when the US/UK/China, etc. sneezes, Japan/Germany, etc. catches cold
when (something) sneezes, (something else) catches a cold
When a person, group, or entity has a problem or experiences a negative situation, a related person, group, or entity will consequently have a worse problem or will experience a more negative situation. When Paris sneezes, Europe catches a cold. Terrorism in France affects security throughout the continent.
when the US/UK/China, etc. sneezes, Japan/Germany, etc. catches coldor
when the US/UK/China, etc. sneezes, Japan/Germany, etc. catches a coldmainly BRITISH
If you say that when a particular country sneezes, another catches cold, or catches a cold, you mean that what happens to the first country has a great effect or influence on the second. And when the American economy sneezes, the City of London catches cold. As they say, when America sneezes the rest of the world catches a cold.