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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
Yudi Ari Adi, Yudi Ari
Departemen Matematika, Fakultas Sains Dan Teknologi Terapan, Universitas Ahmad Dahlan
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Journal : Bulletin of Applied Mathematics and Mathematics Education

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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.
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