Plus, Japan takes public health very seriously, from what I recall, so many people would be wearing face masks from Day 1. The big disadvantage it would have as a nation is sheer population density. If they closed the barn doors after the horses escaped, then they'd have some big, big problems. Even if they did manage to keep the Illness out or even just contained, then you've got the issue of resources and how you're going to feed and care for that population. They'd be in rougher shape than Iceland in that regard, IMO.
In short, I think odds are good of there being a large group of survivors and some infrastructure in Japan, but the population probably took a few big hits from starvation, garden-variety illness and maybe a few contained breakouts. The other variable here is how well they'd be able to rebuild after getting hit by an earthquake.
Right, Japan would probably suffer famine like Iceland is implied to have.
But just to note, they produce about 90% of their own rice and eggs, and produce about half of their meat. Infected whales would probably be a problem since whale meat is still a notable part of Japanese cuisine (also, stranded whale trolls may be a serious problem with such a huge coast line).
Japan has suffered some severe famines in the past, though, without losing their collective minds. Culturally, the Japanese seem rather well-behaved in times of crisis.
A lot of essential things like cooking oil and soy beans are generally imported, though, which presents a severe problem for Japanese cuisine.
Decisive restructuring would be needed to reduce the famine, though, as Japan is only about 40% self-sufficient on a calorie basis, meaning over half of their population would be at risk, not to mention those that would die from otherwise treatable diseases.
But so long as their society would not collapse during the famine, they would be able to become self-sufficient as they used to be in the past.
The first decade would not be very pleasant in any case, even if they did manage to keep the rash sickness out.
Barring infection and societal collapse, the current Japanese population in year 90 would probably be somewhere around 20 million if lucky.
(keeping in mind that the Japanese have very low birthrates already, and famine would not exactly encourage more childbirth, so the population would decline for decades even without the famine)The decline of white collar jobs as the largest fields of employment would probably change a lot of Japanese society, though.
I imagine it would be less school and career focused, which in turn would probably lead to an increase in birth rates again eventually.
Also, Japan has a lot of cats, so that bit shouldn't be much of a problem.
Something I wonder about is the viability of survivors in Korea.
North-Korea, ironically, is best set to survive environmentally, but even today they are basically in a constant state of famine and receive a lot of foreign aid.
The world around them collapsing, particularly China, would have them hit by a famine that would utterly crush their society.
Couple that with the inevitable collapse of their leadership, and you've got a nation that wouldn't even need the rash to be snuffed out. It's not entirely unimaginable for certain farming communities to survive, though.
South-Korea also has winter, but considering what Minna said about Great Britain, the odds of those areas being viable are extremely low.
And I wonder about some of South-Korea's southern islands. Some of them seem farming oriented, and a defensive navy
might be able to save those areas, despite the lack of winter.