How do we get rid of a dry persistent cough?

Find the source: Cough is a reflex - there is always something that triggers the cough. For dry cough, the most common reasons are post-uri hypersensitivity, allergy-related, dry throat, chemical irritants, asthma (if you have a history of it). Once you find the cause, you can then treat yourself accordingly.

Depends...: It depends on the etiology of the dry persistent cough. If it is due to bronchospasm, a bronchodilator inhaler may be needed. If it is due to post-nasal drip, a nasal spray may be needed. If gerd is the culprit, meds to treat gerd may be needed, etc. A dry persistent cough may be due to several factors and all culprits need to be addressed for the cough to resolve.