Mathematical model of tuberculosis considering observed treatment and vaccination interventions

Abstract

In this study, a mathematical model of tuberculosis (TB) spread is constructed, considering vaccination and observed treatment. Slow-fast infection and treatment failures are also considered in the model. Mathematical analysis show that the TB-free equilibrium is locally stable if the basic reproduction number is smaller than unity, and it becomes unstable when this number exceeds unity. Furthermore, the TB endemic equilibrium exists only (and uniquely) if the basic reproduction number is larger than unity. Our results show that even though the basic reproduction number is more sensitive to vaccination than observed treatment interventions, both interventions exhibit potential for controlling the spread of TB in the population.

Subject Classification:

• 97A30
• 92B05

Keywords:

• Vaccination
• Observed treatment
• Basic reproduction number
• Forward bifurcation
• Sensitivity analysis