Effective strategies toward controlling tuberculosis: optimal control and cost-effectiveness analysis

Abstract

This study offers an in-depth investigation of tuberculosis (TB) transmission dynamics and control strategies through a deterministic compartmental SEIT epidemic model. The stability of the disease-free equilibrium (DFE) locally and globally is analyzed corresponding to a basic reproduction number less than one (\(R_0<1)\). Additionally, our analysis uncovers the presence of backward bifurcation, which allows for the coexistence of disease-free and endemic equilibria even when \(R_0<1\). A sensitivity analysis highlights key parameters affecting \(R_0<1\) with the contact rate \((\beta )\) and progression rate \((\alpha )\) being the most influential. These findings inform the creation of effective public health policies to increase awareness through media and education \((\mu _1)\), enhance testing rates \((\mu _2)\), and improve treatment services \((\mu _3)\). The Pontryagin’s Maximum Principle is applied to determine the optimal control levels for the considered three intervention strategies \((\mu _1,\mu _2,\mu _3)\) over the simulation period. The results indicate that the objective function is influenced by the relative costs of each control measure and the optimal system is accessible numerically also. The findings suggest that interventions focused solely on media or educational awareness can be highly cost-effective, achieving low average cost-effectiveness ratio (ACER) alongside a high infection reduction ratio (IAR). These insights provide valuable guidance for public health policymakers in designing effective tuberculosis control programs. Ultimately, our research underscores the importance of comprehensive intervention strategies to successfully curb the spread of TB.