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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Journal of Fundamental Mathematics and Applications (JFMA) AMMA : Jurnal Pengabdian Masyarakat
Renny Renny
Jurusan Matematika, Universitas Jenderal Soedirman
Humanities Chemistry Decision Sciences, Operations Research & Management Education Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Nursing

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Journal : JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI

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Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor Susi Agustianingsih; Rina Reorita; Renny Renny
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (787.721 KB) | DOI: 10.20956/jmsk.v16i3.6942

Abstract

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.
Co-Authors Azhari Kemalasari Nunung Nurhayati Rina Reorita Siti Rahmah Nurshiami, Siti Rahmah Sri Maryani Susi Agustianingsih