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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Zeta - Math Journal Jambura Journal of Mathematics Square : Journal of Mathematics and Mathematics Education Journal of Fundamental Mathematics and Applications (JFMA) International Journal of Computing Science and Applied Mathematics-IJCSAM
Zulaikha Zulaikha
Universitas Islam Negeri Walisongo
Arts Humanities Decision Sciences, Operations Research & Management Education Mathematics

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Kontrol Optimal pada Model Epidemi SEIQR dengan Tingkat Kejadian Standar Zulaikha, Zulaikha; Trisilowati, Trisilowati; Fadhilah, Intan
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Publisher : Mathematics Department

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (749.077 KB)

Abstract

Penelitian ini dilakukan dengan modifikasi model epidemik SEIQR dengan tingkat kejadian standar dan kontrol optimal. Kontrol optimal dilakukan dengan menambahkan dua variabel kontrol yaitu usaha pengontrolan kontak langsung antara populasi rentan dengan populasi terinfeksi, dan pemberian obat pada populasi terinfeksi. Tujuan penelitian ini adalah untuk meminimumkan jumlah subpopulasi yang terinfeksi, jumlah subpopulasi laten, jumlah biaya edukasi dan biaya pemberian obat. Kondisi kontrol optimal pada penelitian ini diperoleh dengan menggunakan prinsip minimum Pontryagin. Selanjutnya, simulasi numerik dilakukan dengan metode Sweep Maju-Mundur untuk menunjukkan bagaimana pengaruh adanya kontrol terhadap model epidemik. Hasil penelitian yang dilakukan menunjukkan bahwa dengan adanya kontrol terlihat efektif dalam menekan jumlah pertumbuhan subpopulasi terinfeksi dengan subpopulasi laten.
Pengaruh Partikel Nano Zn dan ZnO terhadap Aliran MHD Fluida Nano Pada Lapisan Batas Bola Bermagnet Yolanda Norasia; Zulaikha Zulaikha
Square : Journal of Mathematics and Mathematics Education Vol 1, No 2 (2019)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2019.1.2.4792

Abstract

Fluida terdiri atas fluida Newtonian dan fluida non-Newtonian. Fluida newtonian adalah fluida yang tidak mengalami perubahan viskositas ketika terdapat gaya yang bekerja terhadap fluida tersebut. Fluida non-Newtonian bersifat sebaliknya dari fluida newtonian. Beberapa contoh fluida newtonian adalah air, minyak, dan etanol. Fluida nano adalah salah satu fluida newtonian yang terdiri atas fluida dasar air dan partikel nano. Partikel nano terdiri atas logam dan oksida logam. Partikel nano berupa logam adalah Zinc yang memiliki simbol Zn. Partikel nano berupa non logam adalah Zinc Oxide yang memiliki simbol ZnO. Pada penelitian ini dibahas mengenai magnetohidrodinamik (MHD) dari aliran fluida nano  dan  yang mengalir melewati bola bermagnet dengan pengaruh konveksi campuran.Pemodelan aliran fluida diperoleh dari persamaan pembangun dimensional yang meliputi persamaan kontinuitas, persamaan momentum, dan persamaan energi. Persamaan pembangun dimensional yang terbentuk ditransformasikan kedalam persamaan non-dimensional.Persamaan non-dimensional kemudian diubah menjadi persamaan similaritas dan diselesaikan menggunakan metode implicit Euler. Hasi lsimulasi menunjukkan bahwa ketika parameter magnetik ditingkatkan, maka kecepatan dan temperature aliran fluida nano Zn-Air dan ZnO-Air mengalami penurunan.Ketika fluida nano Zn-Air dan ZnO-Air dibandingkan, kecepatan aliran fluida nano Zn-Air lebih cepat mengalami peningkatan dibandingkan dengan fluida nano ZnO-Air. Sedangkan untuk profil temperatur, fluida nano ZnO-Air lebih cepat mengalami penurunan temperature dibandingkan dengan fluida nano Zn-Air.Kata kunci: fluida newtonian, fluida nano, magnetohidrodinamik, implisit euler  
MATHEMATICAL MODELLING OF THE SPREAD OF COVID-19 WITH FIRST, SECOND AND THIRD DOSES OF VACCINATION IN SEMARANG CITY Dewi Purnamasari, Mahardika Karunia; Fitriyah, Aini; Zulaikha, Zulaikha
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.19750

Abstract

This research models the spread of Covid-19 by developing the  model. In this model there are seven compartments, namely the susceptible subpopulation (S), the subpopulation that has received the first dose of vaccine (V1), the subpopulation that has received the second dose of vaccine (V2), the subpopulation that has received the third dose of vaccine (V3), the exposed subpopulation (E), infected subpopulation (I), and recovered subpopulation (R). From the model that has been formed, a search for disease-free and endemic equilibrium points is carried out, then looking for the basic reproduction number (R0) as a benchmark for the presence or absence of the spread of Covid-19 in a population, then numerically simulating it using the Matlab R2017a software. The results of this numerical simulation are in accordance with the dynamic analysis carried out, namely if the condition is  then Covid-19 cannot spread, whereas if the condition is  then Covid-19 can spread in a certain area. In addition, the disease cannot spread quickly if the proportion of those who are vaccinated is increased, so that the use of vaccines can be used as an effort to prevent the spread of Covid-19.
Dynamical Analysis of Online Shopping with Beauty Influencer Andani, Meri Teri; Zulaikha, Zulaikha
Jambura Journal of Mathematics Vol 7, No 2: August 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i2.33363

