The risk of contracting malaria in other parts of the country is very low - speak to your doctor about anti-malarials such as chloroquine and doxycycline if you’re worried. Dengue on the other hand is a consistent problem. As there are no preventative treatments for this, you should be as vigilant as possible when applying mosquito repellent, especially if you go to the Amazon region.
Before you go to Ecuador, make sure you’re vaccinated for all of the following: tetanus, diphtheria, pertussis, hepatitis A and B, typhus, rabies and yellow fever.
Parts of Ecuador, including Quito, are at very high altitude, so be aware that you may suffer from altitude sickness. Unfortunately, there’s not a great deal you can do about this, though locals swear by coca tea.