Mathematical Modelling of Tuberculosis Transmission with Complete Treatment: AI-Assisted Numerical Simulation for Smart Healthcare Systems

Tuberculosis continues to be a serious public health challenge, mainly due to delayed diagnosis, incomplete treatment, and inefficient utilization of healthcare resources. This study proposes a deterministic compartmental mathematical model to analyze the transmission dynamics of tuberculosis with a focus on early diagnosis and treatment completion. The host population is stratified into six epidemiological classes: susceptible, latent infection, diagnosed individuals receiving complete treatment, undiagnosed individuals undergoing incomplete treatment, active tuberculosis infection and, recovered individuals. Theoretical analysis was conducted for existence and stability of the disease-free and endemic equilibrium points, and a threshold condition governed by the basic reproduction number is derived. To complement the theoretical analysis, AI-supported numerical simulation techniques implemented in Python enhances scenario evaluation by efficiently quantifying the effects of improved diagnosis and treatment coverage. Overall, the proposed framework provides a reliable mathematical basis for policymakers aiming to strengthen TB surveillance, supported by intelligent simulation tools and optimizing healthcare resource utilization in smart healthcare systems, particularly in high-burden settings.