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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Jurnal Fisika FLUX Jurnal Matematika Sains dan Teknologi Desimal: Jurnal Matematika 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
Agriculture, Biological Sciences & Forestry 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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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

Abstract

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. 
Pelatihan Olimpiade Sains Nasional Bidang Matematika pada Siswa SMAN 1 Bati-Bati Kabupaten Tanah Laut Provinsi Kalimantan Selatan Karim, Muhammad Ahsar; Yulida, Yuni; Faisal, Faisal; Hidayati, Nor; Arif, Alya Hanifah; Firmansyah, Audinta Sakti; Rosyadi, Gusti Muhammad
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

Abstract

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 SENSITIVITAS MODEL EPIDEMI SIR DAN SVIR PADA PENYAKIT MENULAR Munaira, Hanna; Yulida, Yuni; Karim, Muhammad Ahsar
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
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.v18i1.12139

Abstract

Penyakit menular merupakan penyakit yang disebabkan oleh mikroorganisme patogen seperti bakteri, virus, parasit, atau jamur. Penyakit ini dapat menyebar, baik secara langsung maupun tidak, dari satu individu ke individu lainnya. Penyebaran penyakit menular dapat dimodelkan dengan pemodelan matematika epidemi Kermack-McKendrick. Penelitian ini bertujuan untuk menjelaskan pembentukan model matematika, menentukan titik ekuilibrium serta bilangan reproduksi dasar, dan menganalisis kestabilan lokal pada model matematika. Selain itu, dilakukan analisis sensitivitas terhadap bilangan reproduksi dasar dan simulasi numerik dengan metode Runge-Kutta orde 4. Dari penelitian ini, diperoleh bentuk model epidemi SIR (Susceptible, Infected, Recovered) dan modifikasi model tersebut menjadi model SVIR (Susceptible, Vaccinated, Infected, Recovered). Berdasarkan model yang terbentuk, diperoleh titik ekuilibrium bebas penyakit dan titik ekuilibrium endemik pada masing-masing model. Bilangan reproduksi dasar masing-masing model ditentukan dengan menggunakan metode Next Generation Matrix. Kemudian, dengan menggunakan nilai eigen dari matriks Jacobian, diketahui jenis kestabilan kedua model pada masing-masing titik ekuilibrium adalah stabil asimtotik lokal dengan syarat tertentu. Analisis sensitivitas menunjukkan parameter yang paling sensitif terhadap perubahan bilangan reproduksi dasar jika diurutkan dari yang terbesar untuk model SIR adalah laju penularan, laju kelahiran/kematian, dan laju kesembuhan. Sedangkan, untuk model SVIR adalah laju penularan, laju kelahiran/kematian, laju kesembuhan, dan proporsi populasi yang telah divaksinasi. Analisis-analisis ini juga diperkuat oleh hasil simulasi numerik.
Analysis of stability and bifurcation in logistics models with harvesting in the form of the holling type III functional response Yulida, Yuni; Nurrobi, Firman; Faisal, Faisal; Karim, Muhammad Ahsar
Desimal: Jurnal Matematika Vol. 5 No. 1 (2022): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v5i1.11828

Abstract

The logistic model can be applied in the field of biological studies to investigate population growth problems and some important aspects of the ecological situation. This model is a growth model with a limited population growth rate, and ecologists describe this rate as carrying capacity. Carrying capacity can be interpreted as the ideal population size, where individuals in the population can live properly in their environment. The growth rate of a population can be influenced by the harvesting factor, in this case, it is assumed that harvesting is not constant. The effect of the harvest on the growth rate can be analyzed mathematically by using the Holling type III functional response. In this paper, describe the formation of a logistic model taking into account the effects of harvesting, using the Holling type III functional response. Then,  perform a nondimensional process in the model, namely simplifying a model that has four parameters to a model that only has two parameters. Next, determine the equilibrium point of the model, perform a stability analysis at that equilibrium point, and investigate the possibility of bifurcation. As result, first obtained a logistic model which has two non-dimensional parameters, where one of the equilibrium points is zero and is unstable. Next, determine another equilibrium point through an implicit equation and investigate its stability through simulation. Finally, obtained two equilibrium points, which are fold bifurcation.
ANALISIS KESTABILAN MODEL SEIR UNTUK PENYEBARAN COVID-19 DENGAN PARAMETER VAKSINASI Jannah, Miftahul; Ahsar Karim, Muhammad; Yulida, Yuni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 3 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (532.856 KB) | DOI: 10.30598/barekengvol15iss3pp535-542

