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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Jurnal Abdi Insani InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Fundamental Mathematics and Applications Journal of Mathematics and Applied Statistics
Muhammad Rifki Nisardi
Program Studi Ilmu Aktuaria FSAINS-UM Bulukumba
Agriculture, Biological Sciences & Forestry Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Environmental Science Health Professions Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics

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Fractional Mathematical Model of Covid-19 with Quarantine Muhammad Rifki Nisardi; Kasbawati Kasbawati; Khaeruddin Khaeruddin; Antonin Robinet; Khaled Chetehouna
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.23719

Abstract

This study aims to observe the dynamics of the spread of COVID-19 with the SIR-Model by considering the quarantine (Q) scheme. We also involve a fractional order in the model. Then the basic reproduction numbers were calculated using the generation matrix method, analyzed the local stability of the fractional model for each equilibrium point, and observed its relation to the basic reproduction numbers. We perform the sensitivity analysis to see the effect of parameters on changes in the basic reproduction numbers. We applied the Grunwald-Letnikov method for numerical simulations. Estimation for parameters was also carried out on the existing parameters in the model to obtain parameter values that could represent the actual conditions. Furthermore, with a fractional model, we approximated the model to the data of COVID-19 in West Sulawesi, Indonesia, so that we could obtain a fractional order since it could describe the data more accurately.Keywords: SIR-Q Model; COVID-19; basic reproduction number; Fractional Mathematical Model; Grunwald Letnikov Method. AbstrakPenelitian ini bertujuan untuk mengkaji dinamika penyebaran COVID-19 dengan model matematika orde fraksional penyebaran penyakit SIR-Q dengan mempertimbangkan skema karantina (Q) untuk mengendalikan penyebaran COVID-19. Bilangan reproduksi dasar dihitung menggunakan metode matriks generasi. Kemudian, dianalisa kestabilan lokal model fraksional untuk titik kesetimbangan dan lalu dianalisa kaitannya dengan bilangan reproduksi dasar. Analisis sensitivitas dilakukan untuk mengamati pengaruh parameter terhadap perubahan bilangan reproduksi dasar. Simulasi numerik dilakukan dengan menggunakan metode eksplisit Grunwald-Letnikov. Estimasi juga dilakukan terhadap parameter yang ada pada model untuk memperoleh nilai parameter yang merepresentasikan kondisi aktual penyebaran COVID-19 di Sulawesi Barat. Selanjutnya dengan model fraksional dilakukan pendekatan terhadap data kasus aktif COVID-19 di Sulawesi Barat sehingga diperoleh orde fraksional tertentu yang menghasilkan pendekatan nilai kasus aktif COVID-19 yang lebih akurat terhadap real data.Kata Kunci: Model SIR-Q; COVID-19; bilangan Reproduksi Dasar; Model Matematika Fraksional; Metode Grunwald-Letnikov.
Model Matematika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi Hukmah HUkmah; Muhammad Rifki Nisardi; Sulma Sulma; Suriani M
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 2 (2023): JANUARY 2023
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i2.22301

Abstract

Abstract We present a mathematical model of COVID-19 disease by modifying the SEIR model. The model considers two additional compartments, quarantine (Q) and vaccination (V) which aim to control the spread of COVID-19. Based on the model, we obtained a disease-free equilibrium point and an endemic equilibrium point. The basic reproduction numbers were calculated using the next-generation matrix method. In this model, we analyzed the stability conditions that must be satisfied by the defining parameters. We perform data on the spread of COVID-19 in Indonesia for estimation to provide the parameter value in the model. Based on the result, there is an influence of changes in several parameter values on the number of individuals infected with COVID-19.  
Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi: Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi Sulma Sulma; Muhammad Rifki Nisardi; Suriani Suriani; Hukmah Hukmah; Harianto Harianto; Dian Firmayasari
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 2 (2023): JANUARY 2023
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i2.23989

Abstract

Vaccination and quarantine are effective ways to control the spread of disease. Vaccination helps susceptible individuals to boost immunity. Additionally, quarantine helps reduce interactions which will reduce the infection rate. This study proposed the SEIR mathematical model to describe the dynamics of the spread of COVID-19 by providing control in the form of vaccination and quarantine. Based on Pontryagin's minimum principle, the optimal system for optimal control problems is derived and solved numerically using the Fourth Order Runge-Kutta scheme with the Forward-Backward Sweep approach. A numerical simulation of the optimal problem showed that the spread of disease is eradicated more quickly by vaccination and quarantine. Vaccination in large numbers is needed earlier if the rate of contact transmission is high enough. The provision of quarantine control is required from the beginning until no longer to be applied. A large proportion of quarantine at the beginning of time can suppress the spread of disease in the population.  
FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT Muhammad Rifki Nisardi; Kasbawati Kasbawati; Restu Ananda Putra
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 1 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i1.17174

Abstract

This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number. Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model.
Peramalan Produksi Telur Ayam dengan Metode Holt Double Exponential Smoothing Hukmah; Muhammad Rifki Nisardi; Sulma Sulma; Suriani M; Yusrini Yusrini
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 2 (2023): Matematika dan Pendidikan Matematika: Permasalahan dan Solusinya
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i2.2789

