The relationship between growth rate and serial interval

Some authors argue that, R0 = int(k(x), x=0..infinity) where k(x) is a reproduction kernel. The normalized quantity f(x)=k(x)/R0 satisfies int(f(x), x=0..infinity)=1. f(x) is pdf of the serial interval. This needs proof. In the compartment model setting: SIR for example, the claim is false.

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The relationship between growth rate and serial interval
This has been proved by Wallingua and Lipsitch (Proc B 2007)
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