Dynamical behavior analysis of 2-control strategies on tuberculosis model

We develop and rigorously analyze a deterministic SEITR (Susceptible–Exposed–Infectious–Treated–Recovered) model that incorporates distancing and treatment interventions to examine the transmission dynamics of tuberculosis. The basic reproduction number ( R 0 ) is computed and decomposed to determine the threshold conditions for disease persistence. We propose a next-generation matrix formulation to determine the stability of the disease-free state and demonstrate that tuberculosis dies out whenever R 0 < 1. Numerical implementation is performed using the fourth-order Runge–Kutta scheme and the backward sweep method, while Pontryagin’s maximum principle is utilized for determination of optimal intervention profiles. Sensitivity analysis is performed using normalized forward sensitivity indices, Pearson correlation, and Partial Rank Correlation Coefficient (PRCC). The results indicate that the transmission rate ( β ) is strongly positively correlated with the basic reproduction number ( R 0 ), whereas the control parameters ( u 1 , u 2 ) exhibit negative correlations with R 0 , highlighting their effectiveness in reducing disease transmission. The epidemiological efficacy of dual interventions is demonstrated by a significant decrease in infectious prevalence when both control measures are implemented simultaneously. Incremental cost-effectiveness ratio demonstrate that the combined control strategy is more cost-effective than individual interventions. These integrated analytical and numerical findings support the recommendation for sustained, early implementation of both distancing and treatment measures to achieve economically viable and dynamically stable tuberculosis mitigation.