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All Journal The Journal of Experimental Life Sciences (JELS) Science and Technology Indonesia Limits: Journal of Mathematics and Its Applications
Trisilowati
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Environmental Science Immunology & microbiology Materials Science & Nanotechnology Mathematics Medicine & Pharmacology Neuroscience Physics

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Numerical Simulation and Sensitivity Analysis of COVID-19 Transmission Involves Virus in the Environment Azizah, Maratus Sholihatul; Trisilowati; Shofianah, Nur
The Journal of Experimental Life Science Vol. 13 No. 2 (2023)
Publisher : Graduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2023.013.02.08

Abstract

This paper is aimed to develop a new COVID-19 mathematical model involving viruses in the environment. In this mathematical model, the human population is divided into five subpopulations: susceptible, exposed, infected, hospitalized, and cured individuals. In addition, the model also contains the virus population in the environment. Infection in the model occurs due to interactions between susceptible individual subpopulations and infected individuals and hospitalizations, as well as the spread of the virus in the environment. Based on the results of dynamic analysis, this model has two equilibrium points, the disease-free and endemic equilibrium points. The disease-free equilibrium point always exists, and both equilibrium points are locally asymptotically stable if they meet the Routh-Hurwitz criteria. Model sensitivity analysis was carried out on model parameters that affect the basic reproduction number with the most sensitive parameters are the natural death rate, the recruitment rate, the transmission rate of the virus in the environment, the virus clearance rate, and the rate of wearing PPE (Personal Protective Equipment), as well as the parameter that does not affect the basic reproduction number that is the rate of leaving the recovered population. Numerical simulations performed show results in accordance with the analysis, also from the simulations can be concluded that the increase (or decrease) of the transmission rate of the virus in an environment that has a higher sensitivity index has more significant influences on the basic reproduction number and the number of infected population than the transmission rate of hospitalized individuals. Keywords: Basic Reproduction Number, Dynamics Analysis, Epidemic Models of COVID-19, Local Stability Analysis, Sensitivity Analysis.
An Improved Fifth-Order Runge-Kutta Method with Higher Accuracy and Efficiency for Solving Initial Value Problems Habibah, Ummu; Medrano, Fermin Franco; Permana, Adith Chandra; Ardiana, Dita; Trisilowati
Science and Technology Indonesia Vol. 10 No. 3 (2025): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.3.802-816

Abstract

Solving initial value problems (IVPs) in ordinary differential equations (ODEs) often requires numerical methods, with the fifth-order Runge-Kutta method being a widely used approach due to its balance between accuracy and computational efficiency. A novel and straight forward formula for the fifth order Runge-Kutta method is proposed, aiming to simplify calculations while maintaining high accuracy and stability. The method is derived using an optimized Taylor series expansion, leading to a more efficient formulation. Numerical experiments are conducted to compare the proposed method with existing fifth-order Runge-Kutta methods. The results showthat the proposed formula out performs existing methods in terms of accuracy, stability, and computational efficiency. This new formula provides a practical alternative for solving IVPs in ODEs with improved performance.
Analisis Dinamik Model Hepatitis B dengan Sirosis Hati Muna Afdi Muniroh; Trisilowati; Wuryansari Muharini Kusumawinahyu
Limits: Journal of Mathematics and Its Applications Vol. 19 No. 1 (2022): Limits: Journal of Mathematics and Its Applications Volume 19 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Hepatitis B adalah suatu penyakit peradangan pada organ hati yang memiliki dua fase infeksi yaitu akut dan kronis. Sirosis hati terjadi akibat terbentuknya jaringan parut pada individu hepatitis B berkepanjangan (kronis). Oleh karena itu, pada penelitian ini dibentuk model penyebaran penyakit hepatitis B dengan sirosis hati. Selain itu, pada model diasumsikan virus hepatitis B (HBV) dapat ditularkan baik secara vertikal maupun horizontal. Analisis dinamik dilakukan untuk menentukan eksistensi dan kestabilan titik kesetimbangan. Berdasarkan hasil analisis dinamik, diperoleh dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Angka reproduksi dasar (R0) didapatkan dengan menggunakan matriks generasi selanjutnya. Titik kesetimbangan bebas penyakit eksis tanpa syarat, sedangkan titik kesetimbangan endemik eksis ketika R0>1 . Hasil analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit dan endemik bersifat stabil asimtotik lokal jika kriteria Routh-Hurwitz terpenuhi. Selain itu, titik kesetimbangan bebas penyakit bersifat stabil asimtotik global jika R0<1 dan titik kesetimbangan endemik bersifat stabil asimtotik global jika memenuhi kondisi tertentu. Simulasi numerik mendukung hasil analisis yang telah diperoleh.
Analisis Dinamik pada Model Kanker Serviks dengan Vaksinasi dan Screening Karunia Theda Kristanti; Trisilowati; Agus Widodo
Limits: Journal of Mathematics and Its Applications Vol. 17 No. 2 (2020): Limits: Journal of Mathematics and Its Applications Volume 17 Nomor 2 Edisi De
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Pada paper ini dibahas analisis dinamik model penyebaran kanker serviks dengan melibatkan tindakan vaksinasi dan screening. Penyebab utama terjadinya kanker serviks adalah karena seseorang terinfeksi Human Papillomavirus (HPV). Infeksi ini dapat menular karena adanya kontak langsung melalui hubungan seksual antara subpopulasi wanita rentan dengan pria terinfeksi HPV maupun kontak langsung antara pria rentan dengan wanita terinfeksi HPV. Pada model ini diasumsikan vaksin diberikan pada subpopulasi wanita rentan saja dengan salah satu jenis vaksin. Sementara itu, screening dilakukan oleh subpopulasi wanita terifeksi HPV sebagai upaya deteksi dini untuk mencegah terjadinya kanker serviks. Hasil analisis dinamik menunjukkan bahwa model penyebaran kanker serviks dengan vaksinasi dan screening memiliki dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemi. Eksistensi dan kestabilan lokal titik kesetimbangan bergantung pada nilai angka reproduksi dasar R 0 . Berdasarkan hasil analisis, titik kesetimbangan bebas penyakit eksis tanpa syarat, sedangkan titik kesetimbangan endemi eksis jika R 0 >1. Titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal jika nilai R 0 <1 dan titik kesetimbangan endemi bersifat stabil asimtotik lokal jika memenuhi kriteria Routh-Hurwitz. Simulasi numerik yang dilakukan mendukung hasil analisis dinamik yang diperoleh.
Co-Authors Agus Widodo Ardiana, Dita Azizah, Maratus Sholihatul Karunia Theda Kristanti Medrano, Fermin Franco Muna Afdi Muniroh Permana, Adith Chandra Shofianah, Nur Ummu Habibah, Ummu Wuryasari Muharini Kusumawinahyu