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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

Author-ID : 1456125

Agriculture, Biological Sciences & Forestry Humanities Mathematics Social Sciences

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Pemanfaatan Posdaya Masjid Baitussalam sebagai Pusat Pengolahan Sari Buah Markisa di Dusun Robyong, Desa Wonomulyo, Kabupaten Malang Ari Kusumastuti; Heni Widayani; Angga Dwi Mulyanto; Hisyam Fahmi
Agrokreatif: Jurnal Ilmiah Pengabdian kepada Masyarakat Vol. 5 No. 2 (2019): Agrokreatif Jurnal Ilmiah Pengabdian Kepada Masyarakat
Publisher : Institut Pertanian Bogor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/agrokreatif.5.2.89-95

The formation of the family empowerment post (Posdaya) at Robyong Sub-village of Poncokusumo is intended to increase family income through the application of technology to utilize existing natural potential endowment. The mosque-based family empowerment post could functionalize mosque as a social-economic community center as well as a religious activity center. The community empowerment program at Baitussalam-Mosque Posdaya has become a pilot project in the mosque-based society empowerment. The implementation of the program consisted of family data collection, socialization, and determination of the Posdaya main program according to local potential. Discussion with locals has concluded that the need for training about passion fruit (Passiflora edulis) processing as a main program of Posdaya, since passion fruit has become potential and not yet being utilized optimally. Participants are locals around Baitussalam Mosque, especially housewives. Direct observation shows that locals actively participate in the Posdaya program and supported also by Posdaya organizer and community leaders. The resulting product was responded positively by the market. The product was already marketed out of Java as a souvenir from the Robyong sub-village of Poncokusumo. This program is expected to become a micro-group enterprise from Robyong sub-village with product diversification, good marketing strategy, and good production management in the future.

Pyramid Population Prediction using Age Structure Model Heni Widayani; Nuning Nuraini; Anita Triska
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 6, No 2 (2020): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Population composition in a country by sex and age-structure often illustrated through the Population Pyramid. In this study, an age-structure model will be constructed to predict the population pyramid shape in the coming year. It is assumed that changes in population are affected by natality and mortality number in each age group, ignoring migration rates. The proposed age structure model formulated as a first-order partial differential equation with the non-negative initial condition. The boundary condition is given by the number of births which is proportional to the number of women at childbearing age. Then, this age structure model implemented utilizing United Nations Data to predict population pyramids of Indonesia, Brazil, Japan, the USA, and Russia. The population pyramid prediction of the five countries shows different characteristics, according to whether it is a developing or developed country. The results of this study indicate that the age structure model can be used to predict the composition of the population in a country in the next few years. Indonesia is predicted to be the highest populated country in 2066, compared to the other four countries. This result can be used as a reference for the government to plan policies and strategies according to age groups to control population explosion in the future.

Implementasi Metode Beda Hingga Tak Standar untuk Model Penyebaran Campak Ilfa Wardatul Rizqyah; Ari Kusumastuti; Heni Widayani
Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

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.

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

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 Miftakhul Rosidah; Heni Widayani; Usman Pagalay
Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

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.

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.

Implementasi Fuzzy Multi Criteria Decision Making Pada Seleksi Beasiswa Bank Indonesia Hakmi Rais Fauzan; Evawati Alisah; Heni Widayani
Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

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.

Analisis Dinamik Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan Ummul Aulia KT; Heni Widayani; Ari Kusumastuti
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

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.

Penyelesaian Sistem Persamaan Hukum Laju Reaksi dengan Metode Transformasi Differensial Siti Maftuhah; Heni Widayani; Ari Kusumastuti
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

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.

Co-Authors Aisyiyah, Amadhea Aisyatul Angga Dwi Mulyanto Anita Triska Ari Kusumastuti Ari Kusumastuti Arina Nur Laila Dwi Safitri Dwi Safitri, Dwi Erna Herawati, Erna Evawati Alisah Fauzan, Hakmi Rais Hakmi Rais Fauzan Hisyam Fahmi Icha Zakiyya Nafisah Roza Ilfa Wardatul Rizqyah Karisma, Ria Dhea Nur KT, Ummul Aulia Laila, Arina Nur Layla, Ria Dhea Miftakhul Rosidah Naschicuddin, Achmad Nuning Nuraini Nur Karisma, Ria Dhea Rizqyah, Ilfa Wardatul Rosidah, Miftakhul siti maftuhah Siti Maftuhah Ummul Aulia KT Usman Pagalay

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