Kefalonia is pretty well locked down, the same as everywhere else. Movement restrictions, no restaurants or bars open and the season looks very bleak at the moment.
We have had no known cases of the virus until now, but it appears it is now on the island. Copied below is a report on the only known case, but likely to be others who were in contact.
Apparently the first known coronavirus case on Kef involves a man in his thirties, a summer season chef married to a native of Pyrgi but resident in Sweden with his wife and their three children. They arrived in Attica (greater Athens area) 17 March, instead of self-quarantining there they travelled to Kefalonia by car and ferry, arriving 18 March. That day he displayed symptoms and was tested at Argostoli hospital where he was strongly advised to isolate at home. When the result was known it showed positive.
Since arriving back on Kefalonia the adult female underwent surgery at Argostoli hospital. It's not yet known if she is carrying the virus. At least thirteen hospital employees who came into contact with the adult male are now in quarantine.
Their contacts on Kefalonia and residents in the villages of Pyrgi urged to self-isolate.