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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Fourier BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) KACANEGARA Jurnal Pengabdian pada Masyarakat Jurnal Matematika UNAND Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Jurnal Berdaya Mandiri Jurnal Ilmiah Matematika Unnes Journal of Mathematics Bulletin of Applied Mathematics and Mathematics Education Parameter: Jurnal Matematika, Statistika dan Terapannya
Yudi Ari Adi, Yudi Ari
Departemen Matematika, Fakultas Sains Dan Teknologi Terapan, Universitas Ahmad Dahlan
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MODEL PREDATOR-PREY DENGAN KONTROL OPTIMAL PADA BUDIDAYA BAWANG MERAH Wibowo, Rohman Prasetyo; Adi, Yudi Ari
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.15722

Abstract

Shallot farming creates a predator–prey interaction between leaf miner flies as pests and pesticides as control agents applied by farmers. This article discusses the application of a predator–prey mathematical model to shallot cultivation in Selopamioro Village, Imogiri, Bantul. The interaction between predator and prey is mathematically formulated using the Holling-Tanner response function and analyzed numerically using the fourth-order Runge-Kutta method to examine equilibrium point stability. The model is further developed by introducing optimal control in the form of manual pest removal and reduced insecticide dosage, aiming to improve shallot productivity through more effective pest management. The state and co-state conditions are solved using the Forward–Backward Sweep method based on the fourth-order Runge-Kutta on the Hamiltonian function. Simulation results show that the implementation of control significantly reduces the leaf miner fly population from 997 to 141 individuals and decreases the duration of insecticide application from 39 days to just 10 days
DINAMIKA INTERAKSI SISTEM IMUN TUBUH DAN MYCOBACTERIUM TUBERCULOSIS MENGGUNAKAN PERSAMAAN DIFERENSIAL FRAKSIONAL Rosita, Rosita; Adi, Yudi Ari
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.275-292.2025

Abstract

Tuberkulosis yang disebabkan oleh bakteri Mycobacterium tuberculosis (MTb) merupakan penyakit menular yang utamanya menyerang paru-paru dan masih menjadi penyebab kematian global. Artikel ini mengkaji dinamika interaksi antara sis tem imun tubuh dan bakteri MTb melalui model matematika yang berbentuk persamaan diferensial fraksional dengan mempertimbangkan pemberian vaksinasi. Model fraksional tipe Caputo-Fabrizio yang digunakan dalam model ini merepresentasikan efek memori dan ketergantungan temporal dalam respons imun, salah satu aspek yang penting dalam infeksi MTb. Selanjutnya dilakukan analisis kestabilan titik kesetimbangan dan sensi tivitas model, serta mensimulasikan dinamika sistem imun. Analisis dilakukan untuk menentukan kestabilan titik kesetimbangan dan pengaruh variasi orde fraksional ter hadap kecepatan konvergensi. Hasil menunjukkan adanya dua titik kesetimbangan: titik bebas infeksi yang stabil jika R0 < 1 dan titik infeksi yang stabil pada kondisi tertentu. Simulasi numerik memperlihatkan bahwa semakin kecil orde fraksional, semakin cepat respons sel imun menuju titik kestabilan, menunjukkan pengaruh signifikan dari param eter orde α terhadap kecepatan konvergensi. Temuan ini diharapkan dapat memberikan wawasan baru untuk pengendalian infeksi MTb secara lebih efektif melalui pendekatan model fraksional.
DETERMINISTIC AND STOCHASTIC DENGUE EPIDEMIC MODEL: EXPLORING THE PROBABILITY OF EXTINCTION Ndii, Meksianis Z.; Adi, Yudi Ari; Djahi, Bertha S
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (524.68 KB) | DOI: 10.30598/barekengvol16iss2pp583-596

