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All Journal Jurnal Fakultas Ekonomi : OPTIMAL Jurnal Bisnis Jurnal Manajemen dan Keuangan AKSIOMA: Jurnal Program Studi Pendidikan Matematika Jurnal Hubungan Internasional Jurnal Manajemen Magister Darmajaya Communication in Biomathematical Sciences JURNAL PENDIDIKAN TAMBUSAI EIGEN MATHEMATICS JOURNAL Journal of Information Systems and Informatics MAKILA: Jurnal Penelitian Kehutanan Jurnal Pengabdian Masyarakat Tapis Berseri Jurnal Pengabdian, Pembelajaran dan Pemberdayaan Ekonomi Masyarakat (JP3EM)
Muhammad Rafiq
Jurusan Manajemen, IBI Darmajaya Jl. Z.A. Pagar Alam No. 93 Labuhan Ratu – Bandar Lampung – Indonesia 35142 Telp : (0721) 787214
Agriculture, Biological Sciences & Forestry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Environmental Science Mathematics Social Sciences Other

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Journal : EIGEN MATHEMATICS JOURNAL

 1 
Penerapan Kendali Optimal pada Model Matematika SEITRS Penularan Tuberkulosis dengan Variabel Kendali Sosialisasi dan Terapi Rafiq, Muhammad; Wigantono, Sri; Raming, Indriasri
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.322

Abstract

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis, which remains a serious public health concern. The objective of this study is to develop, analyze, and propose an optimal control strategy for the transmission dynamics of TB using an SEITRS mathematical model. The model consists of five population compartments: Susceptible (S), Exposed (E), Infected (I), Treatment (T), and Recovered (R). The methodology involves constructing the SEITRS model, determining the equilibrium points, and analyzing their stability under different conditions of the basic reproduction number. The model has two equilibrium points, namely the non-endemic and endemic equilibrium. If the basic reproduction number is less than one and certain conditions are satisfied, the non-endemic equilibrium is locally asymptotically stable. Conversely, if the basic reproduction number is greater than one and specific conditions are met, the endemic equilibrium becomes locally asymptotically stable. Furthermore, this study provides optimal control strategies in the SEITRS model. We use two control variables in this model, namely socialization and therapy, to reduce the number of infected individuals. The sufficient conditions for the existence of optimal controls are derived using Pontryagin’s Maximum Principle. Numerical simulations are then conducted to examine the impact of applying these controls on the system. The simulation results indicate that the simultaneous implementation of socialization and therapy controls is effective in reducing the number of TB-infected individuals.
Co-Authors Adistia, Firly Afiatul, Elsa Vanny Yuli Afriyani, Dhea Agusman, Agusman Aris Munandar Aswin - Azroy, Muhammat Baharuddin, Rhamdhani Fitrah Basoka, Muhammad Darmawan Bayu Tri Kurniawan Betty Magdalena, Betty Christiyanto, Tedy Deryanto, Deryanto Dini Safitri Endang Hendrayanti Hasriani Muis Jannah, Nuryana Maghfirotul Jefri Marzal Kamran, Ayesha Lius, Jennifer Maarif, Fadjri Marbun, Posmanto Mario Mario Martiyana, Linda Miranti, Peni Alya Mohamad Noor, Nursyazwani Mohd Yatim, Siti Ainor Muhammad Adam Suni Munawwaroh, Hafizotul Nainggolan, Misdiantri Kurnia Putri, Septiana Yusnita Putri, Shelmy Rahma Sania Rahmatullah, Arif Ramadhani, Viana Nurwidi Raming, Indriasri Sandra, Evita Saputra, Candra Ferdian Saputra, Deli Sheng, Mao Sri Wahyuni Sri Wigantono Sukma, Dinny Suni, Muhammad Adam Suseno, Tri Joko Syamsurizal - - Umar, Mohamad Fahrul Himalaya Widjayanti , Yoan Budi Zeb, Shah Zulfiqar, Sabahat