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All Journal Jurnal Ilmu dan Teknologi Kelautan Tropis Saintek Perikanan : Indonesian Journal of Fisheries Science and Technology STUDIA ISLAMIKA Jurnal Sejarah JURNAL INFORMATIKA Jurnal Masyarakat dan Budaya Kumawula: Jurnal Pengabdian Kepada Masyarakat International Journal Of Science, Technology & Management (IJSTM) Kreatif: Jurnal Pemikiran Pendidikan Agama Islam Idea Pengabdian Masyarakat An Idea Health Journal MOVE: Journal of Community Service and Engagement Implementasi Manajemen & Kewirausahaan Jurnal BILAL: Bisnis Ekonomi Halal ACROPORA: Jurnal Ilmu Kelautan dan Perikanan Papua Indonesian Journal of Physical Education and Sport Science (IJPESS) An Idea Nursing Journal Depik Jurnal Ilmu-Ilmu Perairan, Pesisir dan Perikanan Ihsanika : Jurnal Pendidikan Agama Islam Transcendent Journal of Mathematics and Applications Jurnal Penelitian Ilmu Ekonomi dan Keuangan Syariah Sipakaraya : Jurnal Pengabdian Masyarakat Depik Jurnal Ilmu-Ilmu Perairan, Pesisir, dan Perikanan Health Community Service EBAMUKAI; JURNAL PENGABDIAN ILMU PENGETAHUAN DAN TEKNOLOGI Moral : Jurnal Kajian Pendidikan Islam Rahmad Jurnal Studi Islam dan Ilmu Al-Quran Studia Islamika
Muhammad Hisyam
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Journal : Transcendent Journal of Mathematics and Applications

 1 
Kontrol Optimal pada Penyebaran Penyakit Campak Model SIR Samosir, Restika; Sihombing, Yosina Arni; Sumardi, Sitti Rosnafian; Hisyam, Muhammad
Transcendent Journal of Mathematics and Applications Vol 3, No 2 (2024)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v3i2.42161

Abstract

The SIR model is a model used to group populations into 3 parts, namely susceptible or a subpopulation of individuals who are susceptible to disease, infected or a subpopulation of individuals who are infected and can transmit the disease and recovered or a subpopulation of individuals who have recovered from the disease. Measles is usually treated without a vaccine, so the disease is often found in the community. Giving the right and balanced vaccine will get results that are balanced with what is given. In this research, we develop a SIR model with additional controls. Where the control in this model is vaccination given to subpopulations S and I, so that the recovered subpopulation experiences an increase, because the number of subpopulation I decreases. The method used in this research consists of several steps, namely forming a SIR model which is formed in optimal control and determining the objective function. Next, solve the optimal control problem, which consists of several stages, namely forming the Hamiltonian function and finding states and co-states. Based on the research results, it is concluded that optimal control of the SIR model is obtained by state and co-state equations. Where this model is the result of reducing the Hamiltonian to obtain optimal control in the SIR model.
Co-Authors Abdul Latif Abraham Abraham Agamawan, Lalu Panji I. Agus Kristiyanto Agus, Al Ihksan Agus, Al Ikhsan Ahmad Syahrizal Albida Rante Tasak, Albida Rante Amir, Haeril Asmiddin, Ahmad Maulid Baransano, Natan Bara’padang, Barnabas Barnabas Barapadang Claudius Hendraman B. Tobi Dimara, Makdalena Irpa Dodiman, Dodiman Ervina Indrayani Fadhilah Fadhilah Frans Augusthinus Asmuruf Haryati, Kristina Hasanuddin Hasanuddin Herlini Puspika Sari Herlini Puspita Sari Huwae, Jilian Risky Ibrah Safirah Israwan, LM. Fajar Kainama, Tamara Louraine Jeanette Kalor, John D Kardiyanto, Deddy Whinata Liyatin Gea Lolita Tuhumena Maklon Warpur Manalu, Khristhoper Aris Arianto Mantayborbir, Vyona Mas, Haris Saputra Miftah Miftah Misbach, Imam Musakar, Rafika Dewitasari Kahar Mustika Endah Pratiwi N, Nasrullah Nabilawti, Hijrah Nada Pertiwi Papriani Nasrullah Nasrullah Nazifah Fitri Annisa Nurilfayati, Nurilfayati Nurwahid, Hidayat Papriani, Nada Pertiwi Pattola Paulangan, Yunus Pajanjan Pertiwi, Widya Nur Bhakti Popi Ida Laila Ayer Putri Hadi Utami Rahmat Hidayat Raihan Difari Ramba, Fitria Yunia RARA, ABD RAHMAN Rasyid M Akib, Abd. Rejauw, Korinus Rumahorbo, Basa Tunggul Rumanasen, David Waranda S, Armita Safruddin Samosir, Restika Satyanegara, Diqbal Shindy Dwita Nuansari Sihombing, Yosina Arni Sitti Rosnafi’an Sumardi Sri Pujiyati Suarni S. Sumardi, Sitti Rosnafi'an Sumardi, Sitti Rosnafian Suntin, Suntin Tangkelayuk, Herman Umbekna, Sara Waum, Ida Winda Ade Fitriya B Yenusi, Tien Nova B.