Dynamics of a Mathematical Model for Tuberculosis with Variability in Susceptibility and Disease Progressions Due to Difference in Awareness Level

This work extends a mathematical model for the transmission dynamics of tuberculosis that examined the impact of certain factors on tuberculosis case detection (Okuonghae and Omosigho, 2011). The extended model now classifies the latently infected individuals by their level of tuberculosis awareness (as was done for the susceptible sub-population) and further expands the number of key factors that can positively affect the tuberculosis case detection rate. The effect of these identified factors on the associated reproduction number of the model is considered. It is shown that the system can undergo the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity: in a special case, the effect of exogenous re-infection on the backward bifurcation phenomenon is significantly dictated by the level of awareness of the latently infected individuals. Qualitative and quantitative analysis of the model showed the effect of key identified factors on the dynamics of tuberculosis while suggesting a serious concentration on tuberculosis awareness programmes, active case finding strategies and use of active cough identification for identifying likely TB cases and sustaining awareness campaigns over a long period of time.