Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator
Fatmawati Fatmawati, Muhammad Altaf Khan, Cicik Alfiniyah, Ebraheem Alzahrani
Abstract
Abstract In this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>≈</mml:mo><mml:mn>2.2020</mml:mn></mml:math> . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math> . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.