ABSTRACT
In this work, we generalize the multi-vaccination for COVID-19 mathematical model to the variable-order fractional derivative case by replacing the first-order derivative with the variable-order fractional Atangana-Baleanu-Caputo operator. Moreover, the parameters of the proposed model are dependent on the variable-order fractional derivative. We use an amended numerical technique to build an asymptotically stable difference scheme. The proposed scheme accurately simulates the behavior of the solution of the presented model. Some properties, boundedness, and positivity of the studied system are proved analytically. The introduced scheme preserves these properties of the analytic solutions. Numerical treatment is run out for testing the reliability, applicability, and simplicity of this scheme. Comparitive study bettween the obtained results using the discretization of Atangana-Baleanu-Caputo derivative and nonstandard finite differeance method with the results which obtained using the discretization of the operator Yang-Abdel-Cattani is given.