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You say a mosquito-borne virus. But what do you say a virus infectious from human to human? 
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SupercatYou say "a mosquito-borne virus." But what do you say call a virus infectious that can get passed on from human to human?
Infectious!
You can also call it "communicable."
Emotion: wink
And if it can easily spread (typically by direct contact, e.g. by touching someone), then "contagious" can also be used.
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SupercatIf a virus is carried by an insect or animal such as mosquito and bat, do you call it a mosquito-borne or bat-borne virus?
Yes, those terms are fine.
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If a virus is carried by an insect or animal such as mosquito and bat, do you call it a mosquito-borne or bat-borne virus?
 Mister Micawber's reply was promoted to an answer.
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