The “Sick Man of Asia” originally described China.
   
 
Wikipedia: Sick man of Europe
“Sick man of Europe” is a label given to a European country experiencing a time of economic difficulty or impoverishment. The term was first used in the mid-19th century to describe the Ottoman Empire.
   
Origin
John Russell in 1853, in the run up to the Crimean War, quotes Nicholas I of Russia describing the Ottoman Empire as “a sick man—a very sick man”, a “man” who “has fallen into a state of decrepitude”, or a “sick man ... gravely ill”.
 
It is not easy to determine the actual source of the quotation. The articles cited above refer to documents held or communicated personally. The most reliable, publicly available source appears to be a book by Harold Temperley, published in 1936. Temperley gives the date for the first conversation as 9 January 1853, like Goldfrank. According to Temperley, Seymour in a private conversation had to push the Tsar to be more specific about the Ottoman Empire. Eventually, the Tsar stated, “Turkey seems to be falling to pieces, the fall will be a great misfortune. It is very important that England and Russia should come to a perfectly good understanding… and that neither should take any decisive step of which the other is not apprized.” And then, closer to the attributed phrase: “We have a sick man on our hands, a man gravely ill, it will be a great misfortune if one of these days he slips through our hands, especially before the necessary arrangements are made.”
 
(Oxford English Dictionary)
sick man  n. a term frequently applied, during the latter part of the 19th cent., to the Sultan of Turkey. Also figurative, originally applied to Turkey and hence to other countries, regions, etc., and in extended uses.
Quot. 1853   refers to a conversation between the Tsar Nicholas I and Sir G. Seymour at St. Petersburg on the 21 Feb. 1853.
1853   Ann. Register, Hist. 252   I am not so eager about what shall be done when the sick man dies, as I am to determine with England what shall not be done upon that event taking place.
1855   J. Martineau Ess., Rev., & Addr. I. (1890) 428   It was all right not to let the ‘sick man’ be frightened into convulsions.
1860   J. L. Motley Hist. United Netherlands I. ii. 30   That formidable potentate, not then the ‘sick man’ whose precarious condition and territorial inheritance cause so much anxiety in modern days.
1860   S. S. Cox Eight Years in Congr. (1865) 129   ‘Mexico is our “sick man”.’ ‘Yes; she is to America what Turkey is to Europe.’
       
OCLC WorldCat record
That sick man of Europe,
Author: Nancy Louise Henson
Publisher: [Los Angeles], [Wetzel Pub. Co.], [©1943]
Edition/Format:   Print book : English
 
OCLC WorldCat record
The Ottoman Empire : was it the sick man of Europe.
Author: Stavrianos.
Publisher: New York : Rinehart, [1951]
Series: Source problems in world civilization.
Edition/Format:   Print book : English
   
OCLC WorldCat record
The sick man of Europe : Ottoman Empire to Turkish republic 1789-1923
Author: Charles Swallow
Publisher: London : Benn, 1973
Series: Benn’s world histories
Edition/Format:   Print book : English
   
OCLC WorldCat record
Britain—the sick man of Europe no longer.
Author: Bernard D Nossiter
Publisher: Encyclopedia Americana/CBS News Audio Resource Library [1978]
Series: Vital history cassettes, Nov. 78, no. 2.
Edition/Format:   Audiobook : EnglishView all editions and formats
Summary:
Journalist Bernard Nossiter, author of a recent book on contemporary Britain, alleges that Britain is in much better shape than is generallly supposed. The loss of the Empire was a plus rather than a minus, he says, it is on the road to economic recovery, its democratic government is stable and its people are, by and large, content.
 
OCLC WorldCat record
Italy today : the sick man of Europe
Author: Andrea Mammone
Publisher: New York : Routledge, 2010.
Edition/Format:   Print book : English : 1. publ
Summary:
Offers an analyses of contemporary Italy. This book contains essays that aim to highlight the ‘crisis’ of the country.