It seems correct to write "A host of tools exists..." or "A range of tools exists...", i.e. the verb reflects the fact that you are referring to one collective noun. But, if I want to continue to talk about that collection of things, it often seems natural to say ". They aim to solve..." or ", which attempt to model...", i.e. now I am referring to the capabilities/intentions of the things within the collection. Which is strictly correct? And putting strict grammatical rules aside, which is an English speaker most likely to say?
a) "A host of tools exist, which aim to solve..."
b) "A host of tools exists, which aims to solve..."
c) "A host of tools exists, which aim to solve..."
My instinct is to avoid the construction and write "Several tools exist, with the aim of solving..."