solutions and strengthen the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method with parameters that meet the stability requirements.

MODEL EPIDEMIK CAMPAK DENGAN ADANYA VAKSIN PADA POPULASI RENTAN DAN SUPPORT PADA POPULASI TEREKSPOSE Tri Puspa Lestari; Yuni Yulida; Aprida Siska Lestia
Jurnal Matematika Sains dan Teknologi Vol. 24 No. 1 (2023)
Publisher : LPPM Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/jmst.v24i1.4062.2023

Measles is a highly contagious disease and often occurs in children due to malnutrition, especially children with vitamin A deficiency and a weakened immune system. In addition to vaccination, the role of parents is needed in the form of support to control the development of the virus in the body. This measles disease can be modeled through a mathematical model, especially epidemic model. This study aims to explain the formation of a mathematical model of measles, determine the equilibrium point, basic reproduction number, stability analysis, and to perform numerical simulations on the model. The research procedure begins with construct a model using a system of nonlinear differential equations. The basic reproduction number can be determined using the next generation matrix method and analysis of model stability using the linearization method. While numerical simulation has been carried out using the fourth order Runge Kutta method. The result of this study is the formation of a mathematical model of measles with a population consisting of four compartments, namely Susceptible, Exposed, Infected and Recovered. Disease control is carried out in the model, namely vaccines in the Susceptible population and support measures in the Exposed population. From the model formed, two equilibrium points are obtained, namely the disease-free equilibrium point and the endemic equilibrium point. Furthermore, the basic reproduction number formula and analysis of the stability of the model at the disease-free equilibrium point and endemic equilibrium point are also obtained. Finally, a simulation model is presented to support stability analysis and comparison of solutions for the Infected population before being given control support and after being given control support with variations in vaccine percentages.

Pelatihan Olimpiade Sains Nasional Bidang Matematika pada Siswa SMAN 1 Bati-Bati Kabupaten Tanah Laut Provinsi Kalimantan Selatan Muhammad Ahsar Karim; Yuni Yulida; Faisal Faisal; Nor Hidayati; Alya Hanifah Arif; Audinta Sakti Firmansyah; Gusti Muhammad Rosyadi
Jurnal Abdimas Prakasa Dakara Vol. 3 No. 2 (2023): Pengembangan Pendidikan dan Keterampilan Masyarakat
Publisher : LPPM STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/japd.v3i2.1849

Salah satu bidang favorit di kompetisi Olimpiade Sains Nasional adalah bidang Matematika. Dalam kompetisi ini, siswa memerlukan pemahaman konsep yang mendalam dan ide kreatif terhadap soal-soal olimpiade yang dihadapi. Kegiatan ini bertujuan untuk meningkatkan kemampuan dan pemahaman siswa dalam menyelesaikan soal-soal olimpiade. Metode yang dilakukan berupa ceramah, diskusi, dan latihan mandiri. Penyampaian materi yang paling ditekankan adalah bagaimana memahami soal dan memberikan tips penyelesaian. Untuk mengukur kemampuan dan pemahaman siswa, diberikan soal-soal yang relevan dengan olimpiade. Soal tersebut berupa pretes dan postes merupakan soal yang sama dengan tujuan untuk melihat apakah ada pengaruh sesudah dilaksanakan pelatihan. Hasil evaluasi kegiatan ini dilakukan melalui hasil pretes dan postes yang diperoleh, dengan menggunakan uji Wilcoxon, yaitu ada berpengaruh pelatihan terhadap kemampuan dan pemahaman siswa dalam menyelesaikan soal-soal olimpiade. Dari 21 siswa, 17 siswa mengalami peningkatan dan 4 siswa memiliki nilai yang sama. Nilai minimum dan maksimum yang diperoleh pada saat pretes adalah 0 dan 40 poin, sedangkan saat postes adalah 20 dan 60. Rata-rata total peningkatan nilai sebesar 28.571. Selain itu, hasil evaluasi peserta terhadap seluruh rangkaian kegiatan pelatihan disimpulkan baik dan sangat baik.

ANALISIS KESTABILAN MODEL SI UNTUK PENYAKIT MENULAR DENGAN ADANYA TRANSMISI VERTIKAL DAN TINGKAT KEJADIAN JENUH Ana Rizki Mahmudah; Muhammad Ahsar Karim; Yuni Yulida
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 2 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i2.10826

The transmission of infectious diseases can occur through two pathways: horizontal and vertical. Horizontal transmission occurs through direct or indirect physical contact with the infectious agent, while vertical transmission takes place when an infected mother transmits the disease to a fetus or a newborn. Within the context of disease transmission models, a critical feature is the saturation incidence rate, which refers to the impact of interventions that can reduce the rate of disease transmission among susceptible and infected individuals. This research aims to elucidate the formation of a model, determine equilibrium points, and calculate the basic reproduction number using the Next Generation Matrix method. The analysis involves assessing local stability through linearization methods and global stability using Lyapunov functions. Sensitivity analysis is conducted on the basic reproduction number, and numerical simulations are performed using the fourth-order Runge-Kutta method. The research findings indicate the establishment of an SIS (Susceptible-Infected) model for infectious diseases with vertical transmission and saturation incidence. This model depicts the spread of the disease in a population, where individuals can exist in susceptible or infected conditions. Equilibrium points include a disease-free equilibrium that is locally and globally stable when the basic reproduction number is less than one, and an endemic equilibrium that is locally and globally stable when the basic reproduction number exceeds one. Sensitivity analysis reveals that each parameter has varying influences on the basic reproduction number. An increase in the saturation incidence rate leads to a decrease in the number of infected subpopulations, while an increase in the vertical transmission rate results in a similar decline. Numerical simulations support stability analyses at equilibrium points. These findings provide a deeper understanding of the factors influencing the spread of diseases within a population.

Co-Authors Aji Wiratama Akhmad Yusuf Alya Hanifah Arif Ana Rizki Mahmudah Andi Tri Wardana Annisa Rahayu Arie Wijaya Audinta Sakti Firmansyah Azkia Khairal Jamil Azkia Khairal Jamil Azkia Khairal Jamil Bizaini Bizaini DEWI ANGGRAINI Dewi Sri Susanti Edy Sarwo Agus Wibowo Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na'imah Firman Nurrobi Fitri Nor Annisa Fitriani Fitriani Friska Erlina Gabriel Henokh Gultom Gian Septiansyah Gian Septiansyah Gusti Muhammad Rosyadi Haidir Ahsana Helfa Oktafia Afisha Herlyn Basrina Lestia, Aprida Siska Miftahul Jannah Miftahul Jannah Muhammad Afief Balya Muhammad Ahsar Karim Muhammad Ahsar Karim Muhammad Ahsar Karim Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Mursyidah Pratiwi Mustika Khadijah Na'imah Hijriati Noor Fakhriani Nor Hidayati Nurul huda Pardi Affandi Rahayu, Annisa Rahmi Hidayati Raihan Nooriman Rezky Putri Rahayu Riska Fitria Riska Fitria Rizky Purnama Wulandari Sinar Ismaya Sofia Faridatun Nisa Thresye Thresye Tri Puspa Lestari Vika Astuti Wuri Setyana Sari Yogi Apriyanto

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