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PENGGUNAAN MODEL EPIDEMI SIR (SUSCEPTIBLES-INFECTED-REMOVED) PADA PENYEBARAN PENYAKIT HIV/AIDS DI MAKASSAR Ridwan, Muhammad Rais; Fardinah, Fardinah
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 6 No 2 (2018)
Publisher : Universitas Islam Negeri Alauddin Makassar

Penelitian ini menggunakan data jumlah penduduk Kota Makassar dan jumlah individu yang terinfeksi penyakit HIV/AIDS mulai tahun 2014 s.d 2016 diperoleh model penyebaran penyakit HIV/AIDS dengan penggunaan model epidemi SIR dengan titik ekuilibrium (S,I)=(15625,14276795). Kemudian berdasarkan nilai eigen matriks Jacobi diperoleh titik (S,I) tersebut bersifat stabil asimtotik dengan nilai – nilai eigen -0,01 dan -91,4. Selanjutnya, diperoleh bilangan reproduksi dasar, yakni 91,471 yang menunjukkan bahwa satu individu yang terinfeksi, rata-rata dapat menularkan kepada 91 hingga 92 jiwa individu rentan terhadap penyakit HIV/AIDS. Dalam hal ini, penyakit tersebut di Kota Makassar akan bersifat endemik dalam kurun waktu 100 tahun ke depan. Hal ini dibuktikan dengan simulasi numerik menggunakan software Maple dan Matlab dengan melihat perilaku solusi penyelesaian S(t) dan I(t) untuk kurun waktu yang relatif lama.

Ensembel Fuzzy, Ensembel Rock Pada Pengelompokan Pelamar Bidikmisi Sejawa Timur Tahun 2017 Qadrini, Laila; Fardinah, Fardinah; Fatimah, Meryta Febrilian
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 8 No 1 (2020): Volume 8 Nomor 1
Publisher : Universitas Islam Negeri Alauddin Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24252/msa.v8i1.12939

Permasalahan yang sering ditemui dalam analisis pengelompokan adalah data yang berskala campuran numerik dan kategorik. Metode yang seringkali dilakukan untuk pengelompokan data berskala campuran adalah dengan mentransformasi data kategorik menjadi data numerik atau sebaliknya. Selain pengelompokan dengan metode transformasi tersebut, dikembangkan sebuah metode pengelompokan ensembel untuk data campuran. Pengelompokan ensembel adalah teknik pengelompokan untuk menggabungkan hasil pengelompokan beberapa algoritma pengelompokan dengan tujuan untuk mendapatkan hasil kelompok yang lebih baik, berdasarkan indeks validitas internal kelompok yaitu nilai SSW, Rata-rata koefisien Silhouette dan nilai Indeks Dunn yang dianalisis untuk 2,3 dan 4 Kelompok, diperoleh bahwa metode Ensembel Fuzzy lebih baik dan tepat digunakan pada data campuran yang ada pada penelitian ini daripada metode pengelompokan Ensembel ROCK.

Analisis Model Mangsa Pemangsa dengan Adanya Penyakit dan Pemanenan pada Pemangsa fardinah, Fardinah
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 1 (2023): Volume 6 Nomor 1 tahun 2023
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i1.2167

The interaction between two populations that are prey and predator can be described in a prey-predator model. In fact, in the interaction of prey and predators it can occur that when the density of prey is low, the effect of predation is also low, but if the size of the prey population increases, predation will be more intense which is stated in the Holling III Type response function model. In addition, it can also be found in an environment where there are populations of sick predator that result in death from the disease. This study aims to analyze the stability of the prey-predator model with the Holling III Type response function which consists of three subpopulations namely prey, healthy predator and sick predator. The analysis was carried out using the linearization method and then the type of stability was determined based on the characteristic eigenvalues obtained using the Routh-Hurwitz criteria. From this research it was found that population extinction is not possible while prey exists, extinction of diseased predator and populations exist is still possible if the required conditions are satisfy. Numerical simulations show that an increased harvesting rate in healthy predator populations results in a decrease in healthy predator populations, an increase in prey populations and a decrease in diseased predator populations. Meanwhile, a reduced harvesting rate for sick predator populations does not have a significant effect on the number of diseased predator populations, but results in an increase in the number of healthy predator populations and a decrease in prey populations

