On the Analysis of a Fractional Tuberculosis Model with the Effect of an Imperfect Vaccine and Exogenous Factors under the Mittag–Leffler Kernel

This research study aims to investigate the effects of vaccination on reducing disease burden by analyzing a complex nonlinear ordinary differential equation system. The focuses five distinct sub-classes within system comprehensively explore impact vaccination. Specifically, mathematical model employed in this investigation is fractional representation tuberculosis, utilizing Atangana–Baleanu derivative Caputo sense. validity proposed established through rigorous qualitative analysis. existence and uniqueness solution are rigorously determined applying fundamental theorems fixed point approach. stability analysis conducted using Ulam–Hyers Additionally, employs widely recognized iterative Adams–Bashforth technique obtain an approximate for suggested model. numerical simulation tuberculosis discussed, with particular focus assumptions made regarding assumes that only limited portion population vaccinated at steady rate, efficacy vaccine critical factor burden. findings indicate can effectively assess mitigating spread tuberculosis. Furthermore, underscores significance as effective control measure against