Mrs. Izquierdo is described as a Crazy Cat Lady by the other residents of the building, but we never see her cats. However, she was the first of the infected. Maybe she killed and/or ate her cats.
Most people are possessed within seconds of being infected, but not Jennifer the young girl who was said to be ill for hours before succumbing. The religious background of the infection explains the discrepancy: Children Are Innocent thus take longer to possess than any of the adults who certainly have a fair share of sins to speak of.