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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan
Putri, Devi Marita
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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THE COMPARISON OF EXTENDED AND ENSEMBLE KALMAN FILTERS IN MODELING ENVIRONMENTAL POLLUTION INFLUENCES ON ACUTE RESPIRATORY INFECTION DYNAMICS (ISPA) Norasia, Yolanda; Oktaviani, Dinni Rahma; Putri, Devi Marita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp987-998

Abstract

Acute Respiratory Infections (ISPA) are a significant health issue. According to the World Health Organization (WHO), ISPA is the leading cause of death among children under five worldwide. ISPA can be caused by environments with high levels of air pollution, particularly in urban areas. Predicting the spread of ISPA is a crucial step in controlling the disease. Since pollution sources are diverse, modeling and prediction can be difficult, which makes advanced methods such as the Kalman Filter (KF) desirable. This study compares two estimation methods, the Extended Kalman Filter (EKF) and the Ensemble Kalman Filter (EnKF), in predicting the spread of ISPA triggered by environmental pollution. Simulation results show that both methods can produce accurate estimations, but EnKF demonstrates superior performance in terms of RMSE compared to EKF. It predicts more accurately for susceptible (X) and infected (Y) populations with EnKF than with EKF. Based on the results of the EnKF for the X and Y populations, the RMSEs are 0.0660 and 0.1114, respectively. EnKF's advantage in handling uncertainty and non-linearity in the model makes it suitable for predicting the spread of ISPA.
Mathematical Stability Analysis of Bullying’s Impact on Student's Mental Health Putri, Devi Marita; Zulaikha, Zulaikha
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33212

Abstract

Bullying is a problem that takes root from the previous generation to the next. The most common bullying cases occur in junior high school students or equivalent with an age range of 13-15 years. Bullying can have an impact on student's mental health. This study develops and analysis a SEIRS-type mathematical model to understand the dynamics of mental health disorders due to bullying among junior high school students. The model includes four subpopulations: subpopulations are vulnerable to mental health disorders due to bullying (S), subpopulations who experience bullying but have not shown any mental health disorders (E), subpopulations that experience mental health disorders due to bullying (I), and subpopulations who have recovered from mental health disorders due to bullying (R). Based on the results of the analysis, two equilibrium points were obtained, namely the mental disorder-free equilibrium point (P_1^*) and the endemic equilibrium point (P_2^*). Next, determine the basic reproduction number using the next matrix generation method. Based on the results of numerical simulation using Matlab R2013a software, it was obtained that if R_01 then the mental disorder-free equilibrium point is stable local asymptotic and mental health disorders due to bullying cannot spread in the student population. Meanwhile, if R_01 then the endemic equilibrium point is stable, local asymptotic and mental health disorders due to bullying can spread in the student population. The rate of interaction between subpopulations vulnerable to mental health disorders due to bullying and subpopulations that experience mental health disorders due to bullying (\alpha) has a significant influence on the number of individuals in each subpopulation.
Co-Authors Norasia, Yolanda Oktaviani, Dinni Rahma Zulaikha Zulaikha