Tuberculosis remains a major public health challenge because of its long latent period, incomplete vaccine protection, and spatially heterogeneous transmission. This study develops a reaction–diffusion model incorporating vaccination, latent infection, active disease, treatment, recovery, nonlinear transmission, and population movement. Analytical and numerical investigations examine disease persistence, spatial spread, pattern formation, and control strategies. Results show that spatial heterogeneity and mobility can increase disease persistence and generate localized hotspots, transmission corridors, and clustered outbreaks. Numerical simulations demonstrate that interventions targeted at high-transmission areas reduce disease burden more effectively than uniformly distributed controls under the same resource constraints. These findings highlight the importance of spatial structure in tuberculosis dynamics and support geographically targeted vaccination and treatment strategies for improved disease control.