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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Agrokreatif Jurnal Ilmiah Pengabdian kepada Masyarakat Jurnal Riset Mahasiswa Matematika Journal of Research on Community Engagement
Heni Widayani
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Agriculture, Biological Sciences & Forestry Humanities Mathematics Social Sciences

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Implementasi Metode Beda Hingga Tak Standar untuk Model Penyebaran Campak Rizqyah, Ilfa Wardatul; Kusumastuti, Ari; Widayani, Heni
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.v1i3.14307

Abstract

The measles distribution model is a system of differential equations that is included in a continuous dynamic system. This research focuses on transforming the continuous form into discrete form by discretization using non-standard finite difference and stability analysis which is then carried out by numerical simulations to prove its stability graphically. Based on the analysis, it is found that the measles distribution model which is assumed to have two fixed points, namely the disease-free fixed point (R_01) and the endemic fixed point (R_01), is stable. The stability of the two fixed points is proven by the Schur-Cohn criteria and is obtained stable with the condition 0ϕ(h)≤5 which meets the value of h0. The results of the numerical simulation show that the measles distribution model is dynamically consistent and tends to the fixed point. In addition, numerical simulations show that the larger the value of h, the more the graph tends to the fixed point. 
Penyelesaian Sistem Persamaan Hukum Laju Reaksi dengan Metode Transformasi Differensial Maftuhah, Siti; Widayani, Heni; Kusumastuti, Ari
Jurnal Riset Mahasiswa Matematika Vol 2, No 4 (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.v2i4.16805

Abstract

This research is focused on solving the rate law equation by using the differential transformation method. The rate law equation describes the chemical reaction problem from the concentration of a reactant that produces a product. The differential transformation method is a semi-analytic numerical method that can provide approximate solutions in the form of a series because the method is obtained from the expansion of the Taylor series expansion. With the help of Maple software, a comparison of the solution plots of y_1 (t),y_2  (t) and y_3 (t), can be observed that the difference in computational results between the Runge-kutta method and the differential transformation depends on the order of k. The curve of the differential transformation method is getting closer to the curve of the Runge-Kutta method at a certain value of k for each y_1 (t),y_2  (t) and y_3 (t). The conclusion of this research is that the application of the differential transformation method has been successfully carried out in the case of a system of ordinary differential equations. For further research, the researcher suggests that the next research applies the method of differential transformation in cases and initial values that are more varied.
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

Abstract

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 Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan KT, Ummul Aulia; Widayani, Heni; Kusumastuti, Ari
Jurnal Riset Mahasiswa Matematika Vol 2, No 3 (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.v2i3.16753

Abstract

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If ,  there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.
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

Abstract

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

Abstract

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.
Solusi Eksak Sistem Imun Terhadap Virus Ebola Aisyiyah, Amadhea Aisyatul; Widayani, Heni; Herawati, Erna
Jurnal Riset Mahasiswa Matematika Vol 3, No 2 (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.v3i2.22449

Abstract

The Ebola virus is a deadly disease that causes blood clots in the body's organs and is spread through direct contact with the blood or body fluids of sufferers. Based on this, the immune system in the body will continue to decrease and cause Ebola Hemorrhagic Fever. The 2014-2016 Ebola outbreak in West Africa has accelerated the development of several preventive vaccines against the Ebola virus. The goal of the vaccination is to induce immunity against infectious diseases. And also to stimulate the immune system and its ability to store and remember information about specific pathogens, leading to long-term protective immunity. The model equation for the Ebola virus vaccine in this study involves the concentration of the antigen which is a variable , by means of which the vaccine is inserted into the patient's body where it will attach to B memory cells which are variable , which will then be stimulated by the cells short-lived antibodies are denoted by variables  or long-lived cells are denoted by variables , while antibodies will prove efficacy denoted by variables  on the patient's immune response. The simulation of the exact solution for the Ebola vaccine uses the integration factor method which will later be compared with numerical simulations according to the parameter values from the research of Irene Balelli et al (2020). The simulation obtained has a very small calculation error value for each variable, which means that the exact value of the Ebola virus vaccination model shows that there is no significant difference to the numerical solution using the order 45 Rungge Kutta method, the largest resulting numerical error is 2.29640283510782×〖10〗^9.
Implementasi Fuzzy Multi Criteria Decision Making Pada Seleksi Beasiswa Bank Indonesia Fauzan, Hakmi Rais; Alisah, Evawati; Widayani, Heni
Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (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.v1i4.14463

