Mathematical models have been used extensively to gain insights into the spread and control of
TB epidemics. The dynamics of these models tend to generally be completely determined by a threshold
called the basic reproduction number (denoted by ) which is the total number of secondary infections
that an average infections individual will induce given that the rest of the total population is susceptible
(Dye,2006). In particular, when , a small influx of infected individuals will not generate large TB
outbreaks, the disease dies out and the DFE is asymptotically stable.