While im not sure i its actually confirmed what month the cataclysm takes place in, its raining in the first parts of the prolouge and then snowing by day 9 (pg. 36). Therefore i can assume that it´s around December, maybe November. Because of that, there was probably no tourists at the west coast at all. There are also no permanent residents on Väderöarna. However, on the largest of them, Storön (wich will be the one im talking about mostly) there are several summer houses and even a inn.
We know that people were getting paranoid. Therefore, my guess is that some local families, let's say five, packed their boats (probably sailboats in order to not having to worry about fuel) with supplies and fled to Storön in hopes of getting away from the Rash. There was probably a lot of suspicion towards the other families on the island if they may have the illness, but since they were all from more isolated fishing communities (hereby the dialect) none of them actually had it.
Then, they did their best to survive. After the first suspicion about the others carrying the Rash faded, they decided to all move into the inn in order to try and keep the warmth, looting the other houses on supplies. Living on fish, crabs and seaweed/wrack(im not entirely sure of the english word for it, its called blåstång in swedish).
Maybe the kids had friends they managed to contact via telephone (im unsure about the internet connection) only to hear how society was collapsing, and the horror stories of the dead turning into zombies. Eventually their calls were no longer answered at all. Then the electricity dissapeared.
And then, during a fishing trip, they noticed that what appeared to be a seal turned out to have worms crawling in it's eyes, flesh seeming to be rotting of its body. They were a lot more careful when fishing ater that. (They didn't even know how fortunate they were. That the water was to cold for the beasts to turn into trolls)
Also very fortuneatly, the families had two cats with them. A male and a female. They noticed if beasts were nearby. After the local rodent population started turning into vermin beasts, the cats were kept out of reach, fed from afar with slices of fish. But after maybe a month of chasing and eating the small beasts, the cats were still as healthy as ever. They simply did not get sick. After the people realised that, the cats were taken in again, getting pampered and bred a litteer of kittens. After the kittens grew, there was always a cat on board when fishing, acting as a warning alarm or beasts.
After a while, life on Storön grew a routine. There was always the fear of getting bitten by a vermin beast or attacked at sea, but they had the cats, and the sea beasts were too clumsy on land. Since noone else was fishing anymore, the fish population grew. Someone found a bag of potatoes in a cupboard and planted them on the small slice of soil that they had. They had to make due with some things they didn't have a lot of (like toilet paper. and tampons. dear god why) but they managed. The inn was the best place to live, especially in the winters, so they got used to living cramped up and eventually learned how to get along with as little fighting as possible. (The dialect grew)
After years of living isolated, maybe even decades, they finally made contact with other people. It was an accident, an icelandic ship on its way to Bornholm met one of their sailboats. After the initial confusion, there was a lot of relief of not being alone in the world. Finally they got some information about what the other communities had found out about the illness. Väderöarna still remained mostly isolated, but was put on the maps of the known world, and sometimes traders came from iceland, norway or denmark. Because of this, they finally managed to trade some guns and other things that they very much needed. They almost never got in contact with the rest of sweden though. As iceland and norway began believing in the old gods, they mostly remained agnostic atheism, but religion deveoped into a frequently discussed subject on the island.