A Mathematical Model Analysis of COVID-19 Transmission with Vaccination in Caputo Fractional Derivatives: Case Study in Indonesia

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.

Keywords

• seiar-v model
• covid-19 model
• basic reproduction number
• fractional model
• grunwald-letnikov method.