<p>In this study, we propose and analyze a mathematical model, emphasizing the low infectivity of the <i>M. leprae</i> bacterium, the causative agent of leprosy, and its prolonged incubation period. The model incorporates two time delays that lead to a Hopf bifurcation, allowing for a realistic exploration of system stability. Furthermore, three control intervention measures have been introduced, including early detection and the provision of post-exposure prophylaxis, which plays a crucial role in suppressing the latent transmission of the disease. Additionally, socio-economic indicators such as per capita income and literacy rate are integrated as temporal features in a random forest model to predict future endemic zones in India up to the year 2035. Bayesian inference via the Markov Chain Monte Carlo (MCMC) method is employed to estimate the parameter space and reveals critical influence of biological delays on leprosy transmission. The findings indicate that existing intervention measures, coupled with weak implementation, are inadequate to eliminate the disease. In contrast, the proposed intervention measures have been proved to be more efficient, significantly suppressing latent transmission and substantially reducing case numbers.</p>