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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.
ESTIMASI PARAMETER MODEL LOGISTIK DAN RICHARDS PADA PRODUKSI PADI: STUDI KASUS KALIMANTAN SELATAN Yuni Yulida; Faisal Faisal; Muhammad Ahsar Karim; Abdul Hadi; Noorul Wakhdah; Tiara Amaliya
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
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.v19i2.16648

Abstract

Padi (Oryza sativa) merupakan komoditas pangan strategis di Indonesia karena beras menjadi sumber karbohidrat utama masyarakat dan berperan penting dalam menjaga ketahanan pangan nasional, termasuk di Kalimantan Selatan yang menjadi salah satu daerah produsen utama. Penelitian ini bertujuan mengestimasi parameter dan membandingkan kinerja model logistik dan Richards dalam memodelkan serta memproyeksikan produksi padi berdasarkan data historis dari Badan Pusat Statistik. Estimasi parameter dilakukan dengan metode nonlinear least squares, sedangkan akurasi model dievaluasi dengan Mean Absolute Percentage Error (MAPE). Hasil penelitian menunjukkan bahwa kedua model mampu merepresentasikan pola pertumbuhan sigmoidal produksi padi, dengan model Richards memberikan hasil yang lebih akurat (MAPE <15%) dibandingkan model logistik. Selain itu, analisis data luas panen mengindikasikan adanya penurunan signifikan sejak 2018, dengan kehilangan kumulatif sekitar 3,54 juta hektar pada periode 2003–2024 dan rata-rata penurunan tahunan sebesar 161 ribu hektar, yang diduga dipengaruhi alih fungsi lahan serta bencana banjir. Proyeksi skenario optimis menunjukkan adanya potensi peningkatan produksi, sedangkan skenario pesimis memperlihatkan kecenderungan stagnasi akibat keterbatasan lahan dan tekanan eksternal lainnya. Dengan demikian, model Richards dinilai lebih representatif dalam memproyeksikan produksi padi di Kalimantan Selatan, dan hasil penelitian ini dapat menjadi dasar dalam perumusan kebijakan perlindungan serta rehabilitasi lahan pertanian guna mendukung ketahanan pangan berkelanjutan.
ANALYZING COVID-19 DYNAMICS IN TWO NON-INTERACTING REGIONS THROUGH A STRUCTURED COMPARTMENTAL MODEL Muhammad Afief Balya; Dipo Aldila; Yuni Yulida; Sila Rizqina; Pardi Affandi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 1 (2025)
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.v19i1.15383

Abstract

COVID-19 is an infectious disease caused by the corona virus. Corona Virus or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a virus that attacks the respiratory system. This paper will discuss the effect of the absence of human mobility on the spread of COVID-19. The proposed model consists of ten compartments, including susceptible, exposed, infected (symptomatic and asymptomatic), and recovered individuals in both regions. The model construction in this paper is quite simple, namely it does not involve human mobility at all. This is important because by understanding the characteristics of COVID-19 in a closed population, the spread of COVID-19 locally can be anticipated. Both analytical and numerical approaches are used. The numerical study involves elasticity analysis to identify key influential parameters and autonomous simulations to observe the long-term behavior of the system.
NON-STANDARD SCHEME DISCRETIZATION (NSFD) FOR COMMENSALISM SYMBIOSIS MODEL WITH HARVESTING IN COMMENSAL POPULATIONS Nurmaini Puspitasari; Faisal Faisal; Yuni Yulida; Nur Wahidiyatil Jannah; Muhammad Afief Balya
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
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.v19i2.16551

Abstract

Dynamic analysis on the model of commensalism symbiosis with the discretized Michaelis-Menten cropping by using different schemes to non-standard finite difference (NSFD) is the main focus in this article. The analysis is started by searching the equilibrium points with their existence terms and local stability with their stability terms. In this article, there are four equilibrium points. The points are the extinction point of both populations, the host extinction point, the commensal extinction point, and the point where both populations can coexist (the coexistence equilibrium point). The existence of a host extinction point and a point at which both populations can coexist depends on the conditions of existence that must be met. Among the four equilibrium points, the commensal extinction point and the coexistence equilibrium point are locally asymptotically stable provided that the specified stability conditions are met. In the final analysis, numerical simulations were performed using the 4th order Runge–Kutta scheme for the continuous model and the NSFD scheme for the discrete model. The results show that the NSFD scheme offers greater flexibility in choosing the integration time step to ensure convergence to a feasible solution, outperforming the 4th order Runge–Kutta scheme in this respect.
Co-Authors Abdul Hadi 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 Sri Susanti Dipo Aldila Edy Sarwo Agus Wibowo Faisal Faisal Faisal Faisal Faisal Faisal Faisal Faisal Farohatin Na&#039;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 Hermei Lissa Hijriati, Naimah Lestia, Aprida Siska Miftahul Jannah Miftahul Jannah Muhammad Afief Balya Muhammad Afief Balya Muhammad Ahsar Karim Muhammad Mahfuzh Shiddiq Muhammad Mahfuzh Shiddiq Munaira, Hanna Mursyidah Pratiwi Mustika Khadijah Noor Fakhriani Noorul Wakhdah Nur Wahidiyatil Jannah Nurmaini Puspitasari 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 Sila Rizqina Sinar Ismaya Sofia Faridatun Nisa Thresye Thresye Tiara Amaliya Tri Puspa Lestari Vika Astuti Wiranto, Agung Setyo Wuri Setyana Sari Yogi Apriyanto