The mosquito you call Asian Tiger is possibly from the Aedes family and could be the Aedes aegypti, which is common in east, west and central Africa.
It is known as a vector of yellow fever. It can be identified from other black and white mosquitoes by the absence of any curved scales on the back of the head and vertex and the arrangement of a ‘lyre’ marking on the dorsum of the thorax.
Mosquitoes have been known to be carried by ships and, therefore, it is possible that the “Asian Tiger mosquito” might have come to Malta from Africa on ships. Certainly, it has been found in fresh water lakes in Libya close to coast. It would unlikely to be able to travel across the desert.
I would suggest Malta sends a sample to the School of Hygiene and Tropical Medicine in London for positive identification.