Abstract

Dengue, a vector-borne disease, threatens the life of humans in tropical and subtropical regions. Hence, the dengue transmission dynamics need to be studied. An important aspect to be investigated is the probability of extinction. In this paper, deterministic and stochastic dengue epidemic models with two-age classes have been developed and analyzed, and the probability of extinction has been determined. For the stochastic approach, we use the Continuous-Time Markov Chain model. The results show that vaccination of adult individuals leads to a lower number of adult infected individuals. Furthermore, the results showed that a higher number of initial infections causes a low probability of dengue extinction. Furthermore, factors contributing to an increase in the infection-related parameters have to be minimized to increase the potential reduction of dengue cases.
GLOBAL STABILITY OF DISEASE-FREE EQUILIBRIA IN COVID-19 SPREAD THROUGH LIVING AND INANIMATE OBJECTS MATHEMATICAL MODEL Wiraya, Ario; Adi, Yudi Ari; Fitriana, Laila; Triyanto, Triyanto; Putri, Amellia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp1873-1884

Abstract

Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model.
Pelatihan pengendalian Organisme Pengganggu Tanaman (OPT) pada budidaya pisang di Kelurahan Serut Kabupaten Gunungkidul Aji, Oktira Roka; Adi, Yudi Ari; Salamah, Umi; Ardi, Subhan Zul; Haryadi, Bagus
KACANEGARA Jurnal Pengabdian pada Masyarakat Vol 7, No 4 (2024): November
Publisher : Institut Teknologi Dirgantara Adisutjipto

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28989/kacanegara.v7i4.2224

Abstract

Pertanian adalah sektor penting di Kabupaten Gunung Kidul, DIY, dengan budidaya pisang memiliki potensi ekonomi yang menjanjikan. Program pengabdian kepada masyarakat ini bertujuan meningkatkan pengetahuan dan keterampilan petani dalam pengendalian organisme pengganggu tanaman (OPT) secara ramah lingkungan. Metode yang digunakan mencakup pendataan masalah, persiapan materi, pelatihan, evaluasi, dan tindak lanjut. Pelatihan dilakukan untuk 18 petani muda dari Sanggar Tani Muda di Kelurahan Serut, meliputi teknik pengendalian OPT preventif, biologis, dan kimiawi. Hasil menunjukkan peningkatan pengetahuan signifikan dari pre-test ke post-test, serta umpan balik positif dari peserta. Dengan demikian, program ini efektif dalam meningkatkan pemahaman dan keterampilan peserta, mendorong praktik pertanian berkelanjutan, serta meningkatkan produksi dan kesejahteraannya.
PELATIHAN OPTIMASI IRIGASI SMART FARMING DI KALURAHAN SERUT, GEDANGSARI, GUNUNG KIDUL Adi, Yudi Ari; Salamah, Umi; Haryadi, Bagus; Roka Aji, Oktira; Zul Ardi, Subhan; Rossa Puteri Baharie, Sri
Jurnal Berdaya Mandiri Vol. 6 No. 2 (2024): JURNAL BERDAYA MANDIRI (JBM)
Publisher : Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/jbm.v6i2.6145

Abstract

The banana commodity is one of the prioritized commodities in Gunung Kidul Regency. The Young Farmers' Studio and Youth Organization “Solid Berkarya” in Serut Village are trying to develop banana plants by managing critical land into productive land using smart-farming irrigation systems. The concept of smart farming includes using technology such as sensors, connected devices (IoT), data analytics, artificial intelligence, and agricultural management software to create an efficient farming system. The irrigation system needs to apply optimization of timing and intensity tailored to the needs of the plants. The geographical terraced land conditions require unique methods to maximize agricultural yields. In banana cultivation, geographical conditions, climate, soil conditions, and water availability are crucial, so the community's knowledge and skills in irrigation on critical land must be improved. Therefore, banana irrigation training is conducted in this community service, especially related to water availability optimization. In this training, the participant's level of knowledge is measured by conducting pre-tests and post-tests related to irrigation optimization materials. From the test results, it can be seen that there is an increase in community knowledge from 6.44 before training to 9.0 after training. Thus, there is an increase in knowledge by 53.4%. The level of community satisfaction with the implementation of this service activity is 96.43%. keywords: Serut Village, Optimization, Smart-farming, Irrigation
A Within-host Tuberculosis Model Using Optimal Control Adi, Yudi Ari
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 5, No 1 (2021): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v5i1.3813

