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All Journal Jurnal Sains dan Seni ITS Jambura Journal of Mathematics Vygotsky: Jurnal Pendidikan Matematika dan Matematika CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Sewagati Limits: Journal of Mathematics and Its Applications International Journal of Computing Science and Applied Mathematics-IJCSAM
Didik Khusnul Arif
Departemen Matematika Institut Teknologi Sepuluh Nopember Surabaya
Arts Humanities Computer Science & IT Education Engineering Languange, Linguistic, Communication & Media Mathematics Public Health Social Sciences Other

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State Variable Estimation of Nonisothermal Continuous Stirred Tank Reactor Using Fuzzy Kalman Filter Risa Fitria; Didik Khusnul Arif
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 3 No. 1 (2017)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Increasing safety and product quality, reducing manufacturing cost, minimizing the impact of environment in fault detection system for Nonisothermal Continuous Stirred Tank Reactor (CSTR) are the reason why accurate state estimation is needed. Kalman filter is an estimation algorithm of the stochastic linear dynamical system. Through this work, a modification of Kalman Filter that combines with fuzzy theory, namely Fuzzy Kalman Filter (FKF) is presented to estimate the state variable of Non-Isothermal CSTR. First, we approximate the nonlinear system of CSTR as piecewise linear functions and then change the crisp variable into the fuzzy form. The estimation results are simulated using Matlab. The simulation shows the comparison results, i.e computational time and accuracy, between FKF and Ensemble Kalman Filter (EnKF). The final result of these case shows that FKF is better than EnKF to estimate the state variable of Nonisothermal CSTR. The error estimation of FKF is 72.9% smaller for estimation of reactans concentration, 39.9% smaller for tank temperature, 76.47% smaller for cooling jacket temperature and the computational time of FKF is 76.47% faster than the computational time of EnKF.
Prediksi Penyebaran Covid-19 di Indonesia dan Jawa Timur dengan Metode Extended Kalman Filter Helisyah Nur Fadhilah; Erna Apriliani; Didik Khusnul Arif
Limits: Journal of Mathematics and Its Applications Vol. 18 No. 1 (2021): Limits: Journal of Mathematics and Its Applications Volume 18 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Saat ini pandemi Covid-19 telah menyebar ke seluruh dunia, tidak terkecuali Indonesia. Dalam pemodelan matematika, penyebaran Covid-19 dapat digambarkan melalui model matematika epidemiologi SIRD ( Susceptible, Infected, Recover, Death ). Pertama model non-linier SIRD didiskritkan dan selanjutnya dilakukan prediksi puncak penyebaran Covid-19 dengan menggunakan metode Extended Kalman Filter (EKF). Dengan data aktual Infected, Recover, dan Death yang merupakan data harian, modifikasi EKF dapat memprediksi puncak infeksi Covid-19 untuk satu bulan kedepan. Simulasi dilakukan dengan 3 macam pembatasan pergerakkan pada masyarakat yaitu : tanpa adanya pembatasan (100%), 75%, dan 50% pergerakkan. Hasil prediksi dengan modifikasi EKF menunjukkan dengan dilakukan pembatasan pergerakkan 50% pada masyarakat di Indonesia dan Jawa Timur dapat mempercepat terjadinya puncak infeksi dengan jumlah individu terinfeksi lebih sedikit
Estimation of Dengue Fever Transmission Model in West Java Using the Ensemble Kalman Filter Method Addinda Nur Ameliyah; Didik Khusnul Arif
Vygotsky: Jurnal Pendidikan Matematika dan Matematika Vol. 8 No. 1 (2026): Vygotsky: Jurnal Pendidikan Matematika dan Matematika
Publisher : Universitas Islam Lamongan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30736/voj.v8i1.1325