Abstract

Tingkat konsumsi telur ayam lebih tinggi diantara produk hewani lainnya. Bukan hanya sebagai lauk pauk, tetapi juga sebagai bahan pembuatan kue. Hal tersebut menunjukkan kebutuhan masyarakat terhadap produk hewani ini perlu diatur ketersediaanya. Salah satu cara adalah meramalkan produksi telur ayam pada beberapa periode berikutnya. Peramalan produksi telur dalam penelitian ini menggunakan metode Holt Double Exponential Smoothing. Hasil penelitian menunjukkan bahwa metode tersebut cukup efektif meramalkan produksi telur ayam dengan nilai MAPE sebesar 0,59%. Hasil peramalan menunjukkan bahwa produksi telur ayam untuk 12 minggu berikutnya akan mengalami penurunan produksi. Hal tersebut dipengaruhi oleh usia ternak yang produktivitasnya berkurang dengan pertambahan usia dan faktor lingkungan.
Analisis Teori Antrian Multi Channel Single Phase pada Pelayanan Teller PT Bank Negara Indonesia (Persero) Tbk Cabang Utama Bulukumba Ulfatun Hasanah; Dian Firmayasari S; Muhammad Rifki Nisardi; Harianto
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 2 (2023): Matematika dan Pendidikan Matematika: Permasalahan dan Solusinya
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i2.2932

Abstract

Antrian adalah kondisi ketika pelanggan mengalami waktu tunggu dalam pelayanan di tempat umum misalnya pada bank. Keadaan tersebut terjadi karena ketidakseimbangan antara fasilitas pelayanan dengan nasabah yang dilayani jumlahnya lebih banyak sehingga tingkat kesibukan Teller tinggi dan akhirnya terjadi antrian panjang pada bulan November tahun 2022. Tujuan dalam penelitian ini adalah untuk meminimumkan antrian panjang dengan model Multi Channel Single Phase di PT Bank Negara Indonesia Persero Tbk Cabang Utama Bulukumba. Hasil penelitian memperlihatkan bahwa antrian pada PT BNI Bulukumba tingkat kesibukan untuk 3 Teller sebesar 62% yang membuktikan kesibukan Teller tinggi dalam melayani nasabah. Oleh karena itu, perlu penambahan Teller untuk memininumkan antrian panjang namun tetap memperhatikan waktu mengganggur dari Teller tersebut. Jadi, jumlah Teller yang optimal dalam meminimukan antrian panjang yaitu 4 Teller dengan tingkat kesibukan sebesar 46%. Sementara saat penambahan menjadi 5 orang Teller diperoleh tingkat kesibukan sebesar 37% yang menunjukkan bahwa antrian tersebut kurang optimal karena waktu menganggur lebih banyak dibandingkan dengan jam kerja dari Teller
Calculation of Actuarial Values Using The Result of The 2019 Makeham Mortality Law Contruction and The Cox Ingersoll Ros Suriani M; Muhammad Rifki Nisardi; Nursamsi Nursamsi; Hukmah Hukmah; Sulma Sulma
Journal of Mathematics and Applied Statistics Vol. 1 No. 1 (2023): June 2023
Publisher : Yayasan Insan Literasi Cendekia (INLIC) Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Premium is an amount of money that must be paid by the customer at a certain time based on the insurance policy. This study aims to determine the value of whole life insurance premiums using the Makeham mortality law method and the Cox Ingersoll Ross (CIR) model. The result of the study obtained the calculation of interest rates using the CIR model, the smaller the  value, the greater discount and the premium paid using the Makeham mortality law method was Rp. 102.478 < premium <  Rp. 1.270.630 / Mounth.
PELATIHAN PENGGUNAAN APLIKASI GEOGEBRA UNTUK PENGEMBANGAN MEDIA PEMBELAJARAN MATEMATIKA BAGI GURU SMA DI KOTA PAREPARE Nurul Fuady Adhalia H; Zaitun Zaitun; Muh Rifki Nisardi; Aprizal Resky; Kusnaeni Kusnaeni; Hartina Husain; Rifaldy Atlant Tungga
Jurnal Abdi Insani Vol 11 No 1 (2024): Jurnal Abdi Insani
Publisher : Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/abdiinsani.v11i1.1299

Abstract

The The use of technology in the mathematics learning process by high school teachers in the city of Parepare is still lacking. Even though there are many learning media that can be utilized. The Geogebra application is a technological medium that has great potential in integrating mathematical concepts visually and interactively. The aim of implementing this PKM is to provide training to mathematics teachers who are members of MGMP Parepare to develop mathematics learning media at the high school level. The training method used is providing training assistance on the Geogebra application which consists of two stages. The preparation stages consist of observing, coordinating with partners, preparing the service implementation team and preparing the service implementation team regarding the training module. The implementation stages consist of giving a pre-test, providing an explanation regarding the Geogebra application, providing simulation assistance in making mathematics learning media using Geogebra, and providing a post-test. The results obtained from the training showed that 18 out of 20 people or around 90% of teachers were able to understand and apply the knowledge gained in training activities through a post-test given at the end of the activity. Thus, the implementation of the Geogebra Application training activities was considered successful because it had achieved the specified targets.
Co-Authors Antonin Robinet Aprizal Resky Dian Firmayasari Dian Firmayasari S Harianto Harianto Harianto Hukmah Hukmah Hukmah Hukmah Hukmah Hukmah HUkmah Kasbawati Kasbawati Kasbawati Kasbawati Khaeruddin Khaeruddin Khaled Chetehouna Kusnaeni Kusnaeni Nursamsi Nursamsi Nurul Fuady Adhalia H Restu Ananda Putra Rifaldy Atlant Tungga Sulma Sulma Sulma Sulma Suriani M Suriani M Suriani Suriani Ulfatun Hasanah Yusrini Yusrini Zaitun Zaitun