I think the reason why the rash might still make it to Japan is that, even with the country on lock down, they are still bordered quite closely by mainland China; unlike Iceland which is isolated far from Europe and America, they would have to deal not with dozens of would be refugees, but with probably hundred of thousands; even with the entire Japanese navy mobilised, it would be very hard to prevent them all from passing through and carry the rash with them, especially given the tremondous size of Japan's coastline (29,751 km, compared to the US' 19,924 km and Iceland's 4,970 km) made up of several thousands of islands, in a country that is bigger than Norway.
Eh, the distance between Japan and mainland China is
pretty damn huge.It's no simple day trip going over there, and any boat large enough to make the journey would also be noisy enough to quickly be detected once international traffic around it dies down.
I believe it's also been generally established that most people would not attempt to flee from the rash like you would a regular natural disaster.
Most would board up in their homes, or go further
inland into their own countries, which requires less resources and effort on the refugees' part.
Japan does have a huge coastline, but realistically there's only a fraction of it that actually needs tight defending.
There's the entire pacific ocean on one side, and a sparsely populated Eurasian mainland on almost the entire northern side. It is mostly just the sea between South-Korea and Kyushu that would need defending, and even there most of South-Korea's population lives on the
western coast of the country.
The Japanese naval forces is nothing to sneeze at either when mere defenseless refugees is the "enemy". The Japan Maritime Self-Defense Force
(which would most likely be mobilized as a state of emergency gets declared) has over one hundred ships capable of patrolling. To quote wikipedia
As of 2013, the JMSDF operates a total of 114 ships (excluding minor auxiliary vessels), including; two helicopter destroyers (or helicopter carriers), 26 destroyers, 13 small destroyers (or frigates), six destroyer escorts (or corvettes), 16 attack submarines, 29 mine countermeasure vessels, six patrol vessels, three landing ship tanks, eight training vessels and a fleet of various auxiliary ships. The fleet has a total displacement of approximately 450,000 tonnes (including auxiliary vessels).
They also have several hundred planes.
And that's just the maritime self-defense force. The Japanese coast guard has even more ships. Less deadly, but no problem facing unarmed ships.
The JCG operates 455 watercraft, these include the following:
Patrol Vessels: 121
Patrol craft: 234
Special guard and rescue craft: 63
Hydrographic survey vessels: 13
Aids to navigation evaluation vessels: 1
Buoy tenders: 2
Aids to navigation tenders: 18
Training boats: 3
And they've also got a bunch of planes and helicopters to do reconnaissance with.
These would undoubtedly all be mobilized as the rash started sinking its teeth into the Asian mainland.
We saw how merciless the Icelandic coast guard was, and I do not doubt the Japanese navy and coast guard would be even harsher. And Iceland's coast guard only has four ships, and the country has no armed forces other than that.
I'm not saying it's impenetrable, but defending against refugees is far from a hopeless case.