LOCAL STABILITY OF THE SEIQR EPIDEMIC MODEL APPLIED TO COVID-19 SPREAD CASES
DOI:
https://doi.org/10.25077/jmua.15.1.123-131.2026Keywords:
Kestabilan Model, Covid-19, Stabil AsimtotikAbstract
Pandemi COVID-19 telah memberikan dampak signifikan secara global, menuntut pemahaman yang mendalam mengenai dinamika penyebarannya untuk menentukan langkah intervensi yang efektif. Penelitian ini membahas analisis kestabilan model epidemi SEIQR (Susceptible, Exposed, Infectious, Quarantined, Recovered), yang merupakan pengembangan dari model SIR standar dengan penambahan kompartemen karantina ($Q$) dan masa inkubasi ($E$). Model ini dirancang untuk merepresentasikan kebijakan isolasi mandiri atau karantina rumah sakit yang diterapkan selama pandemi. Metode yang digunakan dalam penelitian ini meliputi pembentukan sistem persamaan diferensial non-linear, penentuan titik ekuilibrium (bebas penyakit dan endemik), serta perhitungan Bilangan Reproduksi Dasar menggunakan metode Next-Generation Matrix. Analisis kestabilan lokal dilakukan dengan menggunakan linearisasi di sekitar titik ekuilibrium dan kriteria Routh-Hurwitz. Hasil analisis menunjukkan bahwa penyebaran COVID-19 akan menghilang jika $\Re_0 < 1$, yang berarti titik ekuilibrium bebas penyakit bersifat stabil asimtotik. Sebaliknya, jika $\Re_0 > 1$, penyakit akan menetap dalam populasi dan mencapai titik ekuilibrium endemik yang stabil. Simulasi numerik disertakan untuk memvalidasi hasil analisis teoritis dan menunjukkan bahwa efektivitas karantina memiliki peran krusial dalam menekan nilai $\Re_0$ dan mempercepat laju pemulihan populasi.
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