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All Journal LOGIK@ Statistika CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Fourier Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Jambura Journal of Biomathematics (JJBM) Innovative: Journal Of Social Science Research The Indonesian Journal of Computer Science
Nina Fitriyati
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Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Industrial & Manufacturing Engineering Law, Crime, Criminology & Criminal Justice Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Journal : Jambura Journal of Biomathematics (JJBM)

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Prediction of the Change Rate of Tumor Cells, Healthy Host Cells, and Effector Immune Cells in a Three-Dimensional Cancer Model using Extended Kalman Filter Fitriyati, Nina; Faizah, Salma Abidah; Sutanto, Taufik Edy
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.24672

Abstract

In this study, we develop and implement the Extended Kalman Filter (EKF) to forecast the rate of change in tumor cells, healthy host cells, and effector immune cells within the Itik-Banks model. This novel application of EKF in cancer dynamics modeling aims to provide precise real-time estimations of cellular interactions, especially in constructing a new state space representation from the Itik-Banks model. We use a first-order Taylor series to linearize the model. The numerical simulations were performed to analyze the accuracy of this new state space with data from William Gilpin's GitHub repository. The results show that the EKF predictions strongly align with actual data, i.e., in the prior and posterior steps for tumor and healthy host cells, there is a strong agreement between the predictions and the actual data. The EKF captures the oscillatory nature of the tumor and healthy host cell population well. The peaks and troughs of the predictions align closely with the actual data, indicating the EKF's effectiveness in modeling the dynamic behavior of the tumor and healthy host cells. However, for effector immune cells, the oscillatory nature of the data in these cells gives rise to slight deviations. This represents a significant challenge in the future for updating the state space representations. Despite minor discrepancies, the EKF demonstrates a strong performance in both the training and testing data, with the posterior step estimates significantly improving the prior step accuracy. This study emphasizes the importance of data availability for accurate predictions, noting a symmetric Mean Absolute Percentage Error (sMAPE) of 35.92% when data is unavailable. Prompt correction with new data is essential to maintain accuracy. This research underscores the EKF's potential for real-time monitoring and prediction in complex biological systems.
The Analysis of Epidemic Dynamical Models for Dengue Transmission Considering the Mosquito Aquatic Phase Inayah, Nur; Manaqib, Muhammad; Fitriyati, Nina; Wijaya, Madona Yunita; Fiade, Andrew; Sari, Flori Ratna
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 3: September 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i3.29332

Abstract

This  study  generalizes the dengue  transmission model  by  considering the dynamics of the human population and  the Aedes  aegypti mosquito  population.  The  mosquito  population is  devided into  two  phases,  i.e.,  the aquatic  phase and the adult  phase.  From  the model,  we seek the disease-free  equilibrium, endemic  equilibrium, and  basic  reproduction number   (R0) points.    The  model  yields a  single   basic  reproduction number   which determines the system’s  behavior.   If  R0    1,  the disease-free  equilibrium is  locally  asymptotically stable, indicating that the disease  will die out.  Conversely, if R0    1, an endemic  equilibrium exists,  and  the disease may  persist  in the  population.    Next,   a  numerical simulation  is  performed  to  geometrically  visualize   the resulting analysis  and  also  to  simulate the  dengue   transmission in  DKI Jakarta   Province,  Indonesia.   The resulting  numerical simulation  supports our  analysis.   Meanwhile, the  simulation in  DKI Jakarta  Province suggests that  the dengue  fever  disappears after  60 days  from  the first  case appearance  after  controlling  the mosquito  population through fogging and the use of mosquito  larvae  repellent.  Lastly, the sensitivity analysis of R0   indicates  that  parameters   related  to  the  mosquito’s  aquatic   phase  have  a  strong   influence   on  dengue transmission, meaning that small  changes  in these parameters  can significantly increase or decrease the value  of R0  and thus the potential  for an outbreak.
Co-Authors . Mahmudi Aceng Komarudin Mutaqin Adjie, Dharma Syadhi Putra Agus Yodi Gunawan Alkadrie, Syarifah Syila Amelia Emaras, Tamara Anas Qolbu, Adinda Andrew Fiade Ayu Puji Rahayu Bisyri, M. Alvi Faizah, Salma Abidah Gina Isma Kusuma Handarbeni, Zalfa Talitha Inna, Suma Irma Fauziah Mahmudi Mahmudi Maysun, Maysun Muhammad Manaqib, Muhammad Nadilia, Nindita Nur Inayah Nuraini, Vita Nurmaleni Nurmaleni NURTITI SUNUSI Rahma, Chelsea Fatihah Rahman, Fathu Sari, Flori Ratna Sri Maliska Sri Wahyuningsih Sutanto, Taufik Edy Sutawanir Darwis Wijaya, Madona Yunita Wulandari, Fitria Sisca Yupinto, Ikhwal Zulkifli, Dhea Urfani