Models for diseases with vertical transmission and nonlinear population dynamics

Vertical transmission, the direct transfer of a disease from an infective parent to a new born offspring, is an important aspect of many diseases. Most of what is known for vertical transmission models assumes birth rates proportional to population size. We consider models with nonlinear population dynamics and finite carrying capacity and analyze the stability of equilibria in the special case in which the overall birth rate does not depend on infective population size.