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Simulasi Model Diskrit Respon Sistem Imun pada Penyebaran Tumor Otak dengan Metode Beda Hingga Standar Icha Zakiyya Nafisah Roza; Usman Pagalay; Heni Widayani
Jurnal Riset Mahasiswa Matematika Vol 1, No 2 (2021): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Tumor otak merupakan penyakit dimana jaringan dalam sistem saraf pusat tumbuh secara abnormal. Pertumbuhan tumor tersebut mengalami interaksi dengan sistem imun untuk menghambat pertumbuhan tumor, hal tersebut dapat dideskripsikan dalam model matematika yang berbentuk persamaan diferensial biasa. Model matematika penyebaran tumor otak dengan respon sistem imun pada penelitian ini terdapat lima variabel yaitu, glioma , makrofag , sel T CD TGF- , dan IFN- . Model tersebut akan didiskritisasi dengan menggunakan metode beda hingga standar. Metode beda hingga standar atau metode euler merupakan metode yang diturunkan dari deret Taylor. Berdasarkan hasil analisis diketahui bahwa model diskrit penyebaran tumor otak dengan respon sistem imun memiliki jenis kestabilan model diskrit sama dengan model kontinunya dan memiliki dua titik kesetimbangan, yaitu kesetimbangan bebas penyakit dan kesetimbangan endemik. Titik kesetimbangan bebas penyakit dan endemik bersifat stabil asimtotik apabila memenuhi kriteria kestabilan Schur-Cohn. Simulasi numerik dilakukan untuk mengilustrasikan dan menguji hasil analisis yang diperoleh. Hasil simulasi numerik diperoleh bahwa model diskrit akan sama dengan model kontinunya saat tertentu.

Analisis Model Stokastik Penularan Virus Hepatitis B Arina Nur Laila; Usman Pagalay; Heni Widayani
Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

The spread of hepatitis B virus (HBV) infection has been widely studied using the deterministic SIR model, in which individuals who recover from acute infection have temporary immunity to the virus. However, this deterministic model uses a constant rate of viral infection over time. This is not in accordance with the fact that the infection rate is a random parameter that depends on time. This study discusses the analysis of the stochastic model of hepatitis B virus transmission. The purpose of this study is to construct the SIR stochastic model by dividing the infection rate into two, namely the rate of acute and chronic infection following the Wiener process. The model is then searched for an analytical solution referring to the Ito formula. The analytical solution and the Wiener process are described by substituting parameter values in the form of acute and chronic infection rates (β+α), cure rate (γ), and initial values (S(0) and I(0)) to obtain the mean value (μ). and the standard deviation (σ) of dS(t) and dI(t). The results of the simulation show that the number of infected individuals (I(t)) will decrease rapidly if (γ) is greater but will increase rapidly if (β+α) and (I(0)) are greater.

Dinamika Model Matematika Reaksi T-Helper Chilvia Tribhuana; Usman Pagalay; Elly Susanti
Jurnal Riset Mahasiswa Matematika Vol 1, No 5 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

T cells are a major component of the human immune system. These T cells have a number that varies depending on the body's immune response when fighting bacteria or viruses. However, the condition of excess immune cells in the body can also be dangerous. Theoretical studies on the dynamics of T-Helper cells in the body are needed to get the right simulation in treating patients without conducting medical tests on every patient on a daily basis. This study discusses the dynamics of the mathematical model of the T-Helper reaction with the influence of antigen and IL-2. From this study, two equilibrium points were obtained, namely disease-free equilibrium and endemic equilibrium. The use of parameter values from the experimental results shows that the disease-free equilibrium point is locally unstable, while the endemic equilibrium point is locally stable. The numerical simulation showed that the antigen increased from 1st day to the highest value at 0.926 on the 11th day until on the 20th day it started to be constant towards at the value which is the antigen could be activate the resting T-Helper. The process of activating T-Helper, create IL-2 which can stimulating the proliferation and activity of T-Helper cells, so they can divide the activated cell of T-Helper into two memory cells.

