Is it permissible for the wife to travel alone if the husband is in America for treatment and unable to travel due to his health condition?

The basic principle is that it is impermissible for a woman to travel without a mahram. However, if there is a legitimate necessity for her to travel without a mahram, then there is no harm in it. For instance, if your wife is compelled to travel and has no mahram other than you, while taking precautions for her safety, such as traveling with a trusted companion and having the mahram meet her at the airport.