Abstract

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.
SACR EPIDEMIC MODEL FOR THE SPREAD OF HEPATITIS B DISEASE BY CONSIDERING VERTICAL TRANSMISSION Yulida, Yuni; Wiranto, Agung Setyo; Faisal, Faisal; Karim, Muhammad Ahsar; Soesanto, Oni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2491-2504

Abstract

Hepatitis B is an infectious disease that causes inflammation of the liver due to infection with the Hepatitis B virus. Hepatitis B is divided into two phases: the acute phase and the chronic phase. Hepatitis B virus (HBV) can be prevented through vaccination and treatment of susceptible and infected individuals. The spread of the virus can be modeled using mathematical modeling of epidemics. In this study, the model used consists of four classes, namely vulnerable individuals (S), acute individuals (A), chronic individuals (C), and recovered individuals (R). The purpose of this study is to explain the formation of the Hepatitis B disease epidemic model, analyze the stability of the model, perform simulations, and conduct parameter sensitivity analysis on the basic reproductive number. The result of this study is the construction of an epidemic model of the spread of hepatitis B disease in the form of a SACR model. This model takes into account the transmission that occurs not only through interactions between susceptible individuals and chronic individuals but also through the birth process, which occurs in chronic subpopulations because babies born can be chronically infected (vertical transmission from mother to baby). The model produces two equilibrium points, the disease-free equilibrium and the endemic equilibrium. Both points were analyzed for stability using the linearization method and were found to be asymptotically stable. Furthermore, the model simulation was carried out using the fourth-order Runge-Kutta method and sensitivity analysis of the basic reproduction number. From the results obtained, it can be concluded that the spread of hepatitis B disease can be minimized by reducing contact between susceptible and chronic individuals, increasing treatment of chronic individuals, and increasing the number of vaccinated individuals in susceptible populations.
Analisa Kestabilan dan Solusi Pendekatan Pada Persamaan Van der Pol Yulida, Yuni; Karim, Muhammad Ahsar
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 3, No 2 (2019): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2719.307 KB) | DOI: 10.31764/jtam.v3i2.1084

Abstract

Abstrak: Di dalam tulisan ini disajikan analisa kestabilan, diselidiki eksistensi dan kestabilan limit cycle, dan ditentukan solusi pendekatan dengan menggunakan metode multiple scale dari persamaan Van der Pol. Penelitian ini dilakukan dalam tiga tahapan metode. Pertama, menganalisa perilaku dinamik persamaan Van der Pol di sekitar ekuilibrium, meliputi transformasi persamaan ke sistem persamaan, analisa kestabilan persamaan melalui linearisasi, dan analisa kemungkinan terjadinya bifukasi pada persamaan. Kedua, membuktikan eksistensi dan kestabilan limit cycle dari persamaan Van der Pol dengan menggunakan teorema Lienard. Ketiga, menentukan solusi pendekatan dari persamaan Van der Pol dengan menggunakan metode multiple scale. Hasil penelitian adalah, berdasarkan variasi nilai parameter kekuatan redaman, daerah kestabilan dari persamaan Van der Pol terbagi menjadi tiga. Untuk parameter kekuatan redaman bernilai positif mengakibatkan ekuilibrium tidak stabil, dan sebaliknya, untuk parameter kekuatan redaman bernilai negatif mengakibatkan ekuilibrium stabil asimtotik, serta tanpa kekuatan redaman mengakibatkan ekuilibrium stabil. Pada kondisi tanpa kekuatan redaman, persamaan Van der Pol memiliki solusi periodik dan mengalami bifurkasi hopf. Selain itu, dengan menggunakan teorema Lienard dapat dibuktikan bahwa solusi periodik dari persamaan Van der Pol berupa limit cycle yang stabil. Pada akhirnya, dengan menggunakan metode multiple scale dan memberikan variasi nilai amplitudo awal dapat ditunjukkan bahwa solusi persamaan Van der Pol konvergen ke solusi periodik dengan periode dua. Abstract: In this paper, the stability analysis is given, the existence and stability of the limit cycle are investigated, and the approach solution is determined using the multiple scale method of the Van der Pol equation. This research was conducted in three stages of method. First, analyzing the dynamic behavior of the equation around the equilibrium, including the transformation of equations into a system of equations, analysis of the stability of equations through linearization, and analysis of the possibility of bifurcation of the equations. Second, the existence and stability of the limit cycle of the equation are proved using the Lienard theorem. Third, the approach solution of the Van der Pol equation is determined using the multiple scale method. Our results, based on variations in the values of the damping strength parameters, the stability region of the Van der Pol equation is divided into three types. For the positive value, it is resulting in unstable equilibrium, and contrary, for the negative value, it is resulting in asymptotic stable equilibrium, and without the damping force, it is resulting in stable equilibrium. In conditions without damping force, the Van der Pol equation has a periodic solution and has hopf bifurcation. In addition, by using the Lienard theorem, it is proven that the periodic solution is a stable limit cycle. Finally, by using the multiple scale method with varying the initial amplitude values, it is shown that the solution of the Van der Pol equation is converge to a periodic solution with a period of two.
INTEGRATING HOUSING ENVIRONMENTAL FACTORS INTO THE SEIR MODEL FOR PULMONARY TUBERCULOSIS TRANSMISSION: A CASE STUDY IN BANJAR, INDONESIA Yulida, Yuni; Suhartono, Eko; Anggraini, Dewi; Arifin, Syamsul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0711-0728

