World Health Organization information on Ecuador vaccinations

Here's some World Health Organization information on they recommend for vaccinations if you're going to Ecuador. The essence of it is Yellow Fever, yes; Malaria, no.

http://www.who.int/ith/countries/ecu/en/

And for more detail, here's the link from the Center for Disease Control. Yellow fever is a must, and the others are recommended, but not required. Err on the side of caution, as they say, so when in doubt, get the shot.