The flipside of this for many (not all) of these poorer countries is that they have quite a bottom heavy population pyramid. IE lots of young people.
Italy & Spain have relatively top-heavy population pyramids & so while they have a lot of medical infrastructure, they also have a LOT of elderly - 23% of Italy's population is over 65. Conversely, Yemen's estimate of over 65s (2010) is 2.6%. So while the vulnerable in Yemen are definitely in the firing line, there's relatively few elderly.
(I know, Yemen isn't the BEST example, as it is also facing a lot of health issues thanks to the ongoing civil war, but I was able to pull the number easily)
The one that worries me is Indonesia. The population is over 230 million (4th in the world) and the over 65s are around 7%. So that's roughly 18 MILLION over 65... in a country with one of the highest smoking rates in the world; some really high population densities (Java has 145 million people and it's smaller than Victoria); a lot of poverty and a relatively undeveloped health infrastructure. It's going to get very ugly in our neighbours to the northwest.