Epidemiological model of COVID-19 with quarantine using reaction–diffusion equation with FTCS, NFSD, MacCormack, and Crank–Nicolson numerical schemes

In this study, we present a spatially extended epidemiological model for the spread of COVID-19, formulated as a system of nonlinear reaction–diffusion equations. Our model extended spatially traditional SEIR model to capture asymptomatic and quarantined individuals. To solve this system, we apply and compare four numerical schemes—Forward Time Central Space (FTCS), Crank–Nicolson, Nonstandard Finite Difference (NSFD), and MacCormack methods. What sets this work apart is its side-by-side implementation of these schemes on the same PDE-based COVID-19 model, offering insights into their relative accuracy, stability, and practical applicability. Our numerical simulations show that while FTCS and MacCormack are computationally straightforward, the MacCormack numerical scheme demonstrated a comparatively slower rate of convergence than the other methods applied in this study, indicating that it is less efficient for solving the SEIQAR model equations; in addition to that, Figures 11–16 present the simulation results under the movement restriction intervention. The numerical solution obtained through the MacCormack scheme exhibits negligible variation in the temporal dynamics of compartmental populations when comparing the state parameters before and after the intervention. This limited response indicates that the MacCormack method may lack sufficient resolution or sensitivity to accurately capture the perturbative effects introduced by the intervention within the SEIQAR model framework. The NSFD and Crank–Nicolson schemes provide more stability and smoother results, especially over longer simulations. These findings are valuable for researchers and public health modelers seeking efficient tools to simulate spatial disease transmission.