A numerical study of dengue internal transmission model with fractional piecewise derivative

The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem’s approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer. •We investigate a Dengue Internal Transmission Model using fractional piece-wise operator.•We study various theoretical and numerical properties.•We use the results of fixed-point theory to study the theoretical aspects of the proposed fractional order model.•We use newly proposed method which is based on Newton polynomial, to derive numerical results.•We simulate the obtained results to investigate effect of piece-wise operator on the transmission of the dengue disease.