Banach contraction method for solving the epidemic model with constant vaccination / Mat Salim Selamat … [et al.] - Selamat, Mat Salim; Zi, Nur Afiqah; Ahmazi, Nurul Nadira; Khairudin, Ruwaidah (Universiti Teknologi MARA, Negeri Sembilan, 2024)
In this study, we employed the Runge-Kutta Fourth Order (RK4) method and the Banach Contraction Method (BCM) to simulate an epidemiological model with constant vaccination, utilizing parameters and initial conditions established according to Fauzi et al. (2021). The solutions for susceptible (S), infected (I), and recovered (R) individuals were obtained and compared between RK4 and BCM over a time range of 0 to 2. Although an exact solution reference was unavailable, our comparative analysis revealed consistent results between RK4 and BCM at the initial time steps for all variables. However, as time progressed, minor differences emerged between the solutions obtained from RK4 and BCM, albeit these differences were relatively small. While the variations observed may not be significant in magnitude, they underscore the importance of selecting appropriate numerical techniques in epidemiological modeling to ensure accurate predictions over time.