The dynamics of dengue infection through fractal-fractional operator with real statistical data

The purpose of this work is to analyze the dynamics of dengue fever in newly introduced operator known as fractal-fractional Atangana-Baleanu. Initially, we formulate a new dengue model with hospitalization class of notified infected cases and present the model basic results. Stability results for the model are shown when R₀<1. We estimate the parameters for the model considering the infected cases occur in East Java Indonesia for the year 2018. We estimated that the basic reproduction number for this model is approximately equal to R₀≈1.8463. We show the application of the fractal-fractional Atangana-Baleanu operator to the dengue model and present its numerical solution with a new method. We show the fractal-fractional model versus model fitting for different values of fractal and fractional orders and suggest that the fractal-fractional model provides better fitting to the infected cases of dengue infection. Some numerical results for different orders of fractal and fractional are shown for the validity and the applicability of the newly introduced operator.