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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences MATEMATIKA The Journal of Experimental Life Sciences (JELS) CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Mahasiswa Matematika Journal of Innovation and Applied Technology Natural B Journal of Mathematical and Fundamental Sciences BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Indonesian Journal of Electrical Engineering and Computer Science Jambura Journal of Biomathematics (JJBM) Jurnal Matematika Integratif
Wuryasari Muharini Kusumawinahyu
Jurusan Matematika, Fakultas MIPA, Universitas Brawijaya
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Environmental Science Immunology & microbiology Mathematics Mechanical Engineering Medicine & Pharmacology Neuroscience Physics Transportation

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Dynamical Analysis and Parameter Estimation of Hepatitis B Disease Model in Malang Aulani, Fitroh; Kusumawinahyu, Wuryansari Muharini; Darti, Isnani
The Journal of Experimental Life Science Vol. 11 No. 3 (2021)
Publisher : Graduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.jels.2021.011.03.03

Abstract

In this article, a model representing the spread of Hepatitis B disease is constructed as a nonlinear autonomous system. The model divides the considered human population into three classes, namely susceptible, infected, and recovered class. The dynamical analysis shows that there are two equilibrium points in the model, namely a disease-free equilibrium point and an endemic equilibrium point. The existence and stability of the equilibrium points depend on the basic reproduction number (R_0). The disease-free equilibrium point is local asymptotically stable when R_0<1 while the endemic equilibrium point exists and is local asymptotically stable if R_0>1. The five parameters of the model are estimated by applying Downhill Simplex (Nelder-Mead) Algorithm and by using the infected data cases taken from such a hospital in Malang. The estimated parameters are the transmission of infection rate, the saturation rate, the vaccination rate, the recovery rate, and the immunity loss rate. The resulting parameter estimation supports the analytical result and is used to illustrate the analytical results numerically. Based on the considered model and the result of the parameters estimation, it can be concluded that the Hepatitis B spread in Malang is controllable. Keywords: downhill simplex (Nelder-mead) algorithm, dynamical analysis, hepatitis B model, parameter estimation. 
Co-Authors Agus Suryanto Andonowati Andonowati Ani Budi Astuti Aulani, Fitroh Deasy Sandhya Elya Ikawati Exviani, Rina Hadinata, Nadia Agus Hidayatulloh, Muhammad Rif’an Ikawati, Deasy Sandhya Elya Isnani Darti Khozaimi, Ach. Kwardiniya Andawaningtyas Lu’luul Wardah Muna Afdi Muniroh Muniroh, Kunnisai Ni’matur Rohmah Noor Hidayat, Noor Nurul Imamah Purnomo, Anna Silvia Puspitasari, Nurmaini Shofiyya, Nada Syafitri, Risyqaa Syaiful Anam Trisilowati Trisilowati Trisilowati Trisilowati, Trisilowati Trisilowati, Trisilowati Ummu Habibah, Ummu Yuni Ayu Anita