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All Journal ACTA VETERINARIA INDONESIANA Jurnal Informatika JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA Journal of Mathematical and Fundamental Sciences Jurnal Penelitian Pendidikan IPA (JPPIPA) BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics InPrime: Indonesian Journal Of Pure And Applied Mathematics Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications International Journal of Disaster Management Jurnal Matematika Integratif MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
Hadi Sumarno
Departemen Matematika, Fakultas MIPA, Institut Pertanian Bogor, Jalan Meranti, Kampus IPB Dramaga 16680, Jawa Barat
Agriculture, Biological Sciences & Forestry Humanities Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation Veterinary

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Parametric Survival Model on IPB University’s Graduation Data Nashiruddin, Muhammad Abdurrasyid; Sumarno, Hadi; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 2 (2023): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i2.12681

Abstract

Graduation is one of the assessment criteria in the college accreditation process. Students who graduate on time will assist in the assessment of college accreditation. This study aims to determine the distribution that best fits student graduation data and determine the best model to analyze the factors that determine student graduation from IPB University. This study presents some parametric models in survival analysis, specifically, the accelerated failure time (AFT) model and the proportional hazard (PH) model. The objective of this research is to compare the performance of PH model and the AFT models in analyzing the significant factors affecting the student graduation at the IPB University. Based on the study's results, the distribution according to student graduation data is the Burr XII distribution, and the best model using the AIC criteria is the PH Burr XII model. The factors that influence the graduation of IPB University students are gender, faculty, GPA, regional origin, and school status. 
Stochastic Model of Pneumonia and Meningitis Co-infection Using Continuous Time Markov Chain Approach Praptaningsih, Anggun; Sumarno, Hadi; Sianturi, Paian
Jurnal Penelitian Pendidikan IPA Vol 9 No 12 (2023): December
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v9i12.6108

Abstract

Pneumonia disease is a lung infection caused by Streptococcus pneumoniae. Meningitis is an infection of the meninges and cerebrospinal fluid caused by Streptococcus pneumoniae. Both diseases may occur at the same time. A mathematical model is needed to represent the spread of pneumonia and meningitis co-infection. This study aims to build the stochastic model of pneumonia and meningitis co-infection with CTMC, determine the transition and outbreak probability, and conduct simulations to assess the effect of increasing the contact rate on pneumonia  and meningitis . Based on the computer simulation undertaken, it can be concluded that if  was decreased while was set to be fixed, the probability of disease outbreak decreased.  If was set to be fixed while  was decreased, the probability of disease outbreak decreased. However, the latter is smaller than the previous. Similarly, if  was increased while was set to be fixed, the probability of disease outbreak increased.  If was set to be fixed while  was increased, the probability of disease outbreak increased. However, the latter is smaller than the previous. Moreover, if both  and  were decreased, the probability of disease outbreak was equal to zero.
A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend Safitri, Nurul Indah; Mangku, I Wayan; Sumarno, Hadi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 4 No. 2 (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.v4i2.25104

