A fractional dynamics of tuberculosis (TB) model in the frame of generalized Atangana–Baleanu derivative

Abstract

In the present paper, we formulate novel fractional tuberculosis (TB) model with a generalized Atangana–Baleanu (GAB) fractional derivative. The parameters in this model are fitted from the real statistical data of cases of TB infections in Yemen from 2000 to 2019. Firstly, pulmonary TB cases of infected people in Yemen during the period (2000–2019) were studied and analyzed. The future trends for possible cases of pulmonary tuberculosis in Yemen for the years (2020–2021) were predicted using the Expert Modeler model and apply statistical analysis programs (SPSS, version23 & Eviews, 9). In addition, we have investigated the spread of TB in Yemen and compared it with some countries around the world. Further, the fundamental properties of this novel fractional tuberculosis (TB) model with a generalized Atangana–Baleanu (GAB) fractional derivative are given. The fixed point theory is used to obtained existence and uniqueness results for this model. Finally, the solutions are obtained using iterative techniques of Adams–Bashforth and are presented using graphical simulations. Here we get numerical values of parameters used in this novel model to display the significance of our novel model, which provides useful information about the dynamics of spread and control of TB.

Keywords

• Forecasting
• Tuberculosis (TB) model
• Atangana–Baleanu (AB) operators
• Fixed point theorem
• Adams–Bashforth technique