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All Journal Prosiding SNATIKA Vol 01 (2011) AKSIOMA: Jurnal Program Studi Pendidikan Matematika The Asian Journal of Technology Management (AJTM) JURNAL NASIONAL TEKNIK ELEKTRO Jurnal Kajian Pembelajaran Matematika JOIV : International Journal on Informatics Visualization JMPM: Jurnal Matematika dan Pendidikan Matematika INOVISH JOURNAL BAREKENG: Jurnal Ilmu Matematika dan Terapan METHOMIKA: Jurnal Manajemen Informatika & Komputerisasi Akuntansi MATRIK : Jurnal Manajemen, Teknik Informatika, dan Rekayasa Komputer Buletin Ilmiah Sarjana Teknik Elektro Jurnal Pengabdian Masyarakat Asia International Journal of Progressive Mathematics Education Jikom: Jurnal Informatika dan Komputer Jurnal Informatika: Jurnal Pengembangan IT Jurnal ilmiah teknologi informasi Asia Limits: Journal of Mathematics and Its Applications
Lilis Widayanti
Institut Teknologi Dan Bisnis Asia Malang
Arts Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Transportation Other

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Journal : Limits: Journal of Mathematics and Its Applications

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Dinamika Solusi dan Kontrol Optimal Model Penyakit ISPA di Kota Malang Hakim, Lukman; Widayanti, Lilis
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 3 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 3 Edisi No
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

The current research provides a mathematical model utilizing nonlinear ordinary differential equations to represent the spread of acute respiratory infections (ARI). The model is divided into five compartments: the susceptible population, the vaccinated population, the latent population, the infected population, and the recovered population. Through dynamic analysis, two equilibrium points were determined. The disease-free equilibrium point is stable under conditions, while the endemic equilibrium point exhibits asymptotic stability. The lsqcurvefit methods was implemented to estimate the parameters, facilitating accurate parameter approximation. The acquisition of estimated values was implemented in the sensitivity analysis, and several parameters sensitive to were obtained: the vaccination rate, the natural death rate, the mortality cause infection rate, and recovery rate. An optimal control problem was designed by incorporating two control variables: firstly, reducing the direct contact between the susceptible and infected populations, and the other focused on increasing the intensity of infected individuals. The solution of optimal control problem was derived using Pontryagin's Principle. The objective function was formulated as a Lagrange to minimize the number of latent and infected individuals, and maximizing the vaccinated and recovered populations. Finally, numerical simulations were performed to validate the theoretical analysis, demonstrating that the results in line with the objective function of optimal control and effectively support the proposed strategies for controlling the disease.
Co-Authors A.N. Afandi Abdul Hadi Achlul Nizar Adriani Kala'lembang Adriani Kala’lembang Adriani Kala’lembang Ahmad Husain Abiyyu Aripriharta - Azwar Riza Habibi, Azwar Riza Fadhli Almu’iini Ahda Farokhah, Lia Fitria, Vivi Aida Hasanah, Mitahatul Heru Wahyu Herwanto Kala'lembang, Adriani Lukman Hakim Mufidatul Islamiyah Puji Subekti Santoso, Risa Suastika Yulia Riska Sulistyo, Danang Arbian Sundafa, Aldo Vivi Aida Fitria Widya Adhariyanty Rahayu Yudistira Arya Sapoetra Zahratul Laily Binti Edaris