We consider a society at the brink of eliminating TB. Individuals enter the population at a rate .
A proportion, , of individuals entering the population are vaccinated and enter the vaccinated class .
We denote classes of suspectible by , latently infected and unvaccinated by , latently infected and
vaccinated by
, actively infected by and recovered by . Susceptible individuals once infected can
either progress quickly to active TB at a rate or develop a latent infection and move slowly to active TB
at a rate . Our model is thus given by