Otto, you have pnemonia, we must only hope for the best.
The group of residents living in the annex are there because of their fears of the German society. They are mainly afraid of being captured and forced to live in a concentration camp. Also, the group fears of what the German society is capable of doing.
The rat infestation is just another problem that the occupants are faced with. Rats can carry diseases, which can spread to one of the people in the group. Also, the occupants must make sure the rats are all gone so they don't have to face any more problems with them.
The occupants living in the annex try their best to not get sick. They try not to because they could die due to lack of medical care. After all, the occupants living in the annex cannot get help even if they tried because the Germans would prevent it.