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The infectious disease renewal equation expresses current incidence as a convolution of past incidence with an infectivity profile, multiplied by a time-varying transmission level.

An infectivity profile describes how an infected individual's transmission rate varies with infection age.

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.