You could also say, "A person may be infected with the disease by a contagious animal". The words "contagious" and "infectious" both refer to epidemic diseases and ways in which they spread. Contagious refers to disease spread from person to person by contact. Infectious refers to disease transmitted through environmental factors such as air, water and food. Hope this helps

Contaminated is a synonym of infected. Sentence: A person may be infected with the disease by a contaminated animal.

Michael, you could say it like this:

A person can be infected with the disease by contact with a sick animal.

A person may became ill through contact with an infected animal.

A sick animal can infect people through contact.

A sick animal transmits disease to people through contact.

A sick animal can transmit disease to people though contact.