A Numerical Scheme For Caputo Fractional Derivative And Its Application To Covid-19 Model
- Dr. M. O. Adewole
- Ibafo Computer Science 2023
- xi;,89pgs.
Abstract
We propose a numerical method for solving a fractional differential equation using the Caputo sense for fractional-order derivatives. The method involves an implicit difference scheme known for its unconditional stability. To adapt the scheme for solving nonlinear fractional differential equations, we transform it into an explicit scheme by replacing the implicit term with the explicit Euler scheme. To maintain the unconditional stability of the implicit scheme and enhance its suitability for solving nonlinear fractional differen- tial equations, we utilize the newly formulated explicit scheme as a predictor, while the implicit scheme serves as the corrector. Through numerical examples, we demonstrate the convergence and superiority of this proposed scheme compared to the implicit and explicit Euler schemes. Next, we apply the proposed scheme to investigate the dynamics of a COVID-19 model comprising six disease compartments: Susceptible, Exposed, Asymp- tomatic, Infected Symptomatic, Quarantined, and Recovered (SEAIQR). We obtain the basic reproduction number, which allows us to assess the local stability of the disease-free equilibrium. Furthermore, we employ the proposed scheme to simulate the COVID-19 model, enabling us to explore the global stability of both the disease-free equilibrium and endemic equilibria. Additionally, we analyze various intervention strategies and investigate the influence of the order of fractional derivative on the dynamics of the virus.