Numerical study for a novel variable-order multiple time delay awareness programs mathematical model (Q2202429)

This paper studies a variable-order multiple time delay awareness programs model involving two types of the Atangana-Baleanu variable-order fractional derivative in Caputo sense. They are variable-order derivative type 1 containing the memory effect changes with time and variable-order derivative type 2 containing the history memory of derivative order itself. For these models, the authors investigate the basic reproduction number, equilibrium points and the asymptotic stability. Numerical studies are performed by introducing two methods including the implicit Adams-Moulton method and the predictor-corrector method. Both stability and convergence are examined. Numerical simulations are provided to illustrate the theoretical algorithms.