BIFURKASI HOPF PADA MODEL DINAMIKA SEIR PENYEBARAN COVID-19 DI INDONESIA
DOI:
https://doi.org/10.24114/jmk.v8i2.34204Keywords:
Analisis kestabilan, bifurkasi, bifurkasi hopf, model SEIR, Covid-19Abstract
Corona Virus Disease 2019 (Covid-19) adalah penyakit yang menyerang sistem pernafasan akibat infeksi SARS-CoV-2 (Severe Acute Respiratory Syndrome). Pada Desember 2019, virus corona pertama kali muncul di Wuhan, provinsi Hubei, China yang berubah menjadi wabah pandemi yang menyebar ke seluruh dunia, termasuk Indonesia. Untuk mengatasi pandemi Covid-19, peneliti dari berbagai bidang memberikan kontribusinya. Ilmuwan matematika mempelajari karakteristik epidemi wabah, memprediksi penyebaran virus serta menawarkan berbagai langkah intervensi melalui pengembangan model matematika sehingga dapat mengendalikan penyebaran penyakit. Penelitian ini bertujuan untuk menganalisis stabilitas dan bifurkasi hopf dengan melihat perubahan struktur orbit pada sistem seiring dengan perubahan nilai parameter. Analisis kestabilan menunjukkan bahwa dinamika Covid-19 di Indonesia akan mencapai titik stabil untuk waktu yang lama, yaitu setelah mencapai 500 bulan. Berdasarkan analisis sensitivitas pada refrensi sebelumnya, parameter ï¡ dan ïŒ disebut parameter bifurkasi. Hasil analisis menunjukkan bifurkasi Hopf terjadi pada simulasi exposed terhadap infected yang ditandai dengan munculnya limit cycle p AbstractCoronavirus Disease 2019 (Covid-19) is an acute respiratory system disease caused by SARS-CoV-2 (Severe Acute Respiratoryiscovered Syndrome 2). In December 2019, coronavirus was first discovered in Wuhan, Hubei province, China which turned into a pandemic outbreak and has been spreading in whole the world, including Indonesia. Research from various disciplines is carried out to overcome the Covid-19 pandemic. Mathematicians develop mathematical models to study the characteristics of epidemic, predict the spread of viruses and offer various intervention measures. This study aims to analyze the stability and hopf bifurcation of the SEIR model for the Covid-19 dynamic in Indonesia by looking at changes in the orbit structure of the system along with changes in parameter values. Stability analysis shows that the dynamics of Covid-19 in Indonesia will stable to occur for a long term, after reaching 500 months. Based on the sensitivity analysis in the previous reference, parameters ï¡ dan ïŒ are bifurcation parameters. The results of the analysis show that the Hopf bifurcation occurs in the exposed to infected simulation which is indicated by the appearance of a limit cycle in the orbit.References
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