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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI PYTHAGORAS: Jurnal Program Studi Pendidikan Matematika Communication in Biomathematical Sciences Limits: Journal of Mathematics and Its Applications Jambura Journal of Mathematics Jurnal Matematika UNAND Contemporary Mathematics and Applications (ConMathA) Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Jambura Journal of Biomathematics (JJBM) Jurnal Diferensial Pattimura International Journal of Mathematics (PIJMath) Limits: Journal of Mathematics and Its Applications Indonesian Journal of Computational and Applied Mathematics
Rahmi, Emli
Universitas Negeri Gorontalo
Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Materials Science & Nanotechnology Mathematics Public Health Social Sciences

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Analisis Kestabilan Model Eko-Epidemiologi dengan Pemanenan Konstan pada Predator Nurhalis Hasan; Resmawan Resmawan; Emli Rahmi
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 2 (2020): JMSK, JANUARY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (841.889 KB) | DOI: 10.20956/jmsk.v16i2.7317

Abstract

Penelitian ini dilakukan untuk menganalisis kestabilan model eko-epidemiologi dengan pemanenan konstan terhadap predator. Populasi dalam model terbagi atas tiga populasi yaitu populasi prey rentan  populasi prey terinfeksi , dan populasi predator . Dikonstruksi model eko-epidemiologi dengan pemanenan konstan terhadap predator. Diperoleh dua titik kesetimbangan, yaitu titik kesetimbangan kepunahan populasi prey terinfeksi, dan titik kesetimbangan interior atau semua populasi ada. Eksistensi dari masing-masing titik kesetimbangan bergantung pada  atau akar-akar realnya masing-masing. Sebelum mencari kestabilan dari titik-titk kestimbangan, ditentukan terlebih dahulu matriks Jacobi. Kestabilan dari masing-masing titik diuraikan pada syarat kestabilannya masing-masing. Simulasi numerik dari titik kesetimbangan dilakukan agar terlihat lebih jelas kestabilan dari masing-masing titik kesetimbangan. Simulasi numerik dilakukan menggunakan metode Runge-Kutta orde 4 dan dibantu software Phyton 3.7.
The Influence of Additive Allee Effect and Periodic Harvesting to the Dynamics of Leslie-Gower Predator-Prey Model Hasan S. Panigoro; Emli Rahmi; Novianita Achmad; Sri Lestari Mahmud
Jambura Journal of Mathematics Vol 2, No 2: Juli 2020
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (504.111 KB) | DOI: 10.34312/jjom.v2i2.4566

Abstract

In this paper, the influence of additive Allee effect in prey and periodic harvesting in predator to the dynamics of the Leslie-Gower predator-prey model is proposed. We first simplify the model to the non-dimensional system by scaling the variable and transform the model into an autonomous system. If the effect Allee is weak, we have at most two equilibrium points, else if the Allee effect is strong, at most four equilibrium points may exist. Furthermore, the behavior of the system around equilibrium points is investigated. In the end, we give numerical simulations to support theoretical results.
The Dynamics of a Discrete Fractional-Order Logistic Growth Model with Infectious Disease Hasan S Panigoro; Emli Rahmi
Contemporary Mathematics and Applications (ConMathA) Vol. 3 No. 1 (2021)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v3i1.26938

Abstract

In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the origin point is always exists and unstable, the disease-free point is always exists and conditionally stable, and the endemic point is conditionally exists and stable. We also investigate the existence of forward, period-doubling, and Neimark-Sacker bifurcation. The numerical simulations are also presented to confirm the analytical results. We also show numerically the existence of period-3 solution which leads to the occurrence of chaotic behavior.
Bifurkasi Periode Ganda dan Neimark-Sacker pada Model Diskret Leslie-Gower dengan Fungsi Respon Ratio-Dependent Reza Mokodompit; Nurwan Nurwan; Emli Rahmi
Limits: Journal of Mathematics and Its Applications Vol 17, No 1 (2020)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v17i1.6809

