Analyzing Tuberculosis Transmission in Bangladesh: Modified SEIHR Framework With Non‐Monotone Incidence, Pseudo‐Recovery, and Treatment Default Mechanisms

ABSTRACT This study introduces a novel SEIHR‐type compartmental model to analyze the transmission dynamics of tuberculosis (TB) in Bangladesh, incorporating several epidemiologically significant features often overlooked in standard formulations. The model's originality stems from three key aspects: (1) A non‐monotone incidence function that captures behavioral adaptations and psychological effects during high‐prevalence periods; (2) a pseudo‐recovery compartment accounting for temporary recovery with relapse potential; and (3) explicit modeling of hospitalization with treatment defaults reflecting healthcare system limitations in resource‐constrained settings. We analytically derive the basic reproduction number () and establish comprehensive stability criteria, demonstrating global stability of the disease‐free equilibrium when and existence of an endemic equilibrium when . Bifurcation analysis confirms the system exhibits forward bifurcation at the critical threshold . Parameter estimation using TB incidence data from Bangladesh (2001–2022) achieves high accuracy (MAPE = 7.12%), with estimated at 4.406658, indicating persistent TB endemicity. Global sensitivity analysis via Latin Hypercube Sampling and Partial Rank Correlation Coefficients identifies the transmission rate () as the most influential parameter affecting disease spread. Numerical simulations reveal that synergistic interventions targeting transmission reduction through preventive measures, decreasing treatment default rates, and optimizing hospitalization protocols can substantially reduce TB prevalence. The study provides a validated mathematical framework for designing targeted intervention strategies in Bangladesh and similar resource‐limited settings, offering both theoretical insights into TB dynamics and practical guidance for public health policy formulation.