Don't talk - just act:
Every time the child is coughing without hiding his face in the elbow - not covering the face with the hand, because the virus can be spread by hand shake and then having contact with hands in the face (nose, mouth openings) - you can order quarantine in the children room.
If you don't act like this your child and yourself and the whole nation will be in a shut down and national quarantine sooner as you think. And then you will have time for discussions and explanations. (And then the children and all others too will be habit.)
If we were in a war the authorities would activate the sirens now. This is not the time of apocalyptics but it is the only chance to stop the spreading of this virus and to keep the hospital beds free for people who need it.
The other alternative would be that everyone has to cough with open mouth that all are infected as soon as possible with probably thousands of deaths. When everyone is infected the virus can't spread any more.
We all know that it - covering the face, but not with the hand - should work like an unconditioned reflex. But at it is not unconditioned it has to be conditioned. There are 2 ways:
- reinforcement of the goal behavior (that’s what Joe describes)
- or negative consequences = “punishment” of the wrong behavior (the alternative we don’t prefer)
My answer 3 days ago was a time out in his room every time the child forgets to cover his face. 3 days we are at the point that all children, coughing are not, can‘t see their grand parents for weeks. And people elder than 65 years are asked to stay inside. A week ago we still were shopping and met young mothers with 4 children in the super market running around. Meanwhile this is forbidden and teenagers are punished if they are in groups outside. Germany, France, Switzerland, Austria ...
Children are not victims of this virus but they can be infected and spread and there is no time to loose! No time to wait for developing habits. Also in the USA they will be isolated or walk around with a mask.
After the discussion about “praise” vs. “punishment” (s.comments below) I’ve edited “punishment” = negative consequences. OP clearly says that he has remembered the child (5 years!). He should have learnt it with 3 years.
Btw. I’d like to emphasize that I wrote “wrong” behavior and not “bad”. Unfortunately “punishment” and “praise” is always associated with good and bad. Consequences should be logical (positive or negative).
It is clear that children - and adults! with naive stereotypes consider negative consequences = punishment. (Look at the religions: negative consequences lacking of hygiene are interpreted as punishment of the gods. Same problem we have with our bad! dealing and habits with our environment and animals.)