PEMODELAN SEIQR PADA PENYEBARAN COVID-19 DENGAN PENGARUH KEEFEKTIFAN VAKSIN
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Abstract
Penyebaran COVID-19 dan strategi pencegahan penularannya melalui karantina dan vaksinasi dapat diprediksi dengan pemodelan matematika epidemologi model SEIQR. Pemodelan ini bertujuan untuk mengetahui model penyebaran COVID-19 beserta titik kestabilan dari model tersebut. Populasi dalam model yang digunakan dibagi menjadi lima sub-populasi, yaitu: S-Suspected, E-Exposed, I-Infected, Q-Quarantined, dan R-Recovery. Model yang telah dibentuk dicari kestabilan titik kesetimbangannya dengan kriteria Routh-Hurwitz, kemudian disimulasikan menggunakan metode numerik Runge-Kutta orde empat. Hasil analisis kestabilan menunjukkan bahwa apabila menggunakan vaksin dengan efektifitas lebih rendah, seperti Sinovac, AstraZeneca, atau Sinopharm, memperoleh R0 > 1 yaitu 2.0554, 2.245, dan 1.302, dengan kata lain COVID-19 akan terus ada, sedangkan apabila menggunakan vaksin dengan efektifitas lebih tinggi, seperti Moderna atau Pfizer, menghasilkan R0 < 1 yaitu 0.3495 dan 0.2666, artinya COVID-19 akan menghilang seiring waktu. Berdasarkan penelitian ini diperoleh bahwa COVID-19 dapat menghilang setelah hari ke-61 atau ke-73. Selain itu, semakin tinggi keefektifan vaksin, maka jumlah individu terinfeksi dan individu yang dikarantina semakin rendah, sedangkan jumlah individu yang sembuh semakin tinggi.
The spread of disease and strategies for preventing transmission through quarantine and vaccination of COVID-19 can be predicted using the SEIQR model which is an epidemic mathematical modeling. This modeling aims to determine the model of the spread of COVID-19 and the stability point of the model. The population in the SEIQR model is divided into five sub-populations, namely S-Suspected, E-Exposed, I-Infected, Q-Quarantined, and R-Recovery. Then from the model that has been formed, the stability of each equilibrium point will be sought using the Routh-Hurwitz criteria, then simulated using the fourth-order Runge-Kutta numerical method. The results of the stability analysis show that when using a vaccine with lower effectiveness, such as Sinovac, AstraZeneca, or Sinopharm, the values of R0 are 2.0554, 2.245, and 1.302, which is R0 > 1, in other words, the COVID-19 disease will continue to exist. If using a vaccine with higher effectiveness, such as Moderna or Pfizer, the value of R0 is 0.3495 and 0.2666, which is R0 < 1, meaning that COVID-19 will disappear over time. Based on this study, the result obtained is that COVID-19 can disappear after 61 to 73 days. In addition, the higher the vaccine effectiveness, the lower the number of infected and quarantined individuals, while the higher the number of recovered individuals.
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