Analisis Dinamik Model Penyebaran Tumor Otak dengan Respon Sel Imun Resti Dwi Anggraini; Usman Pagalay; Achmad Nashichuddin
Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v1i3.14339

The brain tumor distribution model with immune cell response is in the form of a non-linear system of ordinary differential equations with five equations. Each equation describes how immune cells in the brain, namely macrophages ( ), CD8+ T cells ( ), TGF- cytokines ( ) and IFN- ( ) cytokines interact with tumor cells, namely glioma cells ( ). From the calculation of the equilibrium point, the tumor cell-free conditions (DFE) and the endemic conditions (END) were obtained, in which tumor cells in long-term conditions were always present in the patient's brain. By using certain parameter values, it can be illustrated that the END condition is locally asymptotically stable while the DFE condition is locally unstable. This indicates that brain tumor cells, namely glioma cells ( ) will increase to their maximum value of 882650 cells and remain at that number from day 1000 onwards.

Prediction Model of Revenue Restaurants Business Using Random Forest Erfan Ainul Yakin; Ririen Kusumawati; Usman Pagalay
Indonesian Journal of Artificial Intelligence and Data Mining Vol 6, No 2 (2023): September 2023
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/ijaidm.v%vi%i.24984

This research was conducted to predict the level of revenue from the Soto Kwali Pak Wasis restaurant business using Machine Learning. The Random Forest method was chosen because it can predict optimal and fast results with low hardware requirements. Prediction Model results using the Random Forest method resulted in an average accuracy value of 75.4% from a combination of 4 experiments. Thus, the Random Forest method is one of the flexible algorithms and is very suitable for predicting revenue in the Soto Kwali Pak Wasis restaurant business because of its good speed, high accuracy, and requires lower costs.

Innovation in the Utilization of Lemon for Phytonutrient Products as an Effort to Increase Income Generation for the Bocek Village Community Rahmi Annisa; Usman Pagalay; Alvi Milliana; Wirda Anggraini; Fitriyani Fitriyani; M Abbas Arriziq; Roihatul Mutiah
Bubungan Tinggi: Jurnal Pengabdian Masyarakat Vol 6, No 3 (2024)
Publisher : Universitas Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/btjpm.v6i3.10095

Bocek Village is one of the villages in Karangploso District, Malang Regency, East Java Province, which has lemon production reaching 30 tons per month but is not supported by good sales management. Lemon (Citrus lemon) is one of the species of the genus citrus, and it has many benefits, such as anti-inflammatory, antimicrobial, anticancer, and antiparasitic activities. This community service aims to create innovative lemon-based products for phytonutrients to increase income generation for Bocek village, Karangploso district, Malang regency. The method used is ABCD (Asset Based Community Development). The activity was carried out on August 19 2023, in Bocek village, Karangploso district, Malang regency, with the participation of 30 housewives. The results of the activity were successful socialization and demonstrations of lemon slice and lemon squash products that were successfully made, and there were levels of public understanding with good (60%), sufficient (23%), and poor (17%) percentages. So, it can be concluded that training activities on using lemons for phytonutrient products can increase public knowledge and generate income in the future.

Analisis Dinamik Model Respon Inflamasi Pada Paru-Paru Arrofiqi, Muhammad Rosyid; Pagalay, Usman; Nasichuddin, Achmad
Jurnal Riset Mahasiswa Matematika Vol 3, No 1 (2023): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v3i1.22362

This study discusses the dynamic analysis of the inflammatory response model in the lungs. Then proceed with performing numerical simulations. This study was conducted to present the inflammatory response in the lungs. In the mathematical model of the inflammatory response, there are three variables, namely (pathogen), (immune system) and (inflammation). Dynamic analysis is carried out by determining the equilibrium point, the basic reproduction number , stability analysis of the equilibrium point. The results of this study obtained a basic reproduction number . The disease-free equilibrium point is unstable and the endemic equilibrium point is unstable when the parameter values in table 4.1 are used. The results of numerical simulations show that the population of pathogens found in the body starts from the first day, which is 0.01, increases to 2.8 until the second week, decreasing constantly accompanied by the immune system in the human body so that it goes to 0 at infinity. While the immune defense population in the human body rises to 4.4 and decreases slowly and constantly following the development of pathogens in the human body accompanied by the immune system itself. And the pro-inflammatory inflammation population runs steadily at 0 to rises at 4.3 following human immune defense and falls at week 16 and continues to be consistent. The rate of inflammation follows a hyperbolic tan which is affected by when t is infinite towards . When the parameter values and are increased, the pro-inflammatory inflammation will decrease and vice versa.