Abstract

Dinamika model Leslie-Gower dengan fungsi respon ratio-dependent yang didiskretisasi menggunakan skema Euler maju adalah fokus utama pada artikel ini. Analisis diawali dengan mengidentifikasi eksistensi dari titik ekuilibrium dan kestabilan lokalnya. Diperoleh empat titik ekuilibrium yaitu titik kepunahan kedua populasi dan titik kepunahan predator yang selalu tidak stabil, dan titik kepunahan prey dan eksistensi kedua populasi yang stabil kondisional. Selanjutnya dipelajari eksistensi dari bifurkasi periode ganda dan Neimark-Sacker di sekitar titik eksistensi kedua populasi sebagai akibat perubahan parameter h (time-step). Dari hasil analisis ditemukan bahwa bifurkasi periode ganda terjadi setelah melewati h=h_a atau h=h_c dan bifurkasi Neimark-Sacker terjadi setelah melewati h=hb. Di akhir pembahasan, diberikan simulasi numerik yang mendukung hasil analisis sebelumnya.
Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator Siti Maisaroh; Resmawan Resmawan; Emli Rahmi
Jambura Journal of Biomathematics (JJBM) Volume 1, Issue 1: June 2020
Publisher : Department of Mathematics, State University of Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v1i1.5948

Abstract

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.
UNRAVELING THE IMPACT OF THE MEMORY, THE COMPETITION, AND THE LINEAR HARVESTING ON A LOTKA-VOLTERRA MODEL PANIGORO, HASAN S.; RAHMI, EMLI; SAVITRI, DIAN; BEAY, LAZARUS KALVEIN
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.13.4.257-269.2024

Abstract

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exist, non-negative, and bounded. Obeying Matignon condition, Lyapunov function, and generalized LaSalle invariance principle, the local and global stability are investigated. To complete the analytical results, some numerical simulations are given to show the occurrence of forward bifurcation and the impact of the memory index. All results state that three possible circumstances may occur namely the extinction of both populations, the prey-only population, and the co-existence of both populations.
UNRAVELING THE IMPACT OF THE MEMORY, THE COMPETITION, AND THE LINEAR HARVESTING ON A LOTKA-VOLTERRA MODEL PANIGORO, HASAN S.; RAHMI, EMLI; SAVITRI, DIAN; BEAY, LAZARUS KALVEIN
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.13.4.257-269.2024

Abstract

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exist, non-negative, and bounded. Obeying Matignon condition, Lyapunov function, and generalized LaSalle invariance principle, the local and global stability are investigated. To complete the analytical results, some numerical simulations are given to show the occurrence of forward bifurcation and the impact of the memory index. All results state that three possible circumstances may occur namely the extinction of both populations, the prey-only population, and the co-existence of both populations.
Analysis of Optimal Portfolio Formation Using Multi-Objective Optimization Method and Nadir Compromise Programming Aliwu, Randa Resvitasari; Rahmi, Emli; Nuha, Agusyarif Rezka; Yahya, Lailany; Wungguli, Djihad; Arsal, Armayani
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.29065

Abstract

A portfolio is a collection of financial assets in the stocks owned by a company or individual. An optimal portfolio is a selected portfolio that aligns with the investor's preferences, drawn from a set of efficient portfolios that have been formed. This research aims to create an optimal portfolio using the Multi-Objective Optimization method and the Nadir Compromise Programming (NCP) method. Additionally, Value at Risk (VaR) analysis is applied to determine the maximum risk an investor will bear for the portfolio. The data used consists of closing stock prices on the IDX30 Index from February 2022 to July 2023. The findings indicate that the optimization approach produces portfolios that align with investor risk-return preferences. The comparison of Multi-Objective Optimization and NCP methods provides insights into their effectiveness in portfolio selection. Furthermore, the VaR analysis helps investors understand potential risk levels, offering a comprehensive perspective on portfolio performance.
MODEL GEOGRAPHICALLY WEIGHTED BIVARIATE GENERALIZED POISSON REGRESSION DENGAN ADAPTIVE TRICUBE KERNEL Abdussamad, Trizaning Nursahbani; Rahmi, Emli
Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Vol. 6 No. 1 (2025): 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.v6i1.905

