I have two corrections. First, you would say "An epidemic of dengue has broken out"; if you take away the "has", then "broke out" is fine, but if you want the verb to be in the present perfect, you need to change "broke" to "broken". 

Second, I would say the "the state of Sao Paolo". In English when we are talking about states we almost always say "the state of ________", just like we say "the city of _________". So we talk about the state of Texas and the city of Boston, but not Texas state and Boston city.

So your sentences change to: 

An epidemic of dengue has broken out in the state of Sao Paolo.

There is an outbreak of dengue in the state of Sao Paolo.