DINAMIKA MODEL SUSCEPTIBLE INFECTED RECOVERED (SIR) DENGAN STRATEGI VAKSINASI

Authors

  • NANDA MUTIA UTAMA
  • ARRIVAL RINCE PUTRI
  • MAHDHIVAN SYAFWAN

DOI:

https://doi.org/10.25077/jmu.9.4.357-365.2020

Abstract

Vaksinasi merupakan salah satu cara untuk mencegah sekaligus mengendalikan penyebaran penyakit menular. Penelitian ini membahas salah satu model penyebaran penyakit menular, yaitu model Susceptible Infected Recovered (SIR). Model SIR yang dibahas mempertimbangkan strategi vaksinasi, yaitu vaksinasi konstan dan vaksinasi berkala, yang diberikan kepada individu rentan terinfeksi penyakit. Kajian analitik dilakukan dengan menganalisis kestabilan model di sekitar titik ekuilibrium berdasarkan nilai eigen dari matriks Jacobian. Kestabilan model dikaitkan juga dengan parameter ambang batas, yaitu parameter yang menentukan apakah suatu populasi bebas atau terinfeksi dari penyakit. Simulasi numerik dilakukan untuk mengkonfirmasi hasil analitik dengan menggunakan parameter dari kasus penyakit Tuberkulosis (TBC) di Provinsi Sumatera Barat tahun 2018. Hasil analitik maupun numerik memperlihatkan bahwa pemberian stategi vaksinasi efektif sebagai pencegahan dan pengendalian penyebaran penyakit, sehingga dapat mengurangi jumlah individu yang terinfeksi.

Kata Kunci: Model SIR, Vaksinasi, Kestabilan, Parameter Ambang Batas, Simulasi Numerik

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Published

18-02-2021

Issue

Vol. 9 No. 4 (2020)

Section

Articles

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