This virus would be done away with somewhere in August.
The verb is "to be done away with" and is in the "passive future in the past". e.g. It is (historical present) the Spring of 1919 - Spanish 'flu is sweeping (historical present) through the world, but this virus would be done away with somewhere in August."
This virus would have been done away with by autumn.
This requires context, but may be a conditional if the sentence is followed by "if the authorities had taken action."
No one would have anticipated that it would be this long.
This is the past tense of "will".