Daily vacuumimg. Constant washing of anyplace Seamus sleeps. You may want to replace his bed. Throw out the current one and provide a blanket that can be washed. When the infestation is under control get him a new one.
There are websites that recommend different approaches. They will go when the weather gets cold BUT that's when you have to continue the battle until all the eggs and larva are dealt with.
Wonder why the ones at your house bite? Mine are content to annoy the cats. Constant flea combing is order too. Brush and comb; brush and comb. Then do Seamus too.