  We analyze an epidemiological model with treatment and recruitment
considering the risk perception. In this model, we consider an exponential
function as a recruitment rate. We have found that this model undergoes the
transcritical Bogdanov-Takens bifurcation with boundary, where the system
experiences the transcritical bifurcation between the disease-free equilibrium
point and the endemic equilibrium point. The Hopf bifurcation also arises at
the endemic equilibrium point, this is, the appearance or disappearance of a
limit cycle, and finally, the Homoclinic bifurcation which transforms the limit
cycle into a homoclinic cycle, starting and ending at the disease-free
equilibrium point.
