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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS)
Fahreza, Faizal Rifky
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Computer Science & IT Mathematics

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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)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i1.27192

Abstract

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
Chaotic outbreak in discrete epidemic model with vaccination and quarantine interventions and limited medical resources Fahreza, Faizal Rifky; Hasan, Moh; Santoso, Kiswara Agung
Majalah Ilmiah Matematika dan Statistika Vol. 25 No. 1 (2025): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v25i1.53689

Abstract

The spread of infectious diseases can be analyzed dynamically using a discrete dynamic system. The characteristics of the infectious disease phenomenon are interesting to study as parameters considered in a dynamic system. Some of these include vaccination interventions, quarantine, or even an open condition such as limited medical resources. Analysis of a discrete epidemic model system with those three factors can be conducted to understand each of their impacts on the dynamics of disease spread within a population or even to determine the potential for a chaotic outbreak. In this study, an epidemiological model was formulated considering these three factors. Numerical simulations were also conducted to directly observe the influence of these three factors on the dynamics of disease spread. Additionally, efforts to control chaos were also implemented in the system. The limitation of medical resources affects the spread of diseases. Because the coverage of medical resources is limited, it can cause a high surge in cases within the population. This phenomenon of case surges can subsequently be mitigated by vaccination parameters such as vaccine efficacy and the rate of vaccine distribution within the population. Furthermore, the formulated system has the potential to exhibit chaotic behavior when the infection rate increases, in other words, the disease becomes an uncontrollable and unpredictable epidemic. Next, the thing that can be done to suppress this chaotic phenomenon is to directly intervene in the rate of disease spread within the population.
Co-Authors Kiswara Agung Santoso Kusbudiono Kusbudiono, Kusbudiono Moh Hasan Moh. Hasan