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Kajian Model Long And Short-Term Runoff (LST) dan Implementasinya untuk Menghitung Debit Banjir Suharmadi, Ummu Habibah,
CAUCHY Vol 1, No 4 (2011): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Air hujan merupakan salah satu aspek dari siklus hidrologi yang berperan penting dalam ketersediaan air di dalam bumi. Akan tetapi apabila terjadi hujan lebat dalam durasi waktu yang cukup lama maka air hujan tersebut dapat mengakibatkan terjadinya aliran permukaan (surface runoff) yang berpotensi menimbulkan banjir. Untuk mengetahui jumlah potensi air yang ada pada suatu daerah pengaliran, diperlukan perhitungan hidrologi dari data-data curah hujan. Untuk menghitung jumlah air atau debit sungai pada waktu banjir digunakan formulasi model Long- And Short-Term Runoff (LST). Formulasi model LST diperoleh dari model fisisnya. Pada penelitian ini dikaji proses terbentuknya formulasi model LST dari perilaku sistem berdasarkan fenomena siklus hidrologi. Selanjutnya formulasi model LST tersebut akan diimplementasikan untuk menghitung debit banjir pada suatu daerah pengaliran. Hasil penelitian menunjukkan bahwa formulasi model LST dapat digunakan untuk menghitung debit banjir dan merupakan model yang baik karena pada saat implementasi, error yang dihasikan antara debit banjir pengamatan dan debit banjir perhitungan adalah kecil.

Stability of Cancerous Chemotherapy Model with Obesity Effect Yanti, Indah; Habibah, Ummu
CAUCHY Vol 5, No 4 (2019): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

In this paper we present stability of cancerous chemotherapy model with obesity effect. This is a four-population model that includes immune cells, cancer cells, normal cells, and fat cells. The analytical result shows that there are four equilibrium points in case the drugs given and fat cells were not equal to zero, i.e., dead equilibrium, total cancer invasion equilibrium, cancer-free equilibrium, and coexistence equilibrium. Some numerical simulation also presented to illustrate the results.

PENYELESAIAN NUMERIK MASALAH SYARAT BATAS ROBIN PADA PERSAMAAN DIFERENSIAL CAUCHY-EULER Habibah, Ummu; Tuloli, Mohamad Handri; Rimanada, Viva; Ferreira, Tomas Goncalves
MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Vol 3 No 1 (2020): Vol. 3 No. 1 Maret 2020
Publisher : Prodi Pendidikan matematika Universitas Islam Majapahit (UNIM), Mojokerto, Indonesia

This research studied how the numerical solution of the Cauchy-Euler differential equation with Robin boundary conditions. There were several numerical methods that can be used to get the numerical solution of a boundary value problem, namely the finite-difference method, the shooting method, the collocation method, and others. In this study, the numerical solution of Robin's boundary condition problem was obtained by the center finite-difference and the shooting methods. From the two methods, the numerical error was compared to the exact solution. The simulation results shown that the shooting method produces a better numerical solution for approximating the completion of the Cauchy-Euler differential equation than the finite-difference method since it produced smaller numerical errors.

Stability Analysis of HIV/AIDS Model with Educated Subpopulation Habibah, Ummu
CAUCHY Vol 6, No 4 (2021): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v6i4.10275

We had constructed mathematical model of HIV/AIDS with seven compartments. There were two different stages of infection and susceptible subpopulations. Two stages in infection subpopulation were an HIV-positive with consuming ARV such that this subpopulation can survive longer and an HIV-positive not consuming ARV.Â The susceptible subpopulation was divided into two, uneducated and educated susceptible subpopulations.Â The transmission coefficients from educated and uneducated subpopulations to infection stages were Â where Â (( Â and ) ( Â and )) In this paper, we consider the case of Â and Â were zero.Â We investigated local stability of the model solutions according to the basic reproduction number as a threshold of disease transmission. The disease-free and endemic equilibrium points were locally asymptotically stable when Â and Â respectively. To support the analytical results, numerical simulation was conducted.

Local Sensitivity Analysis of COVID-19 Epidemic with Quarantine and Isolation using Normalized Index Muhammad Abdurrahman Rois; Trisilowati Trisilowati; Ummu Habibah
Telematika Vol 14, No 1: February (2021)
Publisher : Universitas Amikom Purwokerto

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35671/telematika.v14i1.1191

This study discusses the sensitivity analysis of parameters, namely the COVID-19 model, by dividing the population into seven subpopulations: susceptible, exposed, symptomatic infection, asymptomatic infection, quarantine, isolation, and recovered. The solution to the ordinary differential equation for the COVID-19 model using the fourth-order Runge-Kutta numerical method explains that COVID-19 is endemic, as evidenced by the basic reproduction number (R0) of 7.5. It means 1 individual can infect 7 to 8 individuals. Then is calculated using the next-generation matrix method. Based on the value of R0, a parameter sensitivity analysis is implemented to specify the most influential parameters in the spread of the COVID-19 outbreak. This can provide input on the selection of appropriate control measures to solve the epidemic from COVID-19. The results of the sensitivity analysis are the parameters that have the most influence on the model.

