The answer to this question is two fold: 
  1. Warts on the feet are caused by a virus, the human papiloma virus (HPV), that commonly causes warts throughout the body.  This virus becomes infective only through direct contact.  This contact can occur in public places (when walking barefoot) such as public swimming pools, showers, locker rooms, gymnastic classes or karate classes.  It may also be encountered with poorly cleaned equipment during a pedicure.
  2. Warts have a genetic component.  Although warts are caused by a virus (and thus can not be inherited), the infection runs in families.  This is both because exposure can happen at home and also that certain individuals inherit the tendency for the virus to present as a wart.  The genetic or familial tendency + viral infection = wart.
Brandt R Gibson, DPM
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Podiatrist, Neuropathy Doctor, Father of 11 and Founder of Mountain West Foot & Ankle Institute