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Infection caused by bacteria are curable by antibiotics. But the common cold is a viral infection. It is in the upper part of our respiratory tract. One of the viruses causing it is the rhinovirus. (It has types A, B and C). The Rhinovirus C is not understood yet. 

The viruses have a strong protein capsid around its DNA / RNA. The antibiotics are unable to penetrate the wall.

Common cold is not curable. It is only treated with medicines and other things.  The natural defenses in our human body slowly acts on the bacteria or virus and cures in about a week.  On the other hand some of the viral diseases can be prevented by vaccines.  But cure, no.

Common cold is due to viral infection. In order  to cure the common cold it will take 5 to 7 daystime .fo that we have to take antibiotics