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INDONESIA
Jurnal Matematika UNAND
Published by Universitas Andalas
ISSN : 2303291X     EISSN : 27219410     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Fokus dan Lingkup dari Jurnal Matematika FMIPA Unand meliputi topik-topik dalam Matematika sebagai berikut : Analisis dan Geometri Aljabar Matematika Terapan Matematika Kombinatorika Statistika dan Teori Peluang.
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Articles 858 Documents
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COMPARISON OF WEIGHT MATRIX IN HOTSPOT MODELING IN WEST KALIMANTAN USING THE GSTAR METHOD Pratiwi, Hesty; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Ayyash, Muhammad Yahya
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.31-45.2025

Abstract

This research aims to investigate the usefulness of the Generalized Space- Time Autoregressive (GSTAR) approach in predicting the number of fire hotspots in West Kalimantan Province. Specifically, the study compares the performance of the Queen contiguity method and the uniform weight matrix. Fires in the forests and on the land in West Kalimantan are severe problems that cause harm to the environment and other adverse effects. Data on fire hotspots were collected from four different regencies in West Kalimantan between January 2018 and March 2023 to provide the information used in this study. Compared to the uniform weight matrix, the study results reveal that the Queen contiguity weight matrix produces more accurate results. This is evidenced by the fact that the Root Mean Squared Error (RMSE) and Mean Absolute Deviation (MAD) values are lower in the Queen contiguity weight matrix. Based on these findings, more effective techniques for preventing forest and land fires are anticipated to be considered for planning purposes.
RAINFALL MODELLING IN EAST JAVA USING A MODIFIED ORNSTEIN-UHLENBECK MODEL Setyorini, Elisabeth Yeyen; Putri, Endah R. M.
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.46-61.2025

Abstract

One of the current global issues is climate change and weather variability. This phenomenon has real impacts on various regions, including East Java Province. East Java is experiencing increased rainfall intensity as one of the effects of climate change. High and continuous rainfall intensity can trigger disasters such as flooding, which has the potential to cause significant financial losses for the community. Therefore, effective risk management becomes crucial. One possible solution to address these risks is through the use of financial derivatives. The initial step in risk management involves modeling the behavior of rainfall. It is assumed that the rainfall pattern follows a mean-reverting process, specifically the Ornstein-Uhlenbeck process. The existing Ornstein-Uhlenbeck model is then modified to ensure that the resulting model accurately reflects the rainfall conditions in East Java. To validate the modified model, simulations of the Ornstein-Uhlenbeck process were conducted using estimated parameter values. The Ornstein-Uhlenbeck simulation achieved a minimum MSE score that approaches zero. This MSE score indicate that the proposed modified Ornstein-Uhlenbeck model is accurate in representing the rainfall patterns in East Java.
On Metric Dimension of Edge Comb Product of Symmetric Graphs Maryati, Tita Khalis; Sobiruddin, Dindin; Hadiputra, Fawwaz Fakhrurrozi
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.349-357.2024

Abstract

Consider a finite graph G that is simple, undirected, and connected. Let W be an ordered set of vertices with |W| = k. The representation of a vertex v is defined as an ordered k-tuple that consists of the distances from vertex v to each vertex in W. The set W is called a resolving set for G if the k-tuples for any two vertices in G are distinct. The metric dimension of G, denoted by dim(G), is the smallest possible size of such a set W. In this paper, we determine the metric dimension of edge comb product of trees with complete multipartites or petersen graphs.
CLUSTERING ANALYSIS OF PROVINCIAL IN INDONESIA BASED ON THE 2023 HUMAN DEVELOPMENT INDEX INDICATORS USING THE K-MEDOIDS ALGORITHM Sabrina, Syafa Marwa; Setiawan, Tabah Heri
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.93-102.2025

Abstract

Indonesia memiliki visi Indonesia Emas pada tahun 2045, namun pencapaian Indeks Pembangunan Manusia (IPM) dalam 20 tahun terakhir menunjukkan tantangan untuk mewujudkan visi tersebut. Penelitian ini menggunakan algoritma k-medoids untuk melakukan clustering provinsi di Indonesia berdasarkan indikator IPM tahun 2023. K-medoids dipilih karena keunggulannya dalam menangani outlier. Berdasarkan hasil perbandingan dengan metode k-means dan fuzzy c-means, metode k-medoids juga terbukti merupakan metode terbaik karena cluster yang terbentuk pada k-medoids terpisah dengan baik dan memiliki struktur yang kuat. Hasil penelitian menghasilkan tiga cluster: C1 memiliki anggota provinsi dengan IPM sangat tinggi, C2 memiliki anggota provinsi dengan IPM tinggi, sementara C3 memiliki anggota provinsi dengan IPM sedang. Analisis ini diharapkan menjadi bahan evaluasi dan referensi bagi pengembangan metode clustering.
ANALISIS KESTABILAN MODEL DINAMIKA PERCERAIAN MVQEDR Bahri, Susila; Hutagalung, Miya Qarlina; EFENDI, EFENDI; MUHAFZAN, MUHAFZAN
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.358-372.2024

