ANALISIS MODEL MATEMATIKA PENYEBARAN PENYAKIT COVID-19 DENGAN LOCKDOWN DAN KARANTINA

  • Muhammad Manaqib UIN Syarif Hidayatullah Jakarta
  • Maghvirotul Azizah Universitas Islam Negeri Syarif Hidayatullah Jakarta
  • Eti Hartati S. Universitas Islam Negeri Syarif Hidayatullah Jakarta
  • Savira Pratiwi Universitas Islam Negeri Syarif Hidayatullah Jakarta
  • Raza Aqil Maulana Universitas Islam Negeri Syarif Hidayatullah Jakarta
Keywords: Lockdown, Karantina, COVID-19, Bilangan Reproduksi Dasar, Kestabilan Titik Ekuilibrium

Abstract

Penelitian ini menggembangakan model matematika penyebaran penyakit COVID-19 SEIR dengan lockdown dan karantina. Pembentukan model diawali dengan membuat asumsi dan diagram kompartemen alur penyebaran COVID-19 dengan lockdown dan karantina. Kemudian dibentuk sistem persamaan diferensial nonlinear berdasarkan diagram kompartemen tersebut. Analisis sistem dilakukan dengan menentukan titik ekuilibrium dan bilangan reproduksi dasar (). Hasilnya diperoleh dua buah titik ekuilibrium yakni titik ekuilibrium bebas penyakit yang eksistensinya tanpa syarat dan titik ekuilibrium endemik yang eksistensinya bergantung pada bilangan reproduksi dasar (> 1). Selanjutnya, analisis kestabilan titik ekuilibrium bebas penyakit menggunakan analisis nilai eigen matriks Jacobi dan Kriteria Routh-Hurwitz diperoleh titik kestimbangan bebas penyakit bersifat stabil asimtotik lokal jika . Terakhir simulasi model dilakukan untuk memberikan gambaran geometris dari solusi dan untuk mendukung teorema yang diperoleh. Hasil simulasi numerik yang dilakukan mendukung hasil analisis dinamik yang diperoleh.

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Published
2021-09-01
How to Cite
[1]
ManaqibM., AzizahM., Hartati S.E., PratiwiS., and MaulanaR. A., “ANALISIS MODEL MATEMATIKA PENYEBARAN PENYAKIT COVID-19 DENGAN LOCKDOWN DAN KARANTINA”, BAREKENG: J. Il. Mat. & Ter., vol. 15, no. 3, pp. 479-492, Sep. 2021.