There is light at the end of the tunnel especially for an island like Cyprus. You have a natural defence, but only if you close down your border to unnecessary travel.
Even when citizens like me come to Cyprus, you must force them and everyone to isolate.
Setting up isolation centers at hotels seem to work well, because the RoC can have the police or security monitor the quarantined.
It seems to be that tight border controls are the most important thing of all. Most of your cases would have been imported. If you put an end to that, then through isolation, you should get on top of things very quickly.
But BEWARE! There are China Virus carriers in the occupied. Any border controls will also have to mean the closure of all check points. That is your weak spot.
Good luck. It is possible to be out of the woods within a month if you play your cards right.