1. People are identical, and have identical susceptibility to the virus.
2. People are identical, and have identical ability to spread the virus.
3. People are identical, and have identical exposure to the virus.
4. People are identical, and have contacts completely at random.
5. The only intervention considered is immunity. No help from behavior adjustments.
All five of these mistakes are large, and all point in the same direction.
I think you are making an error about 5. There are several questions you could ask the SIR model. If you mix them up, you get the wrong answer, but that’s not the fault of the model. The SIR model allows non-immunity changes by just changing R. The question of what would herd immunity be without behavior adjustments is a perfectly reasonable question. It is the question of what level of immunity would allow us to go back to normal without risking an outbreak.
Maybe I don’t understand what you mean by 2 and 3, but I don’t see how they predict systematic deviation from the SIR model, unless the effects in 2 and 3 are correlated. Probably I would just subsume 2 and 3 into 1 and 4.
I see three main deviations from the SIR model. One is natural immunity. Like Owain, I think that this is overplayed, at least in Europe. The second is the network difference you talk about between the connected and the isolated. But the third is the obvious network structure of cities. Talking about whether Italy has achieved herd immunity is an error: Milan can achieve it without protecting Naples. Talking about a national immunity threshold is a category error and using national PCR and antibody numbers is not so useful. (I’m not sure how badly this paper makes this mistake. It does talk about Madrid and Catalonia, but in other countries I think it uses the only data it can.)
I think you are making an error about 5. There are several questions you could ask the SIR model. If you mix them up, you get the wrong answer, but that’s not the fault of the model. The SIR model allows non-immunity changes by just changing R. The question of what would herd immunity be without behavior adjustments is a perfectly reasonable question. It is the question of what level of immunity would allow us to go back to normal without risking an outbreak.
Maybe I don’t understand what you mean by 2 and 3, but I don’t see how they predict systematic deviation from the SIR model, unless the effects in 2 and 3 are correlated. Probably I would just subsume 2 and 3 into 1 and 4.
I see three main deviations from the SIR model. One is natural immunity. Like Owain, I think that this is overplayed, at least in Europe. The second is the network difference you talk about between the connected and the isolated. But the third is the obvious network structure of cities. Talking about whether Italy has achieved herd immunity is an error: Milan can achieve it without protecting Naples. Talking about a national immunity threshold is a category error and using national PCR and antibody numbers is not so useful. (I’m not sure how badly this paper makes this mistake. It does talk about Madrid and Catalonia, but in other countries I think it uses the only data it can.)