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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Matematika UNAND Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Warta Pengabdian Andalas: Jurnal Ilmiah Pengembangan Dan Penerapan Ipteks
Arrival Rince Putri
Universitas Andalas
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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MATHEMATICAL MODELING AND CORRUPTION-FREE FIXED-POINT STABILITY OF CORRUPTION DYNAMIC WITH CONTROL STRATEGY Hanan, Hafizhah Atrya; Putri, Arrival Rince; Muhafzan, Muhafzan
Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Vol. 5 No. 2 (2024): Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistik
Publisher : LPPM Universitas Bina Bangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46306/lb.v5i2.707

Abstract

The given work presents a Susceptible Corrupt Jailed Reformed (SCJR) model on corruption spread with a control strategy: encouragement of punishment (in the form of law enforcement). In this mathematical model, it is assumed that corruption spreads like an infectious disease because corrupt individuals can influence susceptible individuals if they interact frequently. This model also assumes that corruption can occur due to personal desires without influence from other individuals. The study shows that the corruption-free fixed point stability depends on the basic reproduction number. The corruption-free fixed point is asymptotically stable if R0<1. The numerical simulations of the corruption-free fixed point and the difference between the model with and without the control strategy are given to demonstrate the validity of the theoretical analysis using Maple software. software Maple
ANALISIS PERILAKU MODEL SIR TANPA DAN DENGAN VAKSINASI Pertiwi, Julia Indah; Putri, Arrival Rince; Efendi, Efendi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 2 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (940.805 KB) | DOI: 10.30598/barekengvol14iss2pp217-226

Abstract

Vaccination is one of the methods to control and prevent the spread of infectious diseases. SIR model (susceptible, infected, recovered) without and with vaccination were developed. The behavior of the solutions of the two models is analyzed through stability analysis around the equilibrium points. The stability is also associated with a threshold number indicating the population is free or infected. Analytical results are confirmed with numerical results that are presented on the graphic solution and phase portrait. The results of numerical simulations conclude that vaccination is more effective for inhibiting the transmission of the disease than without vaccination
DYNAMICS OF THE RUMOR SPREADING MODEL OF INDONESIA TWITTER CASE Putri, Arrival Rince; Saidah, Muthiah As; Syafwan, Mahdhivan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (456.253 KB) | DOI: 10.30598/barekengvol16iss2pp625-634

Abstract

The study of the spreading of a rumor is significantly important to obtain scientific information and better strategies in reducing its negative impact. Twitter has become a medium for spreading rumors or hoaxes spatially and chronologically because it has a unique community structure. This study demonstrates the model of spreading rumors by considering credibility, correlation, and mass classification based on personality is discussed. The behavior of a model solution around equilibrium points is investigated with the Jacobian matrices. The stability also corresponds to a threshold number indicating the rumor fades away or continues to spread in the population. The analytical results are confirmed by actual data from Twitter in Indonesia with #SahkanRUUPKS. The simulation results show that the free rumor equilibrium point is stable and the threshold number is less than 1. Our study shows that the number of spreaders does not increase and the #SahkanRUUPKS rumor will vanish.
A FRACTIONAL DIFFERENTIAL EQUATION MODEL FOR THE SPREAD OF POTATO LEAF ROLL VIRUS (PLRV) ON POTATOES Jasmine, Prisca; Putri, Arrival Rince; Efendi, Efendi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2213-2224

Abstract

Potatoes infected with the PLRV virus will experience a decrease in production up to 90%. In this paper, The PLRV distribution fractional differential equation model with potato and vector populations is reformulated by adding one new parameter, namely the rate of vector death due to predators. The model is divided into susceptible and infected classes. The PLRV dispersion model was developed and converted to a fractional order form for 0<σ ≤ 1. Next, the invariant region, positive solutions, basic reproduction number, equilibrium point, and stability were determined. Based on the stability analysis, it is shown that the stability of the disease-free equilibrium point is locally stable and globally stable if the basic reproduction number (R0)<1, and the stability of the endemic equilibrium point is globally stable if the basic reproduction number (R0)>1. Numerical solutions were also carried out to determine the effect of several parameters on the PLRV distribution model on potatoes. The numerical solution results show that the elimination rate of infected potatoes and the infection rate of potatoes have a significant role in controlling the spread of PLRV in potatoes.
Stability Analysis and Traveling Wave Solutions of the Dynamic Model of Bird Flu Transmission in Poultry–Human Interaction Dilla, Rahma; Putri, Arrival Rince; Alfiany, Noverina; Syafwan, Mahdhivan
Jurnal Matematika UNAND Vol. 14 No. 4 (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.14.4.355-365.2025

Abstract

This study analyzes the stability of a mathematical model of avian influenza virus spread in poultry-human interaction population. The analysis was conducted to see the dynamics of the spread of avian influenza virus. From the model, the equilibrium points and basic reproduction numbers associated with the stability of the system are obtained. The results obtained show that stability depends on the basic reproduction number. Numerical simulations were carried out using Maple and gave the result that the infection rate is low and the system reaches a stable state where the infection does not disappear but does not spread significantly.
Mathematical Analysis of Sexual Violence Dynamics with Recidivist Perpetrators Zakiyyah, Abqorry; Bahri, Susila; Putri, Arrival Rince
Jurnal Matematika UNAND Vol. 14 No. 4 (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.14.4.411-423.2025

Abstract

Sexual violence remains a serious social issue with far-reaching consequences for both victims and society at large. To capture the dynamics of its spread, this study develops a compartmental mathematical model that divides the population into four subgroups: susceptible individuals ($S$), perpetrators ($V$), punished offenders ($P$), and rehabilitated individuals ($R$). The model incorporates a recidivist parameter, representing the tendency of punished individuals to relapse into offending, that is return from the $P$ to the $V$ class. The analysis includes the determination of equilibrium points, computation of the basic reproduction number using the Next Generation Matrix approach, and assessment of local stability through eigenvalue evaluation of the Jacobian matrix. The results indicate that both equilibrium points are asymptotically stable under certain condition. In addition, the presence of recidivist perpetrators increases the basic reproduction number, thereby amplifying the likelihood of sustained sexual violence within the population. In particular, the relapse rate is shown to play a critical role in destabilizing the violence-free equilibrium, underscoring the importance of addressing recidivism in prevention and intervention strategies. These findings provide new insights into the mathematical modeling of sexual violence and highlight the necessity of targeted policies to mitigate its persistence.
Co-Authors Admi Nazra AGUNG ALVIAN NOOR Alfiany, Noverina Asdi, Yudiantri Bahri, Susila Baqi, Ahmad Iqbal Berliani Nasran Budi Rudianto Budi Rudianto Devianto, Dodi Dilla, Rahma Efendi Efendi Efendi Efendi Hanan, Hafizhah Atrya Haripamyu Haripamyu HAZISYAH HAZISYAH Hazmira Yozza Helmi, Monika Rianti Ikhlas Pratama Sandi Izzati Rahmi HG Jasmine, Prisca Jenizon Jenizon Kintan Febri Cania Maiyastri, Maiyastri Mawanda Almuhayar Muhafzan Muhafzan NANDA MUTIA UTAMA Narwen Narwen Nova Noliza Bakar Noverina Alfiany Pertiwi, Julia Indah Radhiatul Husna Riri Lestari Saidah, Muthiah As Syafwan, Mahdhivan Visca Amelia S Yanita Yanita Yanuar, Ferra Yolanda Putri Zakiyyah, Abqorry Zulakmal, Zulakmal