Modified Numerical Method for Solving Fractional Order Infectious Disease Model

Abstract

In this paper, we consider numerical approximate solutions to space-time fractional differential equations involving Atangana–Baleanu–Caputo (ABC) sense fractional derivative operator. We then enhance the Toufik–Atangana numerical scheme through a complex combination of the trapezoidal scheme and the ABC fractional Euler scheme to improve the  accuracy and robustness of our computational method. Finally, the proposed method is validated through numerical simulation of an infectious disease model. The model consists of a system of fractional differential equations with eight compartments, collectively called SIDARTHE: Susceptible (S), Infected (I), Diagnosed (D), Ailing (A), Recognized (R), Threatened (T), Healed (H), and Extinct (E). The numerical results presented graphically show that different fractional orders lead to different asymptotic behaviors.