After searching in dictionaries, I have found that the phrasal verb 'deal with' is informal and its formal equivalent can be, among others, 'to handle'. However, when I searched for the verb 'to treat', I did not find any reference saying that the verb is informal (in Oxford Thesaurus of English, Pocket Oxford American Dictionary, and Chambers Universal Learners' Dictionary...they all consider it formal/neutral).
though I think it would be very informal to say in academic writing (as am writing an academic disssertation) 'to treat the situation' instead of 'to handle/or to manage the situation'. I think it is informal to be used academically. What do you think?