Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in Caputo sense. This takes into account relationship between Tuberculosis, HIV/AIDS, and diabetes differentiates cases MDR-TB (multidrug-resistant tuberculosis) XDR-TB (extensively drug-resistant tuberculosis). We basic results associated with behavior disease-free equilibrium points different sub-populations, TB-Only, TB-HIV/AIDS, TB-Diabetes. performed computational simulations orders (α-values) an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among obtained, have that all sub-populations decrease at beginning α-values. TB-Only sub-population, there is number cases. TB-HIV/AIDS sub-population differentiated depending on α. knowledge helps design effective control strategy. The diabetics increased throughout period outperformed resistant compartments recommend special attention compartment due growth.