APPROXIMATE ANALYTICAL SOLUTION FOR THE VARIABLE-ORDER FRACTIONAL INFECTIOUS DISEASES MODEL

In this paper, a nonlinear variable-order infectious diseases model is discussed and the derivative operator is in the Caputo sense for the range [Formula: see text]. First, we used the Laplace transformation to the variable-order fractional derivatives and effectively transformed it into an integer-order derivative. Subsequently, the homotopy perturbation method (HPM) is used to obtain the semi-analytical solution of the nonlinear infectious diseases model. Ultimately, we showcase the effects of our new approximate solutions by presenting various graphical illustrations across various values for the relevant biological parameters. Our computation results are compared with existing solutions, and a close agreement is obtained demonstrating our approach’s accuracy and validity.