Model and Simulation of COVID-19 Transmission with Vaccination and Quarantine Interventions in Jember

Fahreza, Faizal Rifky
Hasan, Moh.
Kusbudiono, Kusbudiono

InPrime: Indonesian Journal Of Pure And Applied Mathematics
Vol 5, No 1 (2023)

AbstractIn this study, we model the transmission of COVID-19 by considering vaccination and quarantine interventions. The focus of our study is to measure the effect of these two interventions on controlling the spread of COVID-19. We demonstrate the use of the Kermack-McKendrik model as an SIR model for the number of people infected with COVID-19 applied in Jember, Indonesia. The model parameters are estimated using the Levenberg-Marquardt approach and the model equations are solved using the Runge-Kutta 4th-order method. Through the simulation study, we can determine the peak of the spread of COVID-19 cases and obtain several parameters related to vaccination and quarantine interventions that significantly affected the transmission rate of COVID-19. It is found that a faster rate of vaccinations will reduce the rate of transmission of COVID-19. Moreover, COVID-19 can be fully controlled if the infected patients carry out proper quarantine procedures.Keywords: COVID-19; Kermack-McKendrik; Levenberg-Marquardt; quarantine; SIR; vaccination. AbstrakDalam penelitian ini, kami memodelkan penularan COVID-19 dengan mempertimbangkan intervensi vaksinasi dan karantina. Fokus dari penelitian kami adalah untuk mengukur pengaruh dari kedua intervensi tersebut dalam mengontrol penyebaran COVID-19. Kami mendemonstrasikan penggunaan model Kermack-McKendrik sebagai model SIR untuk kasus pasien yang terinfeksi COVID-19 di Jember, Indonesia. Parameter model diestimasi menggunakan pendekatan Levenberg-Marquardt dan menyelesaikan model menggunakan metode orde-4 Runge-Kutta. Melalui studi simulasi, kami dapat menentukan waktu puncak penyebaran kasus COVID-19 dan mendapatkan beberapa parameter terkait intervensi vaksinasi dan karantina yang berpengaruh signifikan terhadap laju penularan COVID-19. Hasil simulasi menunjukan bahwa laju vaksinansi yang cepat akan mengurangi laju penyebaran COVID-19. Selain itu, COVID-19 dapat dikontrol dengan penuh jika pasien melakukan prosedur karantina yang tepat.Kata Kunci: COVID-19; Kermack-McKendrik; Levenberg-Marquardt; karantina; vaksinasi. 2020MSC: 00A71, 92B05