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All Journal UG Journal Jurnal Matematika & Sains Communication in Biomathematical Sciences Indonesian Journal of Physics (IJP) Jurnal Matematika Integratif
Hengki Tasman
Department Of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
Astronomy Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Health Professions Mathematics Mechanical Engineering Social Sciences Transportation

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 1 
A Note on Singularly Perturbed System Hengki Tasman; Theo Tuwankotta; Wono Setya Budhi
Jurnal Matematika & Sains Vol 7, No 1 (2002)
Publisher : Institut Teknologi Bandung

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Abstract

In this paper the solution of a singularly perturbed nonlinear ordinary differential equation which is obtained by using the asymptotic expansion method and a numerical method is analyzed in various values of the parameter of the equation. The numerical method which we use is Runge-Kutta-Feldbergh method of order 45, combined with the shooting method. Both solutions are verified using the first integral of the equation.
Simulation of Influenza Pandemic Based on Genetic Algorithm and Agent-Based Modeling: A Multi-objective Optimization Problem Solving Ria Lestari Moedomo; Adi Pancoro; Jorga Ibrahim; Adang Suwandi Ahmad; Muhammad Sukrisno Mardiyanto; Mohammad Bahrelfi Belatiff; Hengki Tasman
Jurnal Matematika & Sains Vol 15, No 2 (2010)
Publisher : Institut Teknologi Bandung

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Abstract

This paper describes the analysis, design and development process of simulation software for the Avian Influenza (H5N1) viruses mutation. Influenza Pandemics, which have occurred since 1729, caused by mutation (antigenic drift) and recombination (antigenic shift) of Influenza viruses. The purpose of this research is to define the modeling of virus mutation causing the Influenza Pandemic phenomena. Additionally, the objective of this simulation is to obtain all possible virus strains might be formed from mutation, the scope within this article, which can potentially trigger Influenza Pandemic. These new strains could then be utilized to support the vaccine planning process. The Influenza Pandemic simulation program can be developed based on Genetic Algorithm method, for solving this multi-objective optimization problem. By utilizing the Genetic Algorithm approach, the chromosome solution and fitness values/functions of Influenza Pandemic stages are defined and the maximum fitness values are to be searched. The simulation result of H5N1 mutation gave 3 (three) best fitness values and a more dynamic mean fitness values, including best fitness value from several mutations combination. Simulation program was developed by utilizing MATLAB© software, with Genetic Algorithm Toolbox provided.
PENGARUH STRATEGI PULSE VACCINATION TERHADAP PENCEGAHAN PENYEBARAN PENYAKIT CAMPAK Lestari, Dewi Putrie; Tasman, Hengki
UG Journal Vol 7, No 4 (2013)
Publisher : Universitas Gunadarma

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Abstract

Campak adalah penyakit menular dan sangat berbahaya. Oleh karena itu, perlu dilakukan upaya untuk mencegah penyebarannya. Salah satu cara yang efektif untuk mengatasi penyebaran penyakit ini adalah vaksinasi. Ada dua strategi vaksinasi, yaitu constant vaccination dan pulse vaccination. Penelitian ini Pusat Studi Komputasi Matematika membahas pengaruh strategi pulse vaccination terhadap pencegahan penyebaran penyakit campak dengan menggunakan model epidemik SIR (Susceptible, Infectious, Recovered). Berdasarkan pembentukan model tersebut, diperoleh suatu Departemen Matematika Universitas Indonesia. Nilai ambang batas epidemik yang digunakan sebagai batasan untuk analisis selanjutnya. Analisa sistem dinamik pada model dengan menentukan solusi periodik bebas infeksi menggunakan pemetaan stroboskopik dan titik tetap. Selanjutnya digunakan metode linierisasi dan teori Floquet untuk menentukan kestabilan dari solusi tersebut. Hasil penelitian menunjukkan bahwa kestabilan solusi periodik bebas infeksi bergantung pada pengambilan nilai dari periode pulse vaccination (T). Berdasarkan kriteria kestabilan tersebut diperoleh bahwa strategi pulse vaccination akan berhasil mencegah terjadinya penyebaran penyakit campakjika nilai dari T < Tmax. Untuk mendukung pembahasan teori di dalam penelitian ini, dilakukan simulasi dengan menggunakan software Matlab.
Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model Dipo Aldila; Arthana Islamilova; Sarbaz H.A. Khosnaw; Bevina D. Handari; Hengki Tasman
Communication in Biomathematical Sciences Vol. 4 No. 2 (2021)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2021.4.2.4

Abstract

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field.
Relasi Dispersi dalam Pandu Gelombang Planar Nonlinear Kerr Hengki Tasman; Edy Soewono
Indonesian Journal of Physics Vol 13 No 3 (2002): Vol. 13 No.3, Juli 2002
Publisher : Institut Teknologi Bandung

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Abstract

In this paper planar waveguides with Kerr-type nonlinearity are considered. By using an effective refractive index method and averaging, an implicit dispersion relation is obtained analitically for the waveguides. This dispersion relation can simplify numerical calculation in obtaining dispersion curves. Dispersion relation curves with different averaging schemes for symmetric planar waveguides are shown here.
Model Matematika Penyebaran Penyakit Pneumonia dengan Intervensi Vaksinasi dan Pengobatan Nicola Chandra Darmawan; Hengki Tasman
Jurnal Matematika Integratif Vol 18, No 1: April 2022
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (955.397 KB) | DOI: 10.24198/jmi.v18.n1.36064.63-72

Abstract

Pneumonia merupakan penyakit infeksi saluran pernapasan yang menyerang paru-paru. Salah satu upaya yang dapat dilakukan untuk mengendalikan penyebaran penyakit ini adalah dengan melakukan pengobatan dan vaksinasi. Pada artikel ini dikonstruksi model matematika penyebaran penyakit pneumonia dengan intervensi pengobatan dan vaksinasi. Model matematika tersebut dikaji secara analitik dan dilakukan simulasi numerik. Kajian analitik meliputi keberadaan titik keseimbangan dan kestabilan lokalnya, serta bilangan reproduksi dasar R0. Dengan simulasi numerik didapat informasi bahwa intervensi vaksinasi dan pengobatan mampu mengendalikan penyebaran penyakit pneumonia.
Co-Authors Adang Suwandi Ahmad Adi Pancoro Arthana Islamilova Bevina D. Handari Dewi Putrie Lestari Dipo Aldila Edy Soewono Jorga Ibrahim Mohammad Bahrelfi Belatiff Muhammad Sukrisno Mardiyanto Nicola Chandra Darmawan Ria Lestari Moedomo Sarbaz H.A. Khosnaw Theo Tuwankotta Wono Setya Budhi