Am I using "containment" word in a correct way in this sentence?
Community containment can be a fast measure to halt the virus spread in the first states.

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The grammar is correct, but I am not sure if it expresses the idea that you want to express.

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Yes, I understand the word containment in that sentence. 
Better to say;
Community containment can be used to slow the spread of the virus  early on. 
or...
A way to stop community spread early is to use quarantine methods.