Abstract

The Bank Indonesia Scholarship is a scholarship provided by Bank Indonesia for students at various universities, one of which is UIN Maulana Malik Ibrahim Malang. In the scholarship selection process, there are several criteria that affect the graduation of prospective scholarship recipients. However, often the process is not transparently. So a calculation method is needed, one of which is using Fuzzy Multi Criteria Decision Making (FMCDM). With FMCDM it can help to get an accurate and optimal decision on scholarship recipients. The FMCDM process begins with collecting information related to scholarships, scholarship applicants, and a set of criteria that will be used for consideration of scholarship acceptance. The set of criteria consists of 11 criteria, namely, Academic Achievement Index (GPA), international level achievement, national level achievement, provincial level achievement, district/city level achievement, father's occupation, mother's income, number of family dependents, house area, land and building tax, as well as electricity bills. The next step is to evaluate the fuzzy set by aggregating the weight of the criteria and the degree of compatibility of each alternative with the criteria. The aggregation result is called the fuzzy fit index which consists of 3 values, namely, the y value which represents the lower limit of the aggregation result, the q value which represents the middle limit, and the z value which represents the upper limit value. The three values are ranked using a ranking method for fuzzy numbers with a degree of optimism. So that the total integral value for each alternative will be obtained, which will be the decision in accepting the scholarship. From the results of the FMCDM, there is a ranking of decision alternatives from the highest priority to the lowest in determining scholarship acceptance. 
Asset-Based Community Development: Pengembangan Produk Pertanian Sari Jeruk Khas Dusun Precet Karisma, Ria Dhea Nur; Widayani, Heni; Naschicuddin, Achmad
JRCE (Journal of Research on Community Engagement) Vol 4, No 1 (2022): Journal of Research on Community Engagement
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrce.v4i1.17410

Abstract

Oranges are a type of fruit that contains lots of vitamin C and fiber. One of the citrus producing places in Malang is Dusun Precet, which is part of Sumbersekar Village. The abundant citrus plantation products in Precet Hamlet have not been further processed by the residents, so the price falls during the harvest season. Farmers left some of it to rot in the garden, because the cost of picking during the harvest season is more expensive than the selling prices. Whereas the oranges can have a higher selling value if it is processed into orange juice products. The Asset-Based Community Development (ABCD) strategy was implemented by the UIN Maulana Malik Ibrahim Malang team in the form of training activities for processing orange juice products. The basic mindset in ABCD theory on assisted objects has five key steps, namely discovery, dream, design, define, and destiny. Assets that support the ABCD theory in assisted objects are categorized into four, namely human assets, natural assets, economic assets, and social assets. Dusun Hamlet is potential place to process citrus fruits becomes fresh orange juice that can be consumed by the wider community. Moreover, orange juice is produced without using preservatives so that it can be consumed by various ages.
Pendampingan Pengawetan dan Pengemasan Sayuran Pasca Panen Sebagai Strategi Pendorong Perekonomian Petani Precet Widayani, Heni; Layla, Ria Dhea; Naschicuddin, Achmad
JRCE (Journal of Research on Community Engagement) Vol 3, No 2 (2022): Journal of Research on Community Engagement
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrce.v3i2.15770

Abstract

The impact of Covid-19 pandemic has made vegetable farmers suffer losses due to hampered distribution of fresh vegetables. Fresh vegetables that have been harvested but not immediately processed will easily wilt which will reduce the selling value. This phenomenon occurs in many vegetable plantation areas, one of which is in the Dusun Precet. Vegetable farming products are a source of livelihood for the people of Dusun Precet who mostly work as vegetable farmers. The main problem for vegetable farmers is that the price of vegetables is cheap at harvest time, so that farmers experience losses. Post-harvest vegetable processing and packaging training is one solution that can be done to overcome this problem. Processing and packaging of fresh vegetables is expected to make harvested vegetables last longer and local vegetables can be marketed more widely. In addition, team from UIN Maulana Malik Ibrahim Malang also provide socialization regarding the nutrient of frozen vegetables as still same as the fresh one if packaged properly and correctly. This program is expected to be able to encourage the economy of the people in Dusun Precet in the future.
Co-Authors Aisyiyah, Amadhea Aisyatul Angga Dwi Mulyanto Angga Rusdinar Anita Triska Ari Kusumastuti Ari Kusumastuti Arina Nur Laila Bhandari, Harish Chandra Dwi Safitri Dwi Safitri, Dwi Erna Herawati, Erna Evawati Alisah Fauzan, Hakmi Rais Hakmi Rais Fauzan Hisyam Fahmi Icha Zakiyya Nafisah Roza Ig. Prasetya Dwi Wibawa Ilfa Wardatul Rizqyah Karisma, Ria Dhea Nur KT, Ummul Aulia Laila, Arina Nur Layla, Ria Dhea Meta Kallista Miftakhul Rosidah Naschicuddin, Achmad Nuning Nuraini Nur Karisma, Ria Dhea Ramdhan Nugraha Rizqyah, Ilfa Wardatul Rosidah, Miftakhul siti maftuhah Siti Maftuhah Ummul Aulia KT Usman Pagalay