Fractional-order measles infection model with vaccination effects

The purpose of this work is to investigate the dynamical behavior of a measles disease model adopting fractional and fractal-fractional operators with Mittag-Leffler kernel using two distinct numerical algorithms. First, we discuss the measles model in a fractional framework with Atangana-Baleanu-Caputo derivative and examine some fundamental mathematical assumptions of the considered model. We implement fixed-point theory to explore the existence and uniqueness of model solutions. Next, we apply the novel fractal-fractional concept with Atangana-Baleanu derivative to the measles model and reveal that the model has unique solution. We present the approximate results for the proposed models with graphical illustrations. The results are presented with various choices of fractal and fractional orders. The system behavior to various biological parameters is also investigated. In addition, we compare the considered operators using novel numerical schemes that take into account different rho values.