Abstract

This article discusses the estimation for the expected value, also called the mean function, of a compound periodic Poisson process with a power function trend. The aims of our study are, first, to modify the existing estimator to produce a new estimator that is normally distributed, and, second, to determine the smallest observation interval size such that our proposed estimator is still normally distributed. Basically, we formulate the estimator using the moment method. We use Monte Carlo simulation to check the distribution of our new estimator. The result shows that a new estimator for the expected value of a compound periodic Poisson process with a power function trend is normally distributed and the simulation result shows that the distribution of the new estimator is already normally distributed at the length of 100 observation interval for a period of 1 unit. This interval is the smallest size of the observation interval. The Anderson-Darling test shows that when the period is getting larger, the p-value is also getting bigger. Therefore, the larger period requires a wider observation interval to ensure that the estimator still has a normal distribution.Keywords: moment method; normal distribution; Poisson process; the smallest observation interval. AbstrakPada artikel ini dibahas tentang pendugaan fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat. Tujuan penelitian kami adalah, pertama, memodifikasi penduga yang telah ada untuk menghasilkan penduga baru yang memiliki distribusi normal. Kedua, menentukan ukuran interval pengamatan terkecil sehingga penduga yang diusulkan masih berdistribusi normal. Pada dasarnya, penduga yang kami usulkan diformulasi menggunakan metode momen. Kami menggunakan metode simulasi Monte Carlo untuk memeriksa sebaran distribusinya. Hasil menunjukkan bahwa penduga yang baru untuk fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat memiliki distribusi normal. Hasil simulasi menunjukkan bahwa penduga baru telah berdistribusi normal pada panjang interval pengamatan 100 untuk periode sebesar 1 satuan. Interval pengamatan ini merupakan ukuran interval pengamatan terkecil. Selain itu, hasil uji Anderson-Darling menunjukkan bahwa ketika periode semakin besar maka p-value juga semakin besar. Oleh karena itu, periode yang lebih besar memerlukan interval pengamatan yang lebih panjang untuk menjamin penduga yang kami usulkan tetap berdistribusi normal.Kata Kunci: metode momen; distribusi normal; proses Poisson; interval pengamatan terkecil. 2020MSC: 62E17 
Sensitivity Analysis of SEIRS Model with Quarantine on the Spread of Covid-19 Hardianti, Wiwik Tri; Sumarno, Hadi; Sianturi, Paian
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 4 (2022): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i4.9627

Abstract

Since the Covid-19 pandemic, various mathematical models have been developed to describe its spread using the compartment model. The purpose of this research was to construct a new model of Covid-19. This formulated model is an application of SEIRS epidemic model by Zhang & Teng (2007) and a modification of the Covid-19 model by Chatterjee et al. (2020) by adding variations of quarantine. The model is analyzed by determining the disease-free fixed point and basic reproduction number 〖(R〗_0) through the next generation matrix method. The next step is to analyze the sensitivity to find out the parameters that have the most influence on the spread of Covid-19. The disease will not spread in the population if the value of R_0<1, while the disease will spread if the value of R_0>1. The result of the sensitivity analysis stated the parameters that can be controlled and have the most significant effect, respectively, are the transmission rate from symptomatic infected individuals (β_2 ),transmission rates from asymptomatic infected individuals (β_1 ), quarantine rates for symptomatic infected individuals (θ_3), and quarantine rates for asymptomatic infected individuals (θ_2). Parameters β_2 and β_1 have a negative index, while θ_3 and θ_2 have a negative index. It means decreasing the transmission rate from infected individuals and increasing the quarantine rate for infected individuals can decrease the spread of Covid-19. Therefore there will not be an outbreak in the long term. 
Co-Authors Abdur Rohman Ahmad Fajri Ahmad Fajri Ali Kusnanto Andri Hermawan Andri Hermawan, Andri Annisa, Mutia Ardana, N. K. Kutha Ardana, Ngakan Komang Kutha Benediktus Nugroho Adi Wiyoto Budi Suharjo Cherry Galatia Ballangan Dadang Jaenudin Dadang Rahmat Nugraha Dilla Afriansyah Dini Dessya Luthfiani Eliska, Nur Euis Sunarti Fatimatuzzahroh Fitri Nurjanah Hardianti, Wiwik Tri Hattamurrahman, Muhammad Putra Sani I Gusti Putu Purnaba I Wayan Mangku Intan Islamia Intan Islamia Jaharuddin Jaharuddin, Jaharuddin Jonathan Ryan Wilianto Luthfiani, Dini Dessya M Agus Setiadi Mutia Annisa N. K. Kutha Ardana Nashiruddin, Muhammad Abdurrasyid Niswah Yanfa Nabilah Syams Nugraha, Dadang Rahmat Nur Aziezah Nurul Indah Safitri Paian Sianturi Praptaningsih, Anggun Putri, Nurul Qorima Retno Budiarti Rismawati, Dillah Ruhiyat Ruhiyat Ruhiyat Safitri, Nurul Indah Sri Rahayu Taufik, Akmal Valentinna, Arindria Sekar Putri Wiyoto, Benediktus Nugroho Adi Yolwi Dyatma Yolwi Dyatma