"is desperately concerned" is correct and usable in written English.
You could use this phrase when you want to emphasize how much someone is feeling their concern or worry about a situation. For example, "The mayor is desperately concerned about the impact of the new policy on the local economy."
We should be desperately concerned.
"It's how people act that I'm desperately concerned about.
"Primary school teachers are desperately concerned about what the school day will come to mean for their pupils," she said.
Last summer, Bridgend coroner Philip Walters said he was "desperately concerned" about the number of suicides among young men in the region.
Australia's parliamentary secretary for foreign affairs, Brett Mason, said the families of the missing passengers "must be desperately concerned".
"The families are desperately concerned for them, and our priority is to get them back safely as soon as possible," he said.
The Daily Telegraph reported that police were searching for the couple in the Caribbean, and quoted a school spokesman who said the two families were "desperately concerned".
"But can I just add that the families of the... missing Australian passengers must be desperately concerned and the thoughts of the Australian government and I'm sure all Australians go out to them at the moment".
"That reflects what we learned — that people don't want to lose the health insurance they currently have, that they are desperately concerned about cost, that they want evidence based medicine and prevention.
Along with all bodies funded by the Department for Culture, Media and Sport, the scheme's budget is being reduced this year by 3%, to £7.45m, and authors are desperately concerned that further reductions will be forthcoming in the autumn, when the government's next spending review is published.
