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. We briefly show the stability results of the model for the case when the basic reproduction number is mathcal{R}_{0} <1. 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.
Highlights
In this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator
The model (10) described above for the dengue infection using the fractal-fractional Caputo–Fabrizio operator is used further to obtain its numerical solution by using a novel numerical procedure
3 Novel solution procedure for fractal-fractional model For the numerical solution of the fractal-fractional dengue model (10), we present a novel procedure here that is based on the Adams–Bashforth technique
Summary
We describe a host–vector model for dengue transmission. The host–vector model is divided into three mosquito populations, susceptible (Sm), exposed (Em), and infectious (Im), and five human (host) populations, susceptible (Sh), exposed (Eh), infectious (Ih), hospitalized and/or notified infectious (Ph), and recovered (Rh). The model (10) described above for the dengue infection using the fractal-fractional Caputo–Fabrizio operator is used further to obtain its numerical solution by using a novel numerical procedure . We give the following result: Theorem 1 The dengue model given by (10) at E0 is locally asymptotically stable whenever R0 < 1. Proof In order to prove the given theorem, we need to obtain the Jacobian matrix by evaluating the model (10) at E0, and we have It can be seen from the above matrix J(E0) that the eigenvalues –μm, –νh, –νh, and –π4 are obviously negative, while the remaining four eigenvalues with negative real parts can be obtained through the following equation: λ4 + 1λ3 + 2λ2 + 3λ + 4 = 0, where.
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