Can infectious diseases that do not confer immunity eradicate host species?

In SIS epidemic models with host population dynamics, two classes of incidence functions are identified for their potential to be linked to host extinction. Mildly  upper density-dependent incidences are never linked to host extinction. Incidences that are positively homogeneous of degree one are linked to host extinction for certain parameter constellations and to mere host decline for others; a threshold parameter is identified that separates host decline from host extinction.