I don't whether this idea is tangential or parallel, but we have a similar problem when we use the R number alone to describe contagiousness. A pathogen with an R number of 2 is far more contagious than another with an R number of 3, if the generation time of the former is a week, but that of the latter is a year. The timescale of the effect is essential when describing contagiousness, but I'm not sure I heard anyone in the media ever quoting generation times. Perhaps it wasn't so relevant for Covid if its generation time was stable, but it is necessary if you want to convert the R number into a growth rate, which I think is a more useful piece of information.
Strictly speaking, I wouldn't say R=2 with a shorter generation time is less contagious than R=3 with longer generation time, because contagiousness is typically defined in terms of secondary transmission events rather than timescale. But as you note, growth rate would be larger and hence would reach more cases sooner (even if overall epidemic might be smaller). This tradeoff between generation time and R was often an issue for new COVID variants, because wasn't initially clear if growth was coming from higher transmission at individual level, or shorter timescale, e.g. this paper we had on Delta: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8354568/
This conversation reminded me of studies using UV lights in schools to reduce measles transmission. In 1946, James Perkins of the New York State Health Department studied measles outbreaks in Albany schools. He found that ultraviolet (UV) lights didn’t reduce the total number of cases—the attack rate was the same—but they changed the tempo of transmission. In classrooms with UV lights, outbreaks smoldered. In those without, they exploded. Measles was too contagious to stop entirely, but UV lights slowed its spread. Students in UV-lit classrooms were more likely to catch measles on the school bus than in classrooms.
I don't whether this idea is tangential or parallel, but we have a similar problem when we use the R number alone to describe contagiousness. A pathogen with an R number of 2 is far more contagious than another with an R number of 3, if the generation time of the former is a week, but that of the latter is a year. The timescale of the effect is essential when describing contagiousness, but I'm not sure I heard anyone in the media ever quoting generation times. Perhaps it wasn't so relevant for Covid if its generation time was stable, but it is necessary if you want to convert the R number into a growth rate, which I think is a more useful piece of information.
Strictly speaking, I wouldn't say R=2 with a shorter generation time is less contagious than R=3 with longer generation time, because contagiousness is typically defined in terms of secondary transmission events rather than timescale. But as you note, growth rate would be larger and hence would reach more cases sooner (even if overall epidemic might be smaller). This tradeoff between generation time and R was often an issue for new COVID variants, because wasn't initially clear if growth was coming from higher transmission at individual level, or shorter timescale, e.g. this paper we had on Delta: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8354568/
This conversation reminded me of studies using UV lights in schools to reduce measles transmission. In 1946, James Perkins of the New York State Health Department studied measles outbreaks in Albany schools. He found that ultraviolet (UV) lights didn’t reduce the total number of cases—the attack rate was the same—but they changed the tempo of transmission. In classrooms with UV lights, outbreaks smoldered. In those without, they exploded. Measles was too contagious to stop entirely, but UV lights slowed its spread. Students in UV-lit classrooms were more likely to catch measles on the school bus than in classrooms.