Abstract

Tiga faktor penyebab perceraian, yaitu masalah ekonomi rumah tangga, perselisihan dan pertengkaran terus- menerus, dan kekerasan dalam rumah tangga, masih memberikan kontribusi besar terhadap angka perceraian di Indonesia. Meskipun pemerintah telah melakukan upaya penyuluhan bagi ketiga kelompok rumah tangga tersebut, namun pada kenyataannya kasus perceraian tidak kunjung berkurang. Oleh karena itu, perlu diketahui secara pasti seberapa besar pengaruh penyuluhan yang telah dilaksanakan oleh pemerintah terhadap kelompok ini. Pada penelitian ini, model matematika MVQEDR terlebih dahulu dibangun. Analisis kestabilan titik ekuilibrium model dilakukan dengan menentukan nilai eigen dan matriks Jacobian dan diperoleh bahwa titik ekuilibrium bebas perceraian stabil asimtotik jika R0 = 0, 003111368984 < 1 dan titik ekuilibrium endemik tidak stabil asimtotik jika R0 = 1, 065035325 > 1. Simulasi numerik dilakukan dengan menggunakan perangkat lunak MAPLE.
DYNAMICS OF THE LESLIE-GOWER PREDATOR-PREY MODEL WITH THE BEDDINGTON-DEANGELIS RESPONSE FUNCTION, INCLUDING THE PRESENCE OF INFECTED PREY AND THE FEAR FACTOR OF SUSCEPTIBLE PREY TOWARD PREDATORS Miswanto, Miswanto; Windarto, Windarto; Eridani, Eridani
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.373-387.2024

Abstract

This article presents a stability analysis of the Leslie-Gower predator-prey model that is extended by taking into account prey infection, the presence of prey fear factors towards predators and the Beddington-DeAngelis response function. The Leslie-Gower model is a classic model that describes the dynamics of predator and prey populations, while the Beddington-DeAngelis response function accommodates the effects of population density and more complex interactions between predators and prey. The infected prey factor describes the prey's resistance to predator attacks becoming weak, while the prey fear factor towards predators affects prey growth.This study combines the components of infection in the prey population and the prey fear factor into the model to reflect the dynamics of disease and fear factors that can affect model stability. The model studied uses the Beddington-DeAngelis response function which describes the interaction between the prey population and the predator. This study uses two methods, namely analytical methods and numerical simulations. Analytical methods to study the stability analysis of the equilibrium point of the model by exploring the conditions under which the equilibrium point of the model is stable or unstable, focusing on the influence of infection parameters and the Beddington-DeAngelis response function on the stability of the equilibrium point. The results of the analysis show that prey infection and the shape of the response function can significantly affect the stability of the Leslie-Gower predator-prey model. The last section of this article presents numerical simulations that illustrate the stability of the equilibrium point of the model
LOCATING CHROMATIC NUMBER OF ONE-HEART GRAPH Hamdi, Muhammad; Welyyanti, Des; Sandy, Ikhlas Pratama
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.85-92.2025

Abstract

Bilangan kromatik lokasi merupakan konsep dari dimensi partisi graf dengan pewarnaan titik graf. Bilangan kromatik lokasi dari G, dinotasikan dengan χL(G) adalah jumlah warna minimum yang dipakai untuk pewarnaan lokasi. Dalam Artikel ini dijelaskan cara menentukan bilangan kromatik lokasi graf sehati. Metode yang dipakai agar diperolehnya bilangan kromatik lokasi graf sehati adalah dengan memperoleh nilai eksaknya. Hasil yang didapatkan dari bilangan kromatik lokasi graf sehati adalah χL(Hr_n)=4 untuk n=2 dan χL(Hr_n)=5 untuk n≥3.
MODEL MATEMATIKA PENYEBARAN COMPULSIVE BUYING DISORDER PADA E-COMMERCE DENGAN ADANYA INFLUENCER Asih, Tri Sri Noor; Pertiwi, Diyah Esti Cahyo
Jurnal Matematika UNAND Vol. 14 No. 2 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.2.139-153.2025