Pectin extraction from banana pere peel at various extraction times Musafira, Musafira; Fardinah, Fardinah; Fatimah, Meryta Febrilian; Dzulkifli, Dzulkifli; Mulyani, Andi Siti
Anjoro: International Journal of Agriculture and Business Vol 5 No 1 (2024): Anjoro
Publisher : Agribusiness Department, Agriculture and Forestry Faculty, Universitas Sulawesi Barat, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31605/anjoro.v5i1.3592

For many years, West Sulawesi's signature plant, banana pere, has only been eaten as fruit, while its peel is often discarded as waste or used as animal feed. This study provides information on the utilization of banana pere peel in order to increase its economic value through the utilization of pectin content contained in banana pere peel. This study aims to extract pectin from banana pere peel (Loka Pere) by using the citric acid solvent extraction method. The extraction process was carried out using 5 variations of time, namely 30, 60, 90, 120 and 150 minutes. The results showed that the use of extraction time for 90 minutes resulted in a yield value of 53.11%, moisture content of 1.15%, ash content of 1.56%, methoxyl content of 2.66% and galacturonic content of 30.88%.

Deteksi Formalin pada Makanan dengan Limbah Kulit Buah Naga di Majelis Taklim Permata Babul Maghfirah Majene Musafira, Musafira; Fardinah, Fardinah; Fatimah, Meryta Febrilian; Sikanna, Rismawati; Hikmah, Hikmah
Jurnal Abmas Negeri (JAGRI) Vol. 5 No. 2 (2024): Volume 5 Nomor 2 Desember 2024
Publisher : Sarana Ilmu Indonesia (salnesia)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36590/jagri.v5i2.1241

Berdasarkan survei, pengetahuan masyarakat tentang bahaya formalin dan cara mendeteksinya masih terbatas karena pengujian formalin biasanya memerlukan laboratorium. Untuk itu, pelatihan diberikan dengan memanfaatkan kulit buah naga sebagai bahan alami yang sederhana dan mudah diakses. Program pengabdian masyarakat ini bertujuan meningkatkan kemampuan ibu-ibu di Majelis Taklim Permata Babul Maghfirah, Majene, dalam mendeteksi kandungan formalin pada bahan pangan secara mandiri. Kegiatan ini meliputi beberapa tahapan: persiapan melalui komunikasi dengan mitra, pelaksanaan berupa penjelasan teknik deteksi formalin dan eksperimen langsung, serta monitoring dan evaluasi untuk mengukur keberhasilan pelatihan. Hasilnya menunjukkan peningkatan pemahaman dan keterampilan peserta hingga 80%. Peserta mampu melakukan metode deteksi sederhana secara mandiri dan mengidentifikasi bahan pangan yang dicurigai mengandung formalin. Kesimpulannya, pelatihan ini berhasil meningkatkan pengetahuan dan keterampilan praktis peserta dalam mendeteksi formalin menggunakan bahan alami. Metode sederhana ini terbukti efektif dan mudah diterapkan dalam kehidupan sehari-hari. Disarankan agar program serupa diperluas dengan memanfaatkan bahan alami lain untuk mendeteksi zat berbahaya serta melibatkan peserta yang lebih beragam, termasuk laki-laki dan generasi muda, guna meningkatkan kesadaran dan keterampilan masyarakat secara luas.

