A SIRS epidemiological model with two subpopulation and vital dynamics is analized. Both subpopulations are considered constant by assuming that the birth and the death rate are equal.  We analize the case where one subpopulation is a core, that is, a very infectious small group, responsible for a big fraction of the incidence. For this case a threshold is determined and the corresponding equilibrium points for the four dimensional system are shown to be locally stable by means of the classical Liapunov theorem. This system models the dynamics of typhoid fever, where the core is the group of food manipulators. Computer simulation are used to estimate the effect of vaccination on the population.