Simulation of Tumor Growth Model and Its Interaction with Natural-Killer Cells and T Cells Cholifatul Maulidiah; Trisilowati Trisilowati; Ummu Habibah
Research Journal of Life Science Vol 6, No 3 (2019)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.rjls.2019.006.03.5

This research studies about tumor growth model by involving immune system. Cells in the immune system, for instance natural killer (NK) cells and T cells, have prominent role in recognizing and eliminating tumor cells. In this paper, we construct the tumor growth model consisting of four populations namely tumor cells, NK cells, CD8+T cells, and CD4+T cells which is in the form of a non-linear differential equation. The analysis result shows that there are three tumor free equilibrium points and one coexisting equilibrium point. Some tumor free equilibrium and tumor equilibrium point exist and it is stable under certain conditions. Finally, numerical simulation is carried out to illustrate analysis result. From sensitivity analysis, it is found that the most sensitive parameter that influence the growth rate of tumor cells are the reciprocal carrying capacity of tumor cells and the killing rate of CD8+T cells by tumor cells.

Penyelesaian Numerik Masalah Syarat Batas Robin pada Persamaan Diferensial Cauchy-Euler Ummu Habibah; Mohamad Handri Tuloli; Viva Rimanada; Tomas Goncalves Ferreira
MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Vol. 3 No. 1 (2020): Vol. 3 No. 1 Maret 2020
Publisher : Prodi Pendidikan matematika Universitas Islam Majapahit (UNIM), Mojokerto, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36815/majamath.v3i1.615

This research studied how the numerical solution of the Cauchy-Euler differential equation with Robin boundary conditions. There were several numerical methods that can be used to get the numerical solution of a boundary value problem, namely the finite-difference method, the shooting method, the collocation method, and others. In this study, the numerical solution of Robin's boundary condition problem was obtained by the center finite-difference and the shooting methods. From the two methods, the numerical error was compared to the exact solution. The simulation results shown that the shooting method produces a better numerical solution for approximating the completion of the Cauchy-Euler differential equation than the finite-difference method since it produced smaller numerical errors.

Keakurasian Metode Shooting untuk Menyelesaikan Masalah Kondisi Batas pada Persamaan Sturm-Liouville Ummu Habibah; Nielda Alifah Mulyanti
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 7 No 2 (2023): Januari
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v7i2.4371

Pada penelitian ini dibahas keakurasian metode shooting/tembakan untuk menyelesaikan masalah kondisi batas Dirichlet pada persamaan Sturm-Liouville yang berbentuk persamaan diferensial orde dua, dengan kondisi batas Dirichlet. Persamaan Sturm-Liouville diselesaikan numerik menggunakan metode shooting. Simulasi numerik dilakukan dengan beberapa nilai (ukuran langkah). Keakurasian metode shooting diperoleh dengan cara dibandingkan solusi numeriknya terhadap solusi eksak, serta dibandingkan dengan solusi numerik menggunakan metode beda hingga. Hasil simulasi menunjukkan bahwa metode tembakan (shooting) menghasilkan solusi numerik yang lebih baik untuk mengaproksimasi masalah kondisi batas pada persamaan Sturm-Liouville dibandingkan metode beda hingga karena menghasilkan kesalahan numerik yang lebih kecil.

Dynamical Analysis of the Spread of COVID-19 model and its Simulation with Vaccination and Social Distancing Ummu Habibah; Angelina Renny Christin Octavia Sianturi
Telematika Vol 16, No 1: February (2023)
Publisher : Universitas Amikom Purwokerto

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35671/telematika.v16i1.2373

The model's creation and dynamical analysis were covered in this paper, SEIRS on the effects of vaccination and social isolation on the transmission of COVID-19. The susceptible individual subpopulation (S), the exposed individual subpopulation (E), the infected individual subpopulation (I), and the recovered individual subpopulation (R) are the four subpopulations that make up the human population in this model. This concept is founded on the notion that someone who has recovered from the illness is nonetheless vulnerable to reinfection. The carried out dynamical analysis includes the determination of the equilibrium point, the fundamental reproduction number (R_0), and evaluation of the local stability of the equilibrium point. The outcomes of the dynamical analysis show that there are two equilibrium points in the model: the endemic equilibrium point and the disease-free equilibrium point. Mathematical R_0>1 indicates the presence of an endemic equilibrium point, whereas a disease-free equilibrium point is always present. If the Routh-Hurwitz conditions are met, the endemic equilibrium point is locally asymptotically stable, but the disease-free equilibrium point is locally asymptotically stable if R_0

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