Abstract

This study develops a modified nonlinear mathematical model of online shopping dynamics that explicitly incorporates the direct influence of beauty influencers through promotional content (F) and a parameter α for transition from offline to online shopping without the influence of influencers. The model comprises offline shoppers (L), online shoppers (O), and the amount of promotional content created by beauty influencers (F). Stability analysis shows two equilibrium points: an online shopping-free state E1 locally asymptotically stable when R0 1 and an endemic state E2 locally asymptotically stable when R0 1. Numerical simulations using MATLAB R2013a confirm the analysis, revealing that higher promotional content growth rates (k) and lower decline rates (θ) increase R0 and the online shoppers population. The novelty lies in explicitly modeling influencer-based promotional content as a driver of shopping behavior, offering strategic insights for sustained engagement and customer retention in beauty sector digital marketing.
Deteksi Kartu Tanda Mahasiswa (KTM) Universitas Islam Negeri (UIN) Walisongo dengan Feature Matching Zulaikha, Zulaikha; Alfarabi, Aries Cahya; Aprilianto, Arief Rezky; Fuadi, Maulana Misbahul; Tafrikan, Mohamad; Hardiansyah, Bagus
Zeta - Math Journal Vol 8 No 1 (2023): Mei
Publisher : Universitas Islam Madura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31102/zeta.2023.8.1.1-6

Abstract

UIN Walisongo's student identity card (KTM) does not have much function other than just for student identification. Even if the function is increased, it can be used for absenteeism at lectures, borrowing books, or double as an automated teller card (ATM). Doing absences using KTM requires a feature matching method for matching the intended KTM image with the KTM that is searched for in the student database. The feature matching process is based on feature detection in images using various methods such as ORB and Scale Invariant Feature Transform (SIFT). We can perform the feature matching method using the Brute-Force method and the Fast Library Approximated Nearest Neighbor (FLANN) on Google Colab with Python. The results of feature matching on the FLANN method are more than the Brute-Force method. The validation of the two image feature matching was carried out using the Root Mean Square Error (RMSE) method, resulting in an average value of 10.424. The purpose of this article is to detect student ID cards with matching features in the image. The FLANN and Brute-Force feature matching methods can be used to detect KTM UIN in images. Keywords: feature matching, SIFT, FLANN, Brute-Force, RMSE
Mathematical Stability Analysis of Bullying’s Impact on Student's Mental Health Putri, Devi Marita; Zulaikha, Zulaikha
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33212

Abstract

Bullying is a problem that takes root from the previous generation to the next. The most common bullying cases occur in junior high school students or equivalent with an age range of 13-15 years. Bullying can have an impact on student's mental health. This study develops and analysis a SEIRS-type mathematical model to understand the dynamics of mental health disorders due to bullying among junior high school students. The model includes four subpopulations: subpopulations are vulnerable to mental health disorders due to bullying (S), subpopulations who experience bullying but have not shown any mental health disorders (E), subpopulations that experience mental health disorders due to bullying (I), and subpopulations who have recovered from mental health disorders due to bullying (R). Based on the results of the analysis, two equilibrium points were obtained, namely the mental disorder-free equilibrium point (P_1^*) and the endemic equilibrium point (P_2^*). Next, determine the basic reproduction number using the next matrix generation method. Based on the results of numerical simulation using Matlab R2013a software, it was obtained that if R_01 then the mental disorder-free equilibrium point is stable local asymptotic and mental health disorders due to bullying cannot spread in the student population. Meanwhile, if R_01 then the endemic equilibrium point is stable, local asymptotic and mental health disorders due to bullying can spread in the student population. The rate of interaction between subpopulations vulnerable to mental health disorders due to bullying and subpopulations that experience mental health disorders due to bullying (\alpha) has a significant influence on the number of individuals in each subpopulation.
Optimal Control of HIV-1 Spread in Combination with Nutritional Status and ARV-Treatment Yolanda Norasia; Zulaikha Zulaikha; Mohammad Ghani; Denis Sospeter Mukama
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 8 No. 2 (2022)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Abstract

HIV-1 is a virulent virus, it has the ability to easily spread the virus. This study aims to optimally control the spread of the HIV-1 virus with SIPA (Susceptible-Infection-PreAIDSAIDS) model by using nutritional status and ARV-treatment. Assessment of nutritional status is carried out on people with HIV/AIDS (ODHA). The results showed that the control in the form of nutritional status and ARV-treatment was able to reduce the infected subpopulation. Routine assessment of nutritional status can form balanced nutrition for ODHA. ARV-treatment works by reducing the amount of HIV viral load, so that HIV infection cannot cause disorders of the immune system.
Co-Authors Alfarabi, Aries Cahya Andani, Meri Teri Aprilianto, Arief Rezky Denis Sospeter Mukama Denis Sospeter Mukama Dewi Purnamasari, Mahardika Karunia Fitriyah, Aini Fuadi, Maulana Misbahul hardiansyah, bagus Indira Anggriani Intan Fadhilah, Intan Mohamad Tafrikan Mohamad Tafrikan Mohammad Ghani Mohammad Ghani Norasia, Yolanda Putri, Devi Marita Tafrikan, Mohamad Trisilowati Trisilowati, Trisilowati