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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Journal of Mathematics and Applied Statistics
Hukmah, Hukmah
Program Studi Ilmu Aktuaria FSAINS-UM Bulukumba
Mathematics

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Dynamics of Intra-guild Predation Model with Stage Structure in Prey Hukmah Hukmah; Syamsuddin Toaha; Jeffry Kusuma
Jurnal Matematika, Statistika dan Komputasi Vol. 18 No. 1 (2021): September 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v18i1.14362

Abstract

The Intra-guild predation model is an interaction between three species where two of them compete and prey on each other for the same resource. This study considers the stage structure of prey on and combines Beddington-DeAngelis and Holling type I as functional responses in the model. Furthermore, the equilibrium point and stability of the model will be analyzed. The numerical result at the equilibrium point shows that the solution converging toward the equilibrium point so that the population is stable and will not become extinct with increasing time. In addition, the population tends to be stable when the density of prey is larger than the predator.
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.  
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.
Co-Authors Jeffry Kusuma M, Suriani M. Yogi Riyantama Isjoni Muhammad Rifki Nisardi Nursamsi, Nursamsi Sulma Sulma Suriani M Suriani Suriani Syamsuddin Toaha