R naught is defined as number of infections from one sick person, and most of the paper when simulating the infectious number tends to directly multiply the current infectious number by R naught to get the newly infectious number. However, my doubt is this calculation seems to ignore the possibility that one people might be infected by the same two person, i.e., we would overestimate the newly infected people with direct multiplication.

My question is do we ever need to remove the overlap part in rigorous pandemic simulations or we don't have to at all ?


The correct interpretion of R is on a population-based, statistical level. In your example, if two infected people have contact with one person who becomes infected, we do not say they each have an "individual R" of 1, we say the population has an R of 0.5: 2 infected people result in 1 infected person.

Because you are basing R on population level statistics, you would never count an infected person multiple times based on multiple contacts, they are just one infection.

Sometimes R might be estimated from contact tracing, and in this case the situation you describe may be a problem, if you assume everyone in contact with a patient who goes on to get infected was infected by that person. Breban et al addresses this concern and is strongly relevant to your question (there might be better resources, too, this was just the first I found). The contact tracing method is more accurate if you have very few infected people such that it is unlikely that someone would be exposed to more than one possible source.

Breban, R., Vardavas, R., & Blower, S. (2007). Theory versus data: how to calculate R 0?. PLoS One, 2(3), e282.

  • So basically, it’s a measure of how an infectious population results in newly infected people, which cannot apply to individual analysis. Then direct multiplication makes sense. – exteral Dec 5 '20 at 18:09
  • @exteral Yes. I mean, you can apply it to individuals too, but there will be tons of variability for an individual and you can't count someone twice. – Bryan Krause Dec 5 '20 at 21:12
  • Now with some thoughts, I think that it could actually reduce to the individual analysis assuming that each infected people are contributing a portion to the newly infected people. I think it would be reasonably interpreted this way if we want to transfer a population R0 to a specific group with higher risk (with no data) with adjusted R0. – exteral Dec 7 '20 at 1:51
  • @exteral Yes, you just can't apply it the way you proposed in your original post. As long as you divide it up fractionally that's fine. But remember there is huge variability among people for SARS-like viruses. If, say, R=2, you have some people transmitting to >10 people and others transmitting to 0, it's just that the average works out to around 2. – Bryan Krause Dec 7 '20 at 1:58

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