The triple-whammy of mosquito-borne illnesses — the Zika virus, dengue fever and chikungunya — has pushed Brazil’s universal healthcare system beyond its already stretched capacity at a time when there is little money to shore it up. In the state of Pernambuco, the scope of the epidemics is stunning: Reported mosquito-borne illnesses rose from 20,000 in 2014 to 150,000 in 2015.