The analysis of each words par of speech in the sentence would be the following:
During (prep), that (demonstrative adj), epidemic (n), early (adj), warnings (n), circulated (v), widely (adv)
Preposition: A prepositional phraseconsists on a group of words containing a preposition, a noun or pronoun object of the preposition, and any modifiers of the object.
Demosntrative adjectives: they demonstrate a quality about the noun they modify.
A noun refers to a word (other than a pronoun) employed to identify any of a class of people, places, or things ( common noun ), or to name a particular one of these (proper noun).
Adjective is a word naming an attribute of a noun.
Verb: a word used to describe an action, state, or occurrence, and forming the main part of the predicate of a sentence.
Adverb refers to a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, so on.