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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI BAREKENG: Jurnal Ilmu Matematika dan Terapan Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Journal of Fundamental Mathematics and Applications (JFMA) Journal of Mathematics and Applied Statistics Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M)
Sulma Sulma
Prodi Ilmu Aktuaria, Fakultas Saintek, Universitas Muhammadiyah Bulukumba
Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Library & Information Science Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment Sulma Sulma; Syamsuddin Toaha; Kasbawati Kasbawati
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 1 (2020): JMSK, SEPTEMBER, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/jmsk.v17i1.10031

Abstract

Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.
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.  
FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL Sulma, Sulma; Rasyid, Nur Ahniyanti; Widana, I Nyoman
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 2 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.20150

Abstract

Civil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely  per year or  per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of  per year or by  per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped.
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.
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.
Application of Exponential and Logistic Models in Estimating the Population of Bulukumba Regency in 2020-2030 Sulma, Sulma; Nursamsi, Nursamsi
Journal of Mathematics and Applied Statistics Vol. 1 No. 2 (2023): December 2023
Publisher : Yayasan Insan Literasi Cendekia (INLIC) Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35914/mathstat.v1i2.72

Abstract

Population data is useful as planning material in making various policies, including avoiding imbalances between the number of health facilities and services and the population in an area as well as other facilities such as schools, markets, and other public facilities. Ordinary differential equations of exponential and logistic models are used in modeling population dynamics in Bulukumba Regency to obtain population estimates until 2030. The determination of the future population of Bulukumba Regency is based on the growth rate and capacity obtained using the exponential and logistic approaches. The results obtained show that the estimation using the exponential model and the logistic model estimation for 2015-2019 are close to the data from the Central Bureau of Statistics. However, the logistic model is more accurate than the exponential model which is more significantly close to the data from BPS. So that the results of the logistic model are better than the exponential. The logistic model assumes that Bulukumba Regency has a capacity of K = 450000, while the exponential model assumes that the population increases exponentially.
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
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.
COMPARISON OF PROJECTED UNIT CREDIT AND ENTRY AGE NORMAL METHODS IN PENSION FUND VASICEK AND COX-INGERSOLL-ROSS MODELS Sulma, Sulma; Widana, I Nyoman; Toaha, Syamsuddin; Fitria, Ita
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/barekengvol17iss4pp2421-2432

Abstract

The pension program is one of the pension fund's efforts to anticipate the risks that will be experienced by participants in old age. Actuarial calculations help to determine the benefits that participants will receive by considering life chances, interest rates, age when becoming a participant, and normal retirement age. This study aims to determine normal contributions and actuarial liabilities with the Projected Unit Credit and Entry Age Normal methods using stochastic interest rates, namely Vasicek and Cox-Ingersoll-Ross (CIR). The data used in this study are civil servants who work at the Natural Resources Management Office, Bulukumba Regency. The results of the calculation analysis showed that normal cost using the Projected Unit Credit (PUC) method with the Vasicek and Cox-Ingersoll-Ross (CIR) model interest rates increased as the length of service increased, and at the end of the working period the Cox-Ingersoll-Ross (CIR) model interest rate reached Rp14.773.176,- which was higher than Vasicek by Rp3.849.898,-. The results of the calculation of normal cost using the Entry Age Normal (EAN) method with the Vasicek model increase in the period 0-20 years of service, then decrease towards the contribution value at the beginning of the service period of Rp1.499.725,-. At the beginning of the working year, the normal cost using the Entry Age Normal method with the Cox-Ingersoll-Ross (CIR) model interest rate is Rp7.581.593,- then decreases for 24 years of service to Rp5.849.854,- after which it increases again towards the initial contribution value of the working year. The results of the calculation of actuarial liabilities show an increase as the length of service increases, for the Entry Age Normal (EAN) and Projected Unit Credit (PUC) methods with the Cox-Ingersoll-Ross (CIR) interest rate model at the end of the service period, it is found that both are the same value, namely Rp443.195.285,-. By using the Vasicek interest rate model for both methods, the same result is obtained at the end of the service period of Rp115.496.951,-. This shows that the actuarial liabilities for both methods used are affected by interest rates, and the Cox-Ingersoll-Ross (CIR) model is higher than Vasicek
Co-Authors Fitria, Ita Harianto Hukmah Hukmah Hukmah Hukmah Hukmah HUkmah Hukmah, Hukmah I Nyoman Widana Kasbawati Kasbawati M, Suriani M. Yogi Riyantama Isjoni Muhammad Rifki Nisardi Ni Luh Putu Suciptawati Nur Ahniyanti Rasyid Nursamsi, Nursamsi Nurul Azizah Subhan Khalifah Azis Suriani M Suriani M Suriani M Suriani Suriani Syamsuddin Toaha syamsuddin Toaha Yusrini, Yusrini