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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Square : Journal of Mathematics and Mathematics Education InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Fundamental Mathematics and Applications (JFMA) Journal of Mathematics and Applied Statistics Liquidity : Jurnal Ilmu Manajemen dan Bisnis Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M)
Muhammad Rifki Nisardi
Program Studi Ilmu Aktuaria FSAINS-UM Bulukumba
Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Library & Information Science Mathematics Social Sciences Other

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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

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A Mathematical Model Analysis of COVID-19 Transmission with Vaccination in Caputo Fractional Derivatives: Case Study in Indonesia Nisardi, Muhammad Rifki; Kasbawati, Kasbawati; Khaeruddin, Khaeruddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24711

Abstract

This study aims to investigate a fractional-order mathematical model of COVID-19 transmission using the Caputo derivative definition which suitable to epidemiological cases by its advantage to explain memory effects. The model incorporates compartments for asymptomatic infections and includes a vaccination strategy aimed at mitigating the spread of COVID-19. We derived the disease-free and endemic equilibrium points for the fractional model and computed the basic reproduction number (R_0 )  using the Next-generation Matrix method. Additionally, we conducted sensitivity analyses of parameters affecting R_0. The stability of the fractional model requires specific conditions to be met by the model parameters. To approximate active COVID-19 cases in Indonesia, we utilized the Explicit Grunwald-Letnikov method which well fit with Caputo fractional differential system. Simulation results demonstrate that the fractional-order model offers a flexible approach for modelling active COVID-19 cases in these regions. We found that fractional order for active cases COVID-19 in Indonesia is α=0.9856. The simulation showed that decreasing the vaccination rate and the efficacy of the vaccine would affect the reduction of COVID-19 transmission.
Co-Authors Amar, Muh Ikhsan Antonin Robinet Dian Firmayasari Dian Firmayasari S Dian Firmayasari S Harianto Harianto Harianto Harianto Hukmah Hukmah Hukmah Hukmah Hukmah HUkmah Hukmah, Hukmah Husain, Hartina Kasbawati Kasbawati Khaeruddin Khaeruddin Khaeruddin Khaeruddin Khaled Chetehouna Kusnaeni Kusnaeni, Kusnaeni M, Suriani Nur Ahniyanti Rasyid Nurahmad, Muhammad Fadhil Nursamsi, Nursamsi Nurul Azizah Putra, Restu Ananda Resky, Aprizal Sri Wahyuni Nurzak Subhan Khalifah Azis Sulma Sulma Sulma Sulma, Sulma Suriani M Suriani M Suriani M Suriani Suriani Ulfatun Hasanah Yusrini, Yusrini