Modeling the effect of tobacco smoking on the dynamics of tuberculosis transmission

A mathematical model for the effect of tobacco smoking on the dynamics of tuberculosis transmission is formulated and rigorously analyzed in a feasible region. With the absence and presence of smokers, the model shows that there is a possibility of backward bifurcation where the stable disease free equilibrium co-exists with stable endemic equilibrium when the associated reproduction threshold is less than unity. However the analysis of the associated reproduction thresholds of the model with smokers shows that tobacco smoking has detrimental effect on tuberculosis dynamics. Simulation of the co-existence model supports that; tobacco smoking has a detrimental effect on the dynamics of tuberculosis transmission. For non-smokers’ only model when natural recovery for infectious non-smokers is enhanced by the factor θ1 = 2, tuberculosis can be eliminated within the population. However in the co-existence model, when natural recovery for infectious smokers and non-smokers are enhanced by the factors θ2 = 3 and θ1 = 1.11 due to treatment, tuberculosis can be effectively controlled within the population.