Abstract

The Maternal Mortality Rate (MMR) and Neonatal Mortality Rate (NMR) are significant public health concerns in Indonesia. The elevated Maternal Mortality Rate (MMR) and Neonatal Mortality Rate (NMR) adversely affect the quality of life within the community, particularly for mothers and children. Mitigating maternal mortality rates (MMR) and neonatal mortality rates (NMR) has emerged as a priority to fulfil the Sustainable Development Goals and enhance the quality of healthcare services. Despite a reduction, the maternal mortality rate (MMR) and neonatal mortality rate (NMR) in Indonesia remain substantial, necessitating expedited efforts to achieve the 2024 objectives. Maternal and neonatal mortality are interconnected, as the mother's health status influences the infant's health status. This research used the Geographically Weighted Bivariate Generalised Poisson Regression (GWBGPR) model utilising Adaptive Bisquare and Adaptive Tricube Kernel weights to analyse maternal and neonatal mortality rates. The estimate of the GWBGPR model parameters use Maximum Likelihood estimate (MLE) with the Newton-Raphson iterative approach, alongside hypothesis testing via Maximum Likelihood Ratio Test (MLRT). This study's sample population comprises data on maternal and newborn death rates and their contributing factors throughout 34 provinces in Indonesia for the year 2022, sourced from the Profile of the Ministry of Health of the Republic of Indonesia. The analysis indicates that the GWBGPR model utilising the Adaptive Tricube Kernel is the most effective model, evidenced by the lowest AIC value. The primary independent variables influencing maternal and newborn mortality rates are the percentage of K4 prenatal care visits (X1) and the percentage of mothers getting Fe3 pills (X2).
Density based spatial clustering of application with noise using flower pollination algorithm for leptospirosis clustering Karim, Finansiya S. Abd.; Rahmi, Emli; Abdussamad, Siti Nurmardia; Hasan, Isran K.; Yahya, Nisky Imansyah
PYTHAGORAS : Jurnal Program Studi Pendidikan Matematika Vol 14, No 1 (2025): PYTHAGORAS: Jurnal Program Studi Pendidikan Matematika
Publisher : UNIVERSITAS RIAU KEPULAUAN, BATAM, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33373/pyth.v14i1.7505

Abstract

Leptospirosis is an important health problem in Indonesia, with most cases found in East Java and Central Java provinces. This study aims to identify the distribution pattern of leptospirosis in the two provinces using a clustering approach. The Density-Based Spatial Clustering of Applications with Noise (DBSCAN) method is used to cluster areas based on leptospirosis spread factors, but DBSCAN requires optimal parameter determination for accurate results. Therefore, this research implements Flower Pollination Algorithm (FPA) to optimize the epsilon (ϵ) and minimum points (MinPts) parameters in DBSCAN. This research uses secondary data obtained from data on the Number of Natural Disaster Events by Regency / City in East Java and Central Java Provinces in 2023 and data on Population Density by Regency / City in East Java and Central Java Provinces in 2023. The population in this study uses all observations, namely all people in the districts and cities in East Java and Central Java. The sampling technique is saturated sampling, that is, the entire population in the study is sampled. The clustering results using FPA-DBSCAN resulted in two main clusters, with 30 districts/municipalities detected as noise, 23 districts/municipalities belonging to cluster 0, and 20 districts/municipalities in cluster 1. The validation test using Silhouette Coefficient showed a value of 0.1892, indicating that the clustering is quite valid. The results of this clustering can serve as a strategic reference for local governments in optimizing disease surveillance and targeted health interventions.
Co-Authors Abdussamad, Trizaning Nursahbani Agusyarif Rezka Nuha Ahaya, Sitty Oriza Sativa Putri Aliwu, Randa Resvitasari Armayani Arsal Beay, Lazarus Kalvein Biduli, Meiske DIAN SAVITRI Djihad Wungguli Gani, Friansyah Hasan S. Panigoro Hidayanti, Sri Amalia Ibrahim, Rusdianto Isran K Hasan Karim, Finansiya S. Abd. Kasim, Ranan La Ode Nashar Lailany Yahya Mahmud, Sri Lestari Nadiyyah, Ana NISKY IMANSYAH YAHYA Novianita Achmad Nurhalis Hasan Nurwan Nurwan Nurwan Nurwan, Nurwan Resmawan Resmawan Reza Mokodompit Reza Mokodompit Salmun K. Nasib Sidik, Amelia Tri Rahma Siti Maisaroh Siti Nurmardia Abdussamad