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Yudi Ari Adi, Yudi Ari
Departemen Matematika, Fakultas Sains Dan Teknologi Terapan, Universitas Ahmad Dahlan
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Optimal control on education, vaccination, and treatment in the model of dengue hemorrhagic fever Haafidhoh, Eva Annisa; Adi, Yudi Ari; Irsalinda, Nursyiva
Bulletin of Applied Mathematics and Mathematics Education Vol. 2 No. 2 (2022)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v2i2.7617

Abstract

Dengue hemorrhagic fever (DHF) is an infection caused by the dengue virus which is transmitted by the Aedes aegypti mosquito. In this paper, a model of the spread of dengue disease is developed using optimal control theory by dividing the population into Susceptible, Exposed, Infected, and Recovered (SEIR) sub-populations. The Pontryagin minimum principle of the fourth-order Runge-Kutta method is used in the model of the spread of dengue disease by incorporating control factors in the form of education and vaccination of susceptible human populations, as well as treatment of infected human populations. Optimum control aims to minimize the infected human population in order to reduce the spread of DHF. Simulations were carried out for two cases, namely when the basic reproduction number is less than one for disease-free conditions and greater than one for endemic conditions. Based on numerical simulations of the SEIR epidemic model with controls, it results that the optimal strategy is achieved if education controls, vaccinations, and medication are used.
A mathematical model of meningitis with antibiotic effects Ginting, Rini Sania br; Adi, Yudi Ari
Bulletin of Applied Mathematics and Mathematics Education Vol. 3 No. 1 (2023)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v3i1.9475

Abstract

The mathematical model in this study is a SCIR-type meningitis disease spread model, namely susceptible (S), carrier (C), infected (I), and recovery (R). In the model used, there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The conditions and stability of the equilibrium point are determined by the basic reproduction number, which is the value that determines whether or not the spread of meningitis infection in a population. The results of this study show that the stability of the disease-free equilibrium point and the endemic equilibrium point are locally asymptotically stable and by using the Lyapunov Function method it is found that the disease-free equilibrium point will be globally stable when, while the endemic equilibrium point will be globally stable when numerical simulations perform to support the theoretical results.
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.
Co-Authors A.A. Ketut Agung Cahyawan W Agus Miftakus Surur Agus Miftakus Surur, Agus Miftakus Bagus Haryadi Djahi, Bertha S Feriastuti, Erina Tri Fitriana, Laila Ginting, Rini Sania br Haafidhoh, Eva Annisa Haryadi, Bagus Irsalinda, Nursyiva KHOERUNNISA KHOERUNNISA Kurnia, Titik 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 Subhan Zul Ardi Sugiyanto Sugiyanto Sugiyarto Surono Sugiyarto Surono, Sugiyarto Syafii, Maulan Aziz Thariq Muhariyanto Trimanto, Rido Umi Salamah umi salamah Wibowo, Rohman Prasetyo Wiraya, Ario Zul Ardi, Subhan Zulfatin Nafisah