After the asteroid crashed the virus scattered in the air quickly ready to transform many people. However this wasn't the case, the virus was actually a neural virus that was fed from negative emotions such as desire for power, vengance, lust, killing, and many bad things in people.
When the virus detected the person with strong negative desires it managed to enter inside the person's body, going to their brain and connect with it, leaving the person's mind intact but amplifying their negative thoughts. After the virus connected with the person it starts to change the body, shaping it with the desires of the individual, turning them into a monster girl (regardless of their gender) that can vary from a relatively normal size to a giant kaiju form or monstrous indescribable thing with femenine shape depending the person.
After the person is transformed the virus will gave them special abilities in their new monster form, the list of possible powers is basically infinite, varying between breathing fire, telekinesis, flying, to dangerous abilities such as controlling multiple people's minds, shapeshifting, time manipulation and a large etcetera.
After some incidents with the virus the government decided to take care of people emotions trying to promote their happiness and avoid negative thoughts to prevent more monster girl attacks, but there was always an exception of the person that couldn't control themselves and transform. The other government solution was to involve the military to stop them, but sometimes the monster girls were too powerful and scaped, some of them were trapped and locked up in special prisons, and some are still spreading chaos in some cities.
No cure has been found for this virus, scientist say that the transformation may be permanent, while others try to develop a cure or solution.