Abstract

Dengue Fever Transmission is a serious, potentially fatal infectious if unmanaged disease. It caused by the dengue virus, transmitted by Aedes aegypti and Aedes albopictus mosquitoes. In West Java, cases remain high and fluctuate significantly, requiring precise mathematical modeling to describe transmission dynamics. This is the first study applying Ensemble Kalman Filter (EnKF) in West Java to estimate the SEIR-SI model, compared to Unscented Kalman Filter (UKF), using dengue fever transmission case data from 2010–2023. Performance was assessed via Mean Absolute Percentage Error (MAPE) for the infected human population ( ), showing EnKF’s superior accuracy (2.4%) over UKF (7.8%). EnKF effectively estimates hard-to-measure epidemiological variables and this study can support government prediction-based dengue fever transmission control policies.
Mathematical Modeling and Parameter Estimation of Meningitis Transmission Dynamic using Vaccination Strategies in Indonesia Aufa Al Musyarof; Faris Nur Hibban; Mardlijah Mardlijah; Didik Khusnul Arif
Jambura Journal of Mathematics Vol 8, No 2: August 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i2.39751

Abstract

Meningitis is a public health threat because it progresses rapidly and has serious clinical impacts, including long-term disability. This research develops a six-compartment mathematical model to examine the dynamics of meningitis transmission by dividing the population into susceptible, exposed, infected, recovered without disability, recovered with disability, and vaccinated groups. The model parameters were fitted using the least squares method based on annual meningitis case data in Indonesia from 1990 to 2023 according to estimates originating from the Institute for Health Metrics and Evaluation (IHME)/Global Burden of Disease, accessed through the archived Our World in Data source. Model validation shows high accuracy performance, with a Mean Absolute Percentage Error value of 3.12%. Local sensitivity analysis indicates that the transmission rate (\beta) and vaccination rate (\xi) are the parameters most influencing changes in R0 resulting from parameter variation. Numerical simulation results show that rapid immunization at the onset of an outbreak is the most effective strategy among the vaccination scenarios examined to expedite herd immunity and limit disease spread.
HIV Transmission Dynamics and Workforce Productivity in Indonesia: A Nonlinear Modeling and Parameter Estimation Study Rizqi Aridh Dwi Prasetyo; Nuansa Cahaya Muhammad; Didik Khusnul Arif; Mardlijah Mardlijah
Jambura Journal of Mathematics Vol 8, No 2: August 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i2.39823

Abstract

This article addresses limited multi-compartment clinical data by developing a six-compartment nonlinear mathematical model consisting of susceptible (S), protected (P), exposed (E), non-productive infected (In), productive infected (Ip), and AIDS phase (A) to analyze HIV transmission dynamics and workforce productivity in Indonesia. Utilizing empirical data from 2006 to 2023, parameter estimation via nonlinear least squares yielded a robust Mean Absolute Percentage Error (MAPE) of 14.20%. The system’s local stability is governed by the basic reproduction number, where the baseline estimation R0 = 0.831332 1 theoretically guarantees long-term disease eradication. Linearization around the disease-free equilibrium (E0) proved a stable focus behavior, showing trajectories that approach the steady state via damped oscillations due to clinical progression delays. Sensitivity analysis and numerical simulations identified the transmission rate from exposed individuals (βe) and the transition rate from exposed to non-productive infected (γ) as the most critical parameters controlling R0. While elevated transmission from the exposed compartment forces a continuous rise in the exposed cohort, accelerating the clinical transition rate shifts the non-productive infected peak earlier and rapidly suppresses active clusters to zero. These findings provide critical insights into how clinical manifestation timing and transmission from the exposed compartment interact, which is vital for planning healthcare resource windows and safeguarding workforce productivity.
Co-Authors Addinda Nur Ameliyah Aufa Al Musyarof Bandung Arry Sanjoyo Budi Setiyono Dwi Ratna Sulistyaningrum Erna Apriliani Fadia Nila Sihan Novita Lutfiani Faris Nur Hibban Helisyah Nur Fadhilah Helisyah Nur Fadhilah Indah Rahmadhania Mardlijah - Muhammad Jirov Rexiansyah Grystnop Sutopo Nastitie Nastitie Nastitie Nastitie Nuansa Cahaya Muhammad Prima Aditya Rifki Ilham Baihaki Risa Fitria Rizqi Aridh Dwi Prasetyo Sulthon Amar Al Aziim Valeriana Lukitosari Yunita Indriana Sari Zainullah Zuhri