Tingkat Pengangguran Terbuka Periode Sebelum hingga Sesudah Pandemi Covid-19 dengan Pendekatan Non-Parametrik Mayapada, Retno; Fardinah, Fardinah
ESTIMATOR : Journal of Applied Statistics, Mathematics, and Data Science Vol. 2 No. 1 (2024)
Publisher : Program Studi Statistika Universitas PGRI Argopuro Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31537/estimator.v2i1.1829

The unemployment rate is one of the factors related to a country's economy. During the COVID-19 pandemic, there was a decline in economic growth in Indonesia which also had a negative impact on the labor market. The decreased mobility of people causes reduced economic activity and ultimately the number of poverty increases. This research compares the percentage of unemployment rates in Indonesia in the period before, during, and after the COVID-19 pandemic using a non-parametric approach because the data of unemployment rates in 2020 and 2021 are not normally distributed. The non-parametric tests used in this research are the Friedman test and the Nemenyi post-hoc test. Based on research conducted, it was found that there was a statistically significant difference (?=5%) between the percentage of unemployment rates during the COVID-19 pandemic and the period before and after the COVID-19 pandemic. Meanwhile, the difference between before and after COVID-19 occurred was not statistically significant (?=5%). However, the average unemployment rate in 2023 is the smallest that compared to previous years. This shows that the economy in Indonesia is slowly starting to improve after the COVID-19 pandemic.

Analisis Model Mangsa Pemangsa dengan Adanya Penyakit dan Pemanenan pada Pemangsa fardinah, Fardinah
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 1 (2023): Inovasi Teknologi, Psikologi Belajar, dan Adaptasi Pembelajaran Matematika di E
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i1.2167

The interaction between two populations that are prey and predator can be described in a prey-predator model. In fact, in the interaction of prey and predators it can occur that when the density of prey is low, the effect of predation is also low, but if the size of the prey population increases, predation will be more intense which is stated in the Holling III Type response function model. In addition, it can also be found in an environment where there are populations of sick predator that result in death from the disease. This study aims to analyze the stability of the prey-predator model with the Holling III Type response function which consists of three subpopulations namely prey, healthy predator and sick predator. The analysis was carried out using the linearization method and then the type of stability was determined based on the characteristic eigenvalues obtained using the Routh-Hurwitz criteria. From this research it was found that population extinction is not possible while prey exists, extinction of diseased predator and populations exist is still possible if the required conditions are satisfy. Numerical simulations show that an increased harvesting rate in healthy predator populations results in a decrease in healthy predator populations, an increase in prey populations and a decrease in diseased predator populations. Meanwhile, a reduced harvesting rate for sick predator populations does not have a significant effect on the number of diseased predator populations, but results in an increase in the number of healthy predator populations and a decrease in prey populations

DYNAMIC ANALYSIS OF PREDATOR-PREY MODEL WITH CANNIBALISM INTERVENTION AND DISEASE INFECTION IN PREY USING HOLLING TYPE II RESPONSE FUNCTION Fardinah, Fardinah; Hikmah, Hikmah; Abubakar, Rahmah; Qadrini, Laila; Haris, Haris; Salsabilah, Nadia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1945-1956

This study discusses the intervention of cannibalism and disease spread with Holling Type II response function in the predator-prey model. It is assumed that disease infection is limited to the prey population and cannot be cured so that in this model there are three subpopulations namely susceptible prey, infected prey and predators. In addition, there is cannibalism in the predator population. The objectives of this study include constructing a predator-prey model with cannibalism intervention and disease infection in prey using Holling Type II response function, identifying the stability of the equilibrium point of the model and interpreting the model based on simulation results. Analysis of the stability of the equilibrium point is carried out with a linearization approach and the Routh-Hurwitz criterion was used to determine equilibrium stability. Based on the stability analysis, 5 (five) equilibrium points are obtained, namely population extinction, susceptible prey exists, predator extinction, infected prey extinction and population exists where the population extinction equilibrium point is unstable and the other equilibrium points are stable with the certain conditions. From the simulation, it is obtained that the numerical results are in accordance with the analytical results of the stability analysis of the equilibrium point of the model and for infinite time, there will be no population extinction while the state of susceptible prey exists, predator extinction, infected prey extinction and population exists can occur if the stability conditions are met. Based on the numerical simulations, it was found that changes in the parameter values of the rate of change of susceptible prey to infected prey and the coefficient of predator cannibalism in day-1 can cause changes in the type of stability of the equilibrium point. Thus, rate of change susceptible prey to infected prey and the coefficient of predator cannibalism affects the population of prey and predator.

