Abstract
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes new-born immunization via the fractal-fractional (F-F) derivative in the Atangana-Baleanu sense. The population is divided into four groups by this system: susceptibility S(xi), infectious I(xi), immunized infants V(xi), and restored R(xi). The stochastic technique is used to describe and assess the invariant region, basic reproduction number, and local stability for disease-free equilibrium. This strategy has significant modelling difficulties since it ignores the unpredictability of the system phenomena. To prevent such problems, we convert the deterministic strategy to a randomized one, which seems recognized to have a vital influence by adding an element of authenticity and fractional approach. Owing to the model intricacies, we established the existence-uniqueness of the model and the extinction of infection was carried out. We conducted a number of experimental tests using the F-F derivative approach and obtained some intriguing modelling findings in terms of (i) varying fractional-order (phi) and fixing fractal-dimension (omega), (ii) varying omega and fixing phi, and (iii) varying both phi and omega, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.