Abstract

 In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of  tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of  tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.
Fractional Modeling of the Interaction Between Mycobacterium Tuberculosis and Its Response to Antibiotics Khairiah, Inayah Alifah; Adi, Yudi Ari
Parameter: Jurnal Matematika, Statistika dan Terapannya Vol 4 No 2 (2025): Parameter: Jurnal Matematika, Statistika dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/parameterv4i2pp223-238

Abstract

Mycobacterium tuberculosis is a bacterium that causes tuberculosis, which is the second most common infectious disease in the world and generally attacks the lungs. It is important to formulate the dynamics of interactions and the effects of antibiotic administration on Mycobacterium tuberculosis into a mathematical model, especially using a fractional order approach. In this study, a model was developed using the Caputo-Fabrizio derivative. The purpose of the study was to study the dynamics of interactions between bacteria and antibiotics, where the administration of antibiotics causes the bacterial population to be divided into two types, namely sensitive bacteria and bacteria resistant to antibiotics. Based on the model built, four equilibrium points were obtained. Stability analysis shows that these equilibrium points are locally asymptotically stable under certain conditions. To support the results of the analysis, numerical simulations were carried out using the three-step Adams-Bashforth method with the Caputo-Fabrizio derivative. The simulation results showed that the smaller the value of the fractional order parameter , the faster the system reaches the equilibrium point. Although the value of affects the speed of convergence, it does not affect the stability of the equilibrium point.
MATHEMATICAL MODEL OF THE SPREAD OF HIV/AIDS CONSIDERING THE LEVEL OF IMMUNITY Linarta, Anisa Sukma; Adi, Yudi Ari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0211-0226

Abstract

The immune system, crucial for defending the body against infections, is a primary target of HIV, compromising its ability to resist illnesses that may progress to AIDS. This study develops a mathematical model incorporating the immune response to simulate HIV/AIDS transmission dynamics. The model analysis includes the determination of equilibrium points, the basic reproduction number , and bifurcation behavior. Two equilibrium points are identified: the disease-free and endemic equilibria. The disease-free equilibrium is asymptotically stable when , while the endemic equilibrium is stable when , indicating persistent transmission. A forward bifurcation occurs at , which biologically implies that reducing below one is critical for eliminating the disease. Numerical simulations using actual data yield an estimated with a Mean Absolute Percentage Error (MAPE) of 4.5583%, indicating good agreement between the model and data. Although the model assumes homogeneous mixing and constant parameters, it provides meaningful insights into HIV/AIDS transmission and offers a quantitative basis for evaluating control strategies.
Co-Authors A.A. Ketut Agung Cahyawan W Agus Miftakus Surur Agus Miftakus Surur, Agus Miftakus Ardi, Subhan Zul Djahi, Bertha S Feriastuti, Erina Tri Fitriana, Laila Ginting, Rini Sania br Haafidhoh, Eva Annisa Haryadi, Bagus Irsalinda, Nursyiva Khairiah, Inayah Alifah KHOERUNNISA KHOERUNNISA Kurnia, Titik Linarta, Anisa Sukma Maulan Aziz Syafii Mr. Sugiyanto, Mr. NAFISAH, ZULFATIN Ndii, Meksianis Z Nursyiva Irsalinda Oktira Roka Aji Putri, Amellia Rosita Rosita Rossa Puteri Baharie, Sri SAHRUL AHMAD Sugiyanto Sugiyanto Sugiyarto Surono Sugiyarto Surono, Sugiyarto Syafii, Maulan Aziz Thariq Muhariyanto Trimanto, Rido Umi Salamah Wibowo, Rohman Prasetyo Wiraya, Ario Zul Ardi, Subhan Zulfatin Nafisah