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All Journal Desimal: Jurnal Matematika Jurnal SOLMA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) JIKA: Jurnal Ilmu Keuangan dan Perbankan Value: Jurnal Manajemen dan Akuntansi JP2M (Jurnal Pendidikan dan Pembelajaran Matematika) ESTIMASI: Journal of Statistics and Its Application Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Premium: Insurance Business Journal Jurnal Pijar MIPA Jurnal Sintak Mathematical Sciences and Applications Journal
Anggraeni, Andini Setyo
Institut Teknologi Batam
Humanities Biochemistry, Genetics & Molecular Biology Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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APPLICATION OF DISCRETE HIDDEN MARKOV MODELS IN ANALYZING BLOOD TYPE INHERITANCE PATTERNS Hayati, Nahrul; Sulistyono, Eko; Anggraeni, Andini Setyo
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1501-1512

Abstract

This research investigates the application of a Discrete Hidden Markov Model (DHMM) to analyze inheritance patterns of ABO blood types. Leveraging the DHMM’s ability to model systems with hidden states, the study aims to improve the understanding of blood type inheritance dynamics in populations. The model employs six hidden states representing ABO genotypes (IAIA, IAi, IBIB, IBi, IAIB, and ii) and four observable states corresponding to blood type phenotypes (A, B, AB, and O). The transition and emission matrices followed Mendelian inheritance principles using population allele frequencies, whereas the initial probabilities were computed under Hardy-Weinberg Equilibrium (HWE) assumptions, with parameters calibrated to Indonesian blood type distributions. As a case study, we calculated the likelihood of observing phenotype A across five consecutive generations. Using the forward-backward algorithm, the probability of this sequence was calculated as 19%. The Viterbi algorithm further identified the most probable sequence of hidden genotypes, revealing a transition from the heterozygous IAi to the homozygous IAIA genotype over the five generations. One iteration of the Baum-Welch algorithm improved model accuracy, increasing log-likelihood from -1.661 to 0. Our results demonstrate the DHMM’s efficacy in decoding complex inheritance dynamics and provide a foundation for future population genetics research.
A Daily Transition Analysis of Disaster Events in Riau Islands using Markov Chains: Dominant Disaster Identification and Risk Assessment Hayati, Nahrul; Anggraeni, Andini Setyo; Sulistyono, Eko
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.34024

Abstract

Objectives: This study employs a Markov Chain approach to analyze daily disaster transition patterns in the Riau Islands, with the primary objectives of identifying dominant hazards, quantifying long-term disaster risks, and providing evidence-based recommendations for disaster management. Methods: The research utilized daily disaster records from Indonesia’s National Disaster Management Agency (BNPB) for 2024. A dominant state classification approach was applied to handle days with multiple disaster occurrences, followed by the construction of a transition probability matrix and steady-state analysis to determine long-term disaster distribution. Results: The analysis reveals that no disaster conditions represent the most prevalent state in the region. Among actual disasters, wildfires demonstrate the highest persistence, followed by extreme weather events, floods, and landslides. The transition patterns indicate that most disasters occur as isolated events rather than consecutive sequences, though wildfires show a tendency for temporal clustering. Conclusion: The study provides two key contributions. Methodologically, it demonstrates an effective approach for simplifying complex multi disaster daily data. Practically, it offers scientific evidence for prioritizing wildfire management in the Riau Islands while maintaining preparedness for other episodic disasters. These findings support the development of targeted early warning systems and resource allocation strategies for local disaster management agencies.
Co-Authors Alhamidi, Alhamidi Ananda, Serly Tri Aprilla Handayani, Vitri Budiyono, Budiyono Devikaduri, Laras Dia Cahya Wati Eko Sulistyono Sulistyono Fadilah, Alya Handayani*, Vitri Aprilla Handayani, Vitri Aprilla Ismi Rizqa Lina Jabnabillah, Faradiba Lunardi, Louis Muhammad Agus Muljanto munir, Zainul Munir Nabillah, Faradiba Nahrul Hayati Nur Asikin Pramesti, Getut Puri Rahayu Nengsi Putri, Tia Aura Rifki Chandra Utama Ririt Dwiputri Permatasari Risa Mustika Rusmadi, Garry Sabarinsyah, Sabarinsyah Sadiq Ardo Wibowo, Sadiq Ardo Safitriyana, Safitriyana Tarsila, Huiliana Taufiq Rahman Utama, Rifki Chandra Utami, Arli Magfirah Widya Reza