Agree, but with one amendment.
Coughing is not necessarily the problem. You can cough without having a respiratory disease, and respiratory disease can transmit without coughing.
Coughing is not necessarily the problem. You can cough without having a respiratory disease, and respiratory disease can transmit without coughing.
So what you write is really the basic truth: Try to contribute to the wellbeing of people around you. That shouldn't be so hard.