Abstract

Kini masyarakat telah beralih menggunakan e-commerce untuk memenuhi kebutuhan hidup mereka melalui belanja online. Promosi influencer merupakan salah satu penyebab seseorang melakukan impulsive buying, yaitu pembelian yang tidak rasional dan terjadi secara spontan pada saat itu juga. Perilaku ini jika dilakukan secara berulang akan menimbulkan Compulsive Buying Disorder (CBD) atau yang biasa disebut sebagai kecanduan belanja. Adapun tujuan penelitian ini adalah membangun model matematika, menentukan titik kesetimbangan dan bilangan reproduksi dasar, menganalisis titik kestabilan titik kesetimbangan, serta melakukan simulasi numerik menggunakan Maple. Pada penelitian ini model dibagi menjadi lima populasi yaitu subpopulasi Potential, subpopulasi Medium Compulsive, subpopulasi Influencer, subpopulasi High Compulsive, dan subpopulasi Recovered. Dari hasil analisis kemudian diperoleh dua titik kesetimbangan yaitu titik kesetimbangan bebas CBD dan titik kesetimbangan terdapat CBD yang stabil asimtotik lokal. Berdasarkan hasil simulasi diketahui bahwa perubahan pada peluang influencer dalam mempengaruhi individu medium compulsive melakukan impulsive buying $(\theta)$ memberikan pengaruh signifikan terhadap nilai bilangan reproduksi dasar $(R_0)$ dan titik kesetimbangan yang diperoleh. Semakin tinggi nilai $\theta$ maka semakin cepat meningkat juga jumlah individu yang menderita CBD (high compulsive) dan semakin cepat menuju titik kesetimbangan pada waktu t.
Mathematical Model of COVID-19 with Aspects of Community Compliance to Health Protocols Gautama, I Putu Winada; Wijayakusuma, IGN Lanang; Swastika, Putu Veri; Dwipayana, I Made Eka
Jurnal Matematika UNAND Vol. 14 No. 2 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.2.154-166.2025

Abstract

COVID-19 infection is still a health problem in various countries. Some people who recover from COVID-19 still experience some symptoms. Therefore, it is essential to implement health protocols to minimize transmission of the COVID-19 virus. Based on this, a mathematical model of COVID-19 with aspects of community compliance with health protocols is presented. The population is divided into three subpopulations: the susceptible subpopulation, the exposed subpopulation, and the infected subpopulation. The basic reproduction number, $R_0$, determines whether there are disease-free and endemic equilibrium points. When $R_0$ is less than 1, the disease-free equilibrium is locally asymptotically stable. Conversely, when $R_0$ is greater than 1, the endemic equilibrium point is locally stable. Numerical simulations will demonstrate how COVID-19 spreads, taking into account community adherence to health guidelines. The results of numerical simulations indicate that an increase in public adherence to health protocols leads to a decrease in the number of COVID-19 infections.
OPTIMAL BLOOD GLUCOSE CONTROL IN TYPE 1 DIABETIC PATIENTS BY USING PONTRYAGIN’S MINIMUM PRINCIPLE AND EXTENDED KALMAN FILTER Sa'adah, Aminatus; Paramadini, Adanti Wido
Jurnal Matematika UNAND Vol. 14 No. 2 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.2.117-128.2025

Abstract

Artificial Pancreas (AP) is an advanced diabetes management technology. AP requires an automatic control algorithm to determine the level of insulin injection based on the glucose level calculated on the Continuous Glucose Monitoring (CGM) sensor. Bergman Minimal Model (BMM) is a basic model in describing the dynamics of glucose-insulin in the human body. This study aims to determine the optimal control using Pontryagin’s Minimum Principle (PMP), which is subject to reducing glucose levels in type 1 diabetes patients to be within the normal glucose level interval of 80-120 mg/dL. The BMM parameter values will be estimated using EKF to support the acquisition of precise and personal numerical simulations. Based on the control de sign simulation that has been obtained, the optimal control of insulin injection is given maximally (25 mU/L) during the first two hours of observation; then, the level decreases slowly until it reaches 0 at 12 hours of observation. This scenario successfully reduces the patient’s glucose levels at the end of the observation period from 170.4 mg/dL (with out control) to 121.2 mg/dL. This result providing a confident basis for initial future research and development in diabetes management.

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