A data-driven tuberculosis model with behavioral changes and saturated treatment: Optimal control and cost-effectiveness study

In this study, we develop a data-driven susceptible–exposed–infectious–treatment tuberculosis transmission model. The model incorporates a Holling type-II saturated incidence rate to capture behavioral and contact saturation effects, along with a Verhulst-type treatment function to reflect constraints in treatment capacity. Model parameters are estimated using India’s tuberculosis (TB) incidence data from 2000 to 2020, yielding R0 = 1.4507, which indicates persistent disease transmission in the absence of effective interventions. To identify efficient control strategies, an optimal control problem is formulated by introducing three time-dependent interventions: preventive measures (u1), tuberculosis preventive treatment (u2), and active case finding (u3). The necessary optimality conditions are obtained using Pontryagin’s maximum principle, and the resulting system is solved numerically. Two intervention scenarios are examined: a baseline scenario with limited intervention efficacy (τ = 0.15, θ = 0.05) and an enhanced scenario with improved efficacy parameters (τ = 0.60, θ = 0.67). A comprehensive cost-effectiveness analysis is conducted using incremental averted ratio, Average Cost-Effectiveness Ratio (ACER), and Incremental Cost-Effectiveness Ratio (ICER) to compare competing intervention strategies. The analysis shows that, under the baseline efficacy, strategy E (u1 only) emerges as the most impactful intervention for reducing transmission. Under the with-improvement scenario, strategy C (u1 + u3) demonstrates the most economically efficient, achieving the lowest ACER and most favorable ICER among all strategies considered. These findings provide evidence-based, cost-effective intervention strategies to guide policy formulation and accelerate India’s progress toward the WHO End TB strategy milestones, including a 95% reduction in TB deaths and 90% reduction in incidence by 2035 relative to 2015 levels.