Household and natural waste discharges are key environments for bacteria growth, including Mycobacterium tuberculosis, which causes tuberculosis (TB). Population migration also significantly impacts TB transmission rates. This study presents a nonlinear mathematical model to assess the effects of cumulative household discharges and migration-dependent contact rates on the spread of TB. The model considers four main variables: densities of susceptible and infective human populations, bacteria population density, and cumulative household discharge density. Analyzing the model through stability theory, numerical simulations, and sensitivity analysis reveals that TB incidence rises in areas with low emigration, where population density and contact rates intensify transmission. Additionally, increased household discharges further facilitate TB spread, underscoring the importance of sanitation and environmental factors. Sensitivity analysis identifies influential factors driving transmission, providing key insights for effective health interventions, which are confirmed through numerical simulations.