In early spring of '08 my DD was traveling on vacation in Fiji when she got a very serious bacterial infection in her foot. The treament in the Fijian hospital only made it worse. She moved on to New Zealand where she eventually wound up in a hospital in ChristChurch for 10 days, needing 3 surgeries and a skin graft.

She had purchased travel medical insurance before she left the US and that ended up paying the bulk of the $35K hospital bill. But the insurance company did not pay the VAT (value added tax) of nearly $4000. So be sure to check with whatever policy you do get on whether it will pay any local taxes.

When she travels overseas she always buys that insurance. Also, and I've said this before here, always check in with the US embassy or consulate whenever you're overseas. You can do so on the web at www.state.gov or by visiting the embassy once you're in country. The American Citizens Services (ACS) office was a big help to my DD, visiting her in hospital and advising her on local practices.

My brother taught English in China. His letters home were published as a book. It's available as a free downloadable podcast from Podiobooks

Best wishes to your traveling daughters.
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In a crisis one does not rise to one's level of expectations but rather falls to one's level of training.