The term best describes a disease transmitted to man through animals:
The disease transmitted to man through animals - Zoonoses have different modes of transmission. 
In direct zoonosis, the disease is directly transmitted from other animals to humans through media such as air (influenza) or through bites and saliva (rabies).
In contrast, transmission can also occur via an intermediate species (referred to as a vector), which carry the disease pathogen without getting sick. (Indirect zoonosis).
Communicable
Transmissible
Zoonotic
Vertically transmissible