During plagues, many Romans would flee the cities if they could. It was "every man for himself". Many could survive the plague with only minimal care, such as providing water and a little food.
I highly recommend The Rise of Christianity by Rodney Stark. It is a sociological book that examines how Christianity won over the Roman Empire.
The muslim "aid" workers would sit on stores of food and watch infidels starve all around them, unless they converted to islam, only then would they get any food or other aid.
Off hand I'd say it was at least as effective a conversion tool as the Christians in plague ridden Rome.
Today Indonesia is the world's largest islamic country, after all...
That presupposes that no one had previously had willingness to care for others, and that's nonsense.
One reason epidemics are so devastating is that not enough people flee.