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All Journal Journal of Mathematics and Scientific Computing With Applications Jurnal Pijar MIPA
Fairuz, Ersya Nurul
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Biochemistry, Genetics & Molecular Biology Chemistry Mathematics Physics

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Stochastic Modeling with Poisson Hidden Markov in Hepatitis B Cases Fairuz, Ersya Nurul; Widyasari, Rina; Aprilia, Rima
Jurnal Pijar Mipa Vol. 19 No. 6 (2024): November 2024
Publisher : Department of Mathematics and Science Education, Faculty of Teacher Training and Education, University of Mataram. Jurnal Pijar MIPA colaborates with Perkumpulan Pendidik IPA Indonesia Wilayah Nusa Tenggara Barat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jpm.v19i6.7510

Abstract

Hepatitis B is transmitted through blood or body fluids contaminated with the virus from Hepatitis B sufferers (carriers). The factors that cause a person to contract Hepatitis B are sexual intercourse, blood contact, placental contact from the mother to the baby, and saliva. The incubation period for Hepatitis B Virus (HBV) ranges from 30 - 180 days with an average of 60 - 90 days. HBV can be detected 30 - 60 days after infection and persists for a certain period. Thus, the behaviour of infectious diseases can be observed and described using mathematical modelling. Mathematical modelling is a field of mathematics that represents and explains physical systems or problems that occur in the real world and are solved in mathematical statements. The mathematical model used to overcome uncertainty in variable values ​​is a stochastic model. These causal factors are not directly observed and form a Markov chain. The model that can be used for the uncertainty of an event is the Hidden Markov Model. The Hidden Markov Model (MHM) is a type of stochastic modelling that does not recognize the factors that trigger the problem being modelled. The Poisson Hidden Markov model is used to model Hepatitis B disease. Hepatitis B disease data is a series of observations that experience overdispersion and depend on the trigger of Hepatitis B disease, which is assumed not to be observed directly and forms a Markov chain. The aim to be achieved in this research is to model Hepatitis B disease at the Medan Haji Hospital using the Poisson Hidden Markov model and to find parameter estimates using the Expectation Maximization Algorithm. This type of research uses quantitative research methods. The conclusions that can be drawn based on the results and previous discussions are as follows: the method for determining the average number of patients in patient B can use the PHMM (Poisson Hidden Markov Model) method with the EiM (Expectation-Maximization Algorithm) algorithm, the best model for the number of Hepatitis B patients in Haji Hospital at this hospital is the model with three hidden cases with the parameter estimation value. The average number of Hepatitis B patients is 0.0324 in 1 month, and the average predicted results obtained by the hidden condition model 3 align with the original conditions in the previous months.
ANALYSIS OF FACTORS OF MATERNAL MORTALITY RATE IN MEDAN CITY USING BIVARIAT POISSON REGRESSION Sirait, Anita Ningsih; Fairuz, Ersya Nurul; Nikmah, Khairun; Sembiring, Tesya Yunita
Journal of Mathematics and Scientific Computing With Applications Vol. 3 No. 1 (2022)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1248.759 KB) | DOI: 10.53806/jmscowa.v2i2.57

Abstract

There are several factors that cause maternal death, such as bleeding, hypertension, infection, prolonged labor, abortion and others. Maternal deaths related to pregnancy, childbirth and the puerperium (42 days after delivery), and the number of deaths per 100,000 live births related to pregnancy or medical problems (except accidents or incidents). In this study the case of maternal mortality using the Bivariate Poisson Regression model which aims to determine what factors are the main factors in maternal mortality using the Bivariate Poisson regression method.
ANALYSIS OF FACTORS OF MATERNAL MORTALITY RATE IN MEDAN CITY USING BIVARIAT POISSON REGRESSION Sirait, Anita Ningsih; Fairuz, Ersya Nurul; Nikmah, Khairun; Sembiring, Tesya Yunita
Journal of Mathematics and Scientific Computing With Applications Vol. 3 No. 1 (2022)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v3i1.57

Abstract

There are several factors that cause maternal death, such as bleeding, hypertension, infection, prolonged labor, abortion and others. Maternal deaths related to pregnancy, childbirth and the puerperium (42 days after delivery), and the number of deaths per 100,000 live births related to pregnancy or medical problems (except accidents or incidents). In this study the case of maternal mortality using the Bivariate Poisson Regression model which aims to determine what factors are the main factors in maternal mortality using the Bivariate Poisson regression method.
Co-Authors Nikmah, Khairun Rima Aprilia Sembiring, Tesya Yunita Sirait, Anita Ningsih Widyasari, Rina