Answer:
I don't know the powers you gave the government you created, but in this situation, the most reasonable course of action would be to place an immediate lockdown. Begin procedures as if it is a deadly pandemic. If girls can't transmit or carry the sickness, pair up men with women while in lockdown. Preventing the spread is one of the first steps to stopping the sickness. Assuming that the sickness is spread like a virus, require stay-at-home orders in order to keep citizens locked down and safe. You can fill in the rest by yourself?
Hope this helps in any way!!