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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Square : Journal of Mathematics and Mathematics Education InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Fundamental Mathematics and Applications (JFMA) Journal of Mathematics and Applied Statistics Liquidity : Jurnal Ilmu Manajemen dan Bisnis Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M)
Muhammad Rifki Nisardi
Program Studi Ilmu Aktuaria FSAINS-UM Bulukumba
Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Library & Information Science Mathematics Social Sciences Other

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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 Nisardi, Muhammad Rifki; Kasbawati, Kasbawati; Putra, Restu Ananda
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; Nisardi, Muhammad Rifki; 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
Penentuan Portofolio Saham Optimal Menggunakan Metode Markowitz Sebagai Dasar Keputusan Investasi Nisardi, Muhammad Rifki; Husain, Hartina; Kusnaeni, Kusnaeni; Resky, Aprizal
Square : Journal of Mathematics and Mathematics Education Vol 6, No 1 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.1.20441

Abstract

A stock portfolio is a combination of two or more securities invested over a specific period and under certain conditions. This study analyzes the combination of stocks that can be formed into an optimal portfolio using the Markowitz method. The Markowitz method is employed to maximize returns and minimize the risks associated with a portfolio. This method uses a mathematical formulation that allows for adjustments based on risk tolerance levels and expected returns to achieve an optimal portfolio. The data used in this study comprises the monthly closing prices of stocks from five selected companies, namely ICBP, BBCA, TLKM, BBNI, and INCO, for the period from June 2019 to December 2022. The findings indicate a recommended portfolio with the lowest risk, known as the Minimum Variance Portfolio (MVP). The MVP comprises the following proportions: ICBP 36.10%, BBCA 36.28%, TLKM 17.84%, INCO 8.39%, and BBNI 1.39%. This combination of stock proportions yields an expected return of 8.58% and a portfolio risk of 21.52%.Keywords: Markowitz method, Minimum Variance Portfolio, Portfolio Optimization.
Sosialisasi dan Pelatihan Pengelolaan Keuangan Keluarga untuk Persiapan Pendidikan Anak Sejak Usia Dini Harianto; Nur Ahniyanti Rasyid; Dian Firmayasari S; Muhammad Rifki Nisardi; Hukmah; Sulma; Suriani M; Nurul Azizah; Subhan Khalifah Azis
Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat Vol. 3 No. 2 (2024): Volume 03 Nomor 02 (Oktober 2024)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jhp2m.v3i2.3848

Abstract

Abstrak. Pendidikan adalah salah satu aspek penting yang harus dipenuhi dalam kehidupan manusia. Kehadiran pendidikan diharapkan mampu menjadi sarana untuk mengembangkan potensi dan memperhalus budi pekerti seseorang serta bekal menghadapi tantangan dunia yang semakin berkembang pesat. Setiap orang tua memiliki tanggung jawab untuk memberikan jaminan pemenuhan kebutuhan anaknya, termasuk kebutuhan dari segi Pendidikan yang memadai. Faktanya, salah satu hal yang sering menjadi kendala bagi orang tua siswa adalah biaya pendidikan anak. Berdasarkan data, semakin tinggi jenjang Pendidikan di Indonesia maka semakin tinggi pula biaya yang akan dikeluarkan. Adanya kenaikan biaya Pendidikan sering kali menjadi penyebab orang tua tak mampu lagi membiayai sekolah anaknya, sehingga angka putus sekolah pada anak yang masih dalam usia sekolah menjadi lebih tinggi. Untuk mengatasi masalah tersebut, salah satu usaha yang dapat dilakukan adalah kegiatan pengabdian masyarakat dengan mensosialisasikan pentingnya mempersiapkan dana Pendidikan anak bagi orang tua di TK Fatimah dan SDIT Khadijah Bulukumba. Luaran yang akan dicapai dari kegiatan ini adalah memberikan informasi dan pelatihan singkat kepada orang tua siswa mengenai persiapan pendidikan anak.Kata Kunci: Pendidikan, Biaya Pendidikan Anak, Putus Sekolah
Calculation of Actuarial Values Using The Result of The 2019 Makeham Mortality Law Contruction and The Cox Ingersoll Ros M, Suriani; Nisardi, Muhammad Rifki; 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 | DOI: 10.35914/mathstat.v1i1.32

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.
A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening Amar, Muh Ikhsan; Nisardi, Muhammad Rifki; Nurahmad, Muhammad Fadhil
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.14.1.14-30.2025

Abstract

This study aims to examine the mathematical model of meningitis transmission as a deterministic model. The model includes five compartments: susceptible (S), carrier (C), infected (I), treatment (T), and recovered (R). We also consider vaccination and screening as interventions in disease transmission. In this work, we obtained two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next generation matrix is employed to compute the basic reproduction numbers ($R_0$). We also analyzed the sensitivity of parameters concerning $R_0$. If $R_0 < 1$, then the disease-free equilibrium point exists and is locally stable, whereas the endemic equilibrium point exists when $R_0 > 1$ and is locally stable if the Routh-Hurwitz criterion is satisfied. We use the Runge-Kutta 4th order method to confirm the stability properties of the equilibrium points and also show that vaccination and screening affect the transmission dynamics of Meningitis
Co-Authors Amar, Muh Ikhsan Antonin Robinet Dian Firmayasari Dian Firmayasari S Dian Firmayasari S Harianto Harianto Harianto Harianto Hukmah Hukmah Hukmah Hukmah Hukmah HUkmah Hukmah, Hukmah Husain, Hartina Kasbawati Kasbawati Khaeruddin Khaeruddin Khaeruddin Khaeruddin Khaled Chetehouna Kusnaeni Kusnaeni, Kusnaeni M, Suriani Nur Ahniyanti Rasyid Nurahmad, Muhammad Fadhil Nursamsi, Nursamsi Nurul Azizah Putra, Restu Ananda Resky, Aprizal Sri Wahyuni Nurzak Subhan Khalifah Azis Sulma Sulma Sulma Sulma, Sulma Suriani M Suriani M Suriani M Suriani Suriani Ulfatun Hasanah Yusrini, Yusrini