Sleeping sickness in farm animals is usually

Sleeping sickness in farm animals (also called nagana in cattle) is caused by a trypanosome - a flagellated protozoan parasite of the genus Trypanosoma. The most common species affecting livestock in sub-Saharan Africa are Trypanosoma congolense, Trypanosoma vivax, and Trypanosoma brucei brucei. The parasite lives in the blood and tissue fluids of the host and is transmitted by the bite of the tsetse fly (Glossina species).

The option "transmitted by trypanosomiasis" is linguistically and scientifically incorrect. Trypanosomiasis is the name of the disease itself (the condition caused by trypanosomes); a disease cannot transmit itself. The correct statement would be "transmitted by the tsetse fly" or "caused by a trypanosome."

Brucellosis is an entirely different disease caused by bacteria of the genus Brucella, leading to abortion and infertility in cattle, goats, and pigs. Coccidiosis is caused by protozoan parasites of the genus Eimeria (coccidia), which infect the intestinal lining, primarily in poultry and young ruminants.