Hereditary and antimicrobial factor shaping extracellular bacteria dynamics in an in-host mathematical model of tuberculosis for disease control

Tuberculosis (TB) remains a global health challenge, necessitating deeper insights into the dynamics of extracellular bacterial populations within infected hosts. This study presents an in-host mathematical model that incorporates hereditary and antimicrobial factors influencing TB progression. The biological feasibility of the model is established by analyzing the boundedness of solutions within a realistic parameter space. The equilibrium states, including the disease-free and endemic equilibria, are examined, revealing conditions under which the system remains locally asymptotically stable. Sensitivity analysis is conducted to determine the key parameters driving infection dynamics, providing insights into potential control strategies. Notably, the model exhibits a backward bifurcation, indicating the possibility of multiple stable states and suggesting that reducing the basic reproduction number R₀ below unity may not be sufficient for disease eradication. These findings highlight the importance of targeted interventions to effectively control extracellular bacterial populations and mitigate TB infection.