On mathematical modeling of fractional-order stochastic for tuberculosis transmission dynamics

Abstract

Tuberculosis remains one of the most dangerous diseases globally and has affected many people in Sub-Saharan Africa. In this paper, a fractional stochastic model of tuberculosis disease was formulated and analyzed. The existence and uniqueness of solutions are presented in the new approach far from the deterministic fractional operators. We carry out numerical simulations of the model using three fractional operators. Our numerical results suggest that the Caputo–Fabrizio operator has a more random effect among the three different operators than the Atangana–Baleanu and the Caputo operators. Further, it is envisaged that the fractional-order derivatives significantly impact the dynamics of the disease.

Keywords

• Fractional stochastic
• Mathematical model
• Tuberculosis
• Random effect
• Mittag-Leffler