Capitalization is stylistic choice, and people may choose to capitalize things that you don't normally see capitalized. There are a couple of guidelines that come up in a simple search, and this is one of them. There's no unilateral consensus, but there are conventions. Chicago Manual of Style is another eminent manual that is both loathed and loved at the same time.
Back to your question, just like most of the words in this sentence, words in text and descriptions shouldn't be capitalized by default. That explains the yellow fever's case.
In the other two cases, the origins of the words are helpful:
The virus was first isolated in April 1947 from a rhesus macaque monkey that had been placed in a cage in the Zika Forest of Uganda, near Lake Victoria, by the scientists of the Yellow Fever Research Institute. A second isolation from the mosquito A. africanus followed at the same site in January 1948. When the monkey developed a fever, researchers isolated from its serum a "filterable transmissible agent" that was named Zika virus in 1948.
Thus, "Zika" is the name of a forest, and generally proper nouns, including the names of places, get capitalized.
The word 'chikungunya' is believed to have been derived from a description in the Makonde language, meaning "that which bends up", of the contorted posture of people affected with the severe joint pain and arthritic symptoms associated with this disease.
Often terms that enter English from foreign languages don't get capitalized. There is a related question on this on ELU.