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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 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.

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

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

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

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

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.

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

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

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

APPLICATION OF THE EQUIVALENCE PRINCIPLE TO THE CALCULATION OF EDUCATION INSURANCE PREMIUMS FOR VILLAGE-OWNED ENTERPRISES (BUMDes) Widana, I Nyoman; Suciptawati, Ni Luh Putu; Sulma, Sulma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2555-2562

Program Education plays a vital role in improving human resources. But on the other hand, education costs are not cheap. For this reason, people need to prepare education funds from an early age. One way is to take part in an education insurance program. This is a business opportunity that a village-owned enterprise (BUMDes) can run by offering education insurance services to the public. This research aims to develop and use programming software to calculate education insurance premiums offered by BUMDes. The method used is The Equivalence Principle method. Based on the case study, the premium price calculated using software that has been developed is very competitive – below market price, depending on the interest rate and fees charged.

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