There actually is a public health system here, plus a second back-up system. The public hospitals are notoriously underfunded, though, and basically give out Paracetamol for everything. For check up and tests and such, you have to get your own supplies, they give you a list for needles, syringes, bandaids, infusion water, almost everything.
The back up system is a combined social security and health insurance. During the good years, when Ecuador was running well, it worked nicely. But then the oil price fell, and corruption became obvious, and the state started "borrowing" money from that insurance, bleeding it dry to fund prestige projects. So, that isn't working well, either.
I have a private insurance that covers me up to 30k. I hope I'll never need it, until now, my awareness regarding my health seems to be working. Lily is insured there, too, but most of her little illnesses are the typical children stuff, so I don't even bother uploading the receipts as it's below the self-paying threshold most years.