Abstract

Pulmonary Tuberculosis (TB) remains one of the serious public health issues in Indonesia, including in Banjar Regency. The transmission of TB is not only influenced by biological and behavioral factors but also highly depends on the characteristics of the living environment. This study aims to analyze the influence of physical environmental factors of housing on the incidence of pulmonary TB, and to integrate the analysis results into a modified SEIR model. The research was conducted using a cross-sectional observational approach involving 73 respondents from the working areas of Puskesmas Martapura 1 and Martapura 2. Data were collected through direct observation and interviews, and analyzed using binary logistic regression to identify significant variables. The significant variables were subsequently integrated into the transmission rate parameters in the SEIR model. The results show that ventilation area and room temperature have a significant impact on the incidence of pulmonary TB. Empirical findings show that the probability of pulmonary TB incidence is highest (86.68%) when both ventilation and temperature are below standard, and lowest (26.23%) when both meet the standards. Partial compliance still results in a high probability of incidence (around 60%). The SEIR model simulation with environmental scenarios shows that living conditions that do not meet ventilation area and temperature standards result in more aggressive TB transmission. Conversely, living conditions that meet both standards significantly reduce the number of infected individuals and increase the recovery rate. This research emphasizes the importance of environment-based interventions in a comprehensive TB control strategy.
Co-Authors Ahsar Karim, Muhammad Aji Wiratama Akhmad Yusuf Ana Rizki Mahmudah Andi Tri Wardana Annisa Rahayu Arie Wijaya Arif, Alya Hanifah Azkia Khairal Jamil Azkia Khairal Jamil Azkia Khairal Jamil Balya, Muhammad Afief Bizaini Bizaini Dewi Anggraini DEWI ANGGRAINI Dewi Sri Susanti Edy Sarwo Agus Wibowo Eko Suhartono Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na'imah Firman Nurrobi Firmansyah, Audinta Sakti Fitri Nor Annisa Fitriani Fitriani Friska Erlina Gabriel Henokh Gultom Gian Septiansyah Gian Septiansyah Haidir Ahsana Helfa Oktafia Afisha Herlyn Basrina Hijriati, Naimah Lestia, Aprida Siska Miftahul Jannah Miftahul Jannah Muhammad Ahsar Karim Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Munaira, Hanna Mursyidah Pratiwi Mustika Khadijah Noor Fakhriani Nurrobi, Firman Nurul huda Oni Soesanto Pardi Affandi Rahayu, Annisa Rahmi Hidayati Raihan Nooriman Rezky Putri Rahayu Riska Fitria Riska Fitria Rizky Purnama Wulandari Rosyadi, Gusti Muhammad Sinar Ismaya Sofia Faridatun Nisa Syamsul Arifin Thresye Thresye Tri Puspa Lestari Vika Astuti Wiranto, Agung Setyo Wuri Setyana Sari Yogi Apriyanto