A new epidemiological model for the transmission dynamics of Tuberculosis incorporating vaccination and impact of environmental intervention

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Tuberculosis (TB) remains one of the most lethal infectious diseases globally, with a disproportionate impact on low- and middle-income countries. Its continued transmission is fueled by airborne spread, delayed diagnosis, and inadequate access to treatment. In response, this study develops a comprehensive mathematical model to assess the combined effects of vaccination and environmental interventions on TB transmission dynamics. The model incorporates key control strategies including vaccination, treatment, isolation, improved ventilation, environmental disinfection, and public awareness campaigns. Using the next-generation operator method, the basic reproduction number (R0) is derived to determine the threshold conditions for disease eradication or persistence. A thorough analytical investigation is carried out to examine the stability of both the
disease-free and endemic equilibrium. Numerical simulations conducted in MATLAB confirm the theoretical findings, illustrating that TB can be eliminated when R0 < 1, but persists when R0 > 1. Sensitivity analysis identifies the most impactful parameters, showing that early diagnosis, timely treatment, and environmental improvements significantly reduce disease transmission. This study presents a new integrated modeling approach that incorporates both biomedical interventions and
environmental control strategies, offering a more holistic a more holistic and realistic framework for TB control. The proposed model incorporates several critical features including vaccination, treatment, environmental interventions, and re-infection dynamics that are often absent or under- represented in many existing models. By capturing the complex interactions between these factors, the model provides deeper insights into the mechanisms driving TB transmission and control. Furthermore, the study emphasizes the importance of incorporating localized epidemiological data and realtime surveillance systems to enhance model accuracy and relevance through data fitting. It is recommended that future research should focus on using region-specific parameters and realtime monitoring to guide the development of targeted, evidence-based public health policies aimed at
reducing TB burden more effectively.