The time-dependent reproduction number Rt tells you how fast an epidemic is spreading right now. It is estimated from case data using renewal equations, which require one key input: the generation time distribution — how long, on average, between when a person is infected and when they infect someone else.
This distribution is typically assumed to be the same for everyone. But it isn't. Different population groups — age classes, geographic regions, communities with different contact patterns — can have systematically different generation times. The question is whether using a single, homogeneous generation time distribution gives the right Rt when the population is actually structured.
It does not (arXiv:2603.09451). When the true population has heterogeneous generation times, the one-group model can produce Rt estimates that diverge from the structured model in ways that would change public health decisions. The analytical results, simulations, and real epidemic data all agree: the homogeneity assumption bites.
The structural observation is about the direction of the error. The generation time distribution is a clock — it sets the timescale that converts case counts into transmission rates. Average over a structured population and you get the wrong clock. Not a noisier clock, not a slightly miscalibrated clock — a clock that can be systematically fast or slow depending on which subpopulation is currently driving transmission. If fast-transmitting groups dominate early and slow-transmitting groups dominate later, the averaged clock underestimates Rt at first and overestimates it later. The bias shifts sign as the epidemic evolves. The homogeneity assumption doesn't introduce random error — it introduces systematic error whose direction depends on the phase of the epidemic.