Analisis Clustering berdasarkan Faktor-Faktor Kemiskinan di Provinsi Sulawesi Selatan menggunakan Algoritma K-Medoids Saranty, Saranty; Hidayatullah, Muhammad; Fardinah, Fardinah
Technologica Vol. 4 No. 2 (2025): Technologica
Publisher : Green Engineering Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55043/technologica.v4i2.342

Penelitian ini fokus pada pengelompokan wilayah kabupaten/kota di Provinsi Sulawesi Selatan dengan mempertimbangkan karakteristik kemiskinan menggunakan teknik klasterisasi K-Medoids. Urgensi penelitian ini muncul dari kebutuhan untuk memahami pola kemiskinan yang berbeda di wilayah tersebut agar kebijakan pembangunan daerah dapat lebih terarah dan efektif. Sebanyak 24 kabupaten/kota dianalisis menggunakan sembilan indikator kemiskinan, yaitu indeks kedalaman kemiskinan, indeks keparahan kemiskinan, tingkat pengangguran terbuka, harapan hidup, Indeks Pembangunan Manusia (IPM), pengeluaran per kapita, rata-rata lama sekolah, Produk Domestik Regional Bruto (PDRB), dan kepadatan penduduk. Hasil evaluasi menggunakan tiga metrik validitas internal—Silhouette Coefficient, Dunn Index, dan Davies-Bouldin Index—menunjukkan bahwa konfigurasi dua cluster (k=2) lebih optimal dibandingkan tiga cluster (k=3). Pada Tahun 2019, dari 24 kabupaten/kota, 23 kabupaten/kota masuk ke dalam cluster 1 (wilayah tertinggal) yang ditandai dengan indeks kemiskinan dan keparahan tinggi serta IPM dan pengeluaran per kapita rendah, sedangkan 1 kabupaten/kota berada di cluster 2 (wilayah maju) dengan kondisi sebaliknya. Analisis tren dari 2019 sampai 2023 menunjukkan komposisi cluster tetap stabil dengan adanya pergeseran positif pada 2 kabupaten/kota dari cluster 1 ke cluster 2 pada 2023

Analisis Model Mangsa-Pemangsa dengan Fungsi Respon Holling Tipe II dan Adanya Infeksi Penyakit pada Mangsa fardinah, fardinah; Hikmah, Hikmah; Salsabila, Nadia
Jurnal Sains Matematika dan Statistika Vol 10, No 2 (2024): JSMS Juli 2024
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/jsms.v10i2.30041

This research discusses the predator-prey model with the Holling Type II response function and the presence of disease in the prey population. It is assumed that the disease infection only spreads within the prey population and cannot be cured so there are three subpopulations in the model, namely susceptible prey, infected prey and predators. This research aims to construct a prey-prey model with a Holling Type II response function and the presence of disease infection in the prey population, analyze the stability of the model equilibrium point and interpret the model. Analysis of the stability of the equilibrium point begins with the linearization method, and then the type of stability is determined based on the characteristics of the eigenvalues using the Routh-Hurwitz criterion. The results of this research obtained 5 (five) equilibrium points, namely population extinction, vulnerable prey existing, extinction of infected prey, extinction of predators and existing population. The results of the equilibrium point analysis show that all equilibrium points are stable if they fulfill the specified conditions. Based on the numerical simulations carried out, the interpretation was obtained that if the parameter values of the interaction rate of susceptible prey and infected prey as well as the rate of death due to disease were changed, this could cause a change in the stability of the equilibrium point.

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