HOUSTON — The menu includes pork or chicken dumplings, fried rice or chicken congee soup with jasmine rice and ginger. It’s an enviable repast that diners take in bed — hospital beds.

When it comes to ordering meals at Houston’s Memorial Hermann Southwest Hospital, immigrant patients can choose from dishes similar to what they might eat at home: dumplings or noodles for Asian palates, curry to accommodate Indian tastes.

These and other choices at medical facilities nationwide reflect intense competition to attract one of health care’s most desirable demographics — affluent, foreign-born patients with generous insurance coverage or cash to pay out of pocket.