To derive simple estimating equations for R (t ), I consider the case where this function is separable, which corresponds to saying that the relative progression of infectiousness as a function of time since infection is independent of calendar time. In this case b (t, t) can be written as the product of two functions w 1 (t ) and w 2 (t), i.e. b t,t ð Þ~w 1 t ð Þw 2 t ð Þ ð4Þ