Analisis Dinamik Model Predator-Prey dengan Faktor Kanibalisme Pada Predator Safitri, Dwi; Widayani, Heni; Pagalay, Usman
Jurnal Riset Mahasiswa Matematika Vol 1, No 2 (2021): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v1i2.14019

Kajian dinamika populasi predator-prey di suatu ekosistem dengan adanya kanibalisme pada predator dilakukan pada penelitian ini. Ketika ada kanibalisme di tingkat predator dikhawatirkan populasi predator itu akan menurun atau terjadi kepunahan, sehingga populasi prey menjadi tidak terkontrol dan akan terjadi ketidakseimbangan ekosistem. Oleh karena itu, pada penelitian ini dibangunlah model matematika predator-prey dengan faktor kanibalisme pada predator berbentuk sistem persamaan diferensial biasa non linier dengan tiga persamaan. Pada model predator-prey tersebut ditemukan dua titik kesetimbangan yang memiliki kemungkinan stabil yaitu titik kesetimbangan ketika tidak ada prey dan titik kesetimbangan ketika kedua spesies eksis di ekosistem tersebut . Hasil sensitivitas analisis menunjukkan bahwa sifat kestabilan lokal dari titik maupun bergantung pada parameter kanibalisme yakni dan . Lebih lanjut, untuk titik telah dibuktikan sifat kestabilan global menggunakan fungsi lyapunov. Hasil simulasi numerik mengilustrasikan hasil analisa yang sudah diperoleh, sehingga ditemukan kemungkinan terjadinya limit cycles yang menandakan adanya bifurkasi hopf.

ANALISIS DINAMIK PENYEBARAN HUMAN PAPILLOMAVIRUS DENGAN PENGARUH VAKSINASI DAN SKRINING Rosidah, Miftakhul; Widayani, Heni; Pagalay, Usman
Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i1.14712

Cervical cancer caused by Human Papillomavirus (HPV) is a serious health problem in Indonesia. The spread of HPV is still an unresolved problem even though a vaccine has been found and screening has been carried out in health facilities in Indonesia. In this study, the dynamic analysis of the HPV spread model was studied by categorizing the population into 6 sub-populations, namely the susceptible individual population (S(t)), the vaccinated individual population (V(t)), the infected individual population who were not aware 〖(I〗_u (t)), population of infected and screened individuals 〖(I〗_s (t)), population of individuals exposed to cervical cancer (C(t)), and population of cured individuals (R(t)). The model describes the dynamic rate of HPV spread which has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The results of this study indicate that the disease-free equilibrium point is unstable, meaning that there is still a possibility that infection will occur in the population. The numerical simulation illustrates that the percentage of individuals who are vaccinated will reduce the increase in the number of unconscious infected individuals and individuals with cervical cancer. Increasing the screening rate in the population will also reduce the number of unconsciously infected individuals and individuals with cervical cancer.

Analisis Model Stokastik Penularan Virus Hepatitis B Laila, Arina Nur; Pagalay, Usman; Widayani, Heni
Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i1.14467

The spread of hepatitis B virus (HBV) infection has been widely studied using the deterministic SIR model, in which individuals who recover from acute infection have temporary immunity to the virus. However, this deterministic model uses a constant rate of viral infection over time. This is not in accordance with the fact that the infection rate is a random parameter that depends on time. This study discusses the analysis of the stochastic model of hepatitis B virus transmission. The purpose of this study is to construct the SIR stochastic model by dividing the infection rate into two, namely the rate of acute and chronic infection following the Wiener process. The model is then searched for an analytical solution referring to the Ito formula. The analytical solution and the Wiener process are described by substituting parameter values in the form of acute and chronic infection rates (β+α), cure rate (γ), and initial values (S(0) and I(0)) to obtain the mean value (μ). and the standard deviation (σ) of dS(t) and dI(t). The results of the simulation show that the number of infected individuals (I(t)) will decrease rapidly if (γ) is greater but will increase rapidly if (β+α) and (I(0)) are greater.

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