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The generation-interval distribution gives the probability law of the generation interval. In discrete time, its probabilities $g_{\tau }$ form a nonnegative sequence summing to one.

Assume the infectivity profile is separable:Then $g_{\tau }$ is the discretized generation-interval distribution, $R_t$ is the instantaneous reproduction number, and the infectious disease renewal equation becomesHence $R_t={\Delta }_t/{\Lambda }_t$ whenever the total infectiousness ${\Lambda }_t$ is positive.