Is the Delta variant really more than twice as transmissible as the original strain of the virus?

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The Delta variant, which was first detected in India in October and has recently been spreading very quickly in many regions of the world, is widely believed to be more than twice as transmissible as the original strain of the virus. In this post, I start by explaining what people mean when they say that a variant is more transmissible than another, which leads me to make a distinction between a transmissibility advantage and a transmission advantage. In fact, by looking at French data beyond Delta’s initial expansion, I show that, as it became the dominant strain in France, Delta’s transmission advantage collapsed rapidly. Finally, I propose a theory that can explain why Delta’s transmission advantage was initially very high before collapsing, just as Alpha’s before it.

The effect of complex population structure on transmission has far-reaching implications beyond the debate about Delta’s transmissibility advantage, which I will explore in a forthcoming blog post where I will present modeling work I have done on this question. The Delta variant of SARS-CoV-2, first detected in India last October, has recently been spreading rapidly in many countries and is now the dominant variant of the virus in most of them. While there is compelling evidence that vaccines work fine against Delta, such as this study based on data from England, many are concerned that Delta’s high transmissibility means that vaccination will not be sufficient to contain the virus and that non-pharmaceutical interventions such as masking or even lockdowns and curfews will be necessary again. But I think the consensus on Delta’s transmissibility is deeply flawed and I will explain why in this post.

I will start by explaining how epidemiologists have reached the conclusion that Delta is more than twice as transmissible as the original strain of the virus and why the inference they’re making could easily be misleading. Finally, I will argue that, by not taking into account that evidence and assuming that Delta is more than twice as transmissible as the original strain in the models they used to make projections, epidemiologists are providing misleading guidance to decision-makers that might lead them to implement suboptimal policies.

Looking at the data beyond the initial expansion of the lineage shows that Delta is not as transmissible as claimed

One of those mutations, L452R, is present in Delta but not in other variants that are currently circulating in France, so we can use those data to estimate the prevalence of Delta over time. As I explained above in my review of the literature on Delta’s transmissibility advantage, one approach to estimate that advantage is to look at the relationship between the reproduction number for the whole epidemic and the prevalence of that lineage. The idea is that, if Delta is more transmissible than the other strains, a greater prevalence of Delta somewhere should be associated with a greater reproduction number for the epidemic in that place. However, finding such a relationship would hardly be conclusive evidence that Delta is more transmissible and failing to find it would not be conclusive evidence that it’s not, because Delta could have a large transmissibility advantage but spread in contexts that slow transmission down relative to the contexts in which the other variants are spreading and it could also have no transmissibility advantage or even be less transmissible than the other variants but spread in contexts that facilitate transmission relative to the contexts in which the other variants are spreading.

You can try to take into account that possibility by controlling for various factors that might confound the relationship between the prevalence of Delta and the epidemic’s reproduction number, but the problem is that we don’t really know what those factors are. Vaccination could be part of the reason why the reproduction number has recently fallen, but it can’t be the whole or even the main reason, because the vaccination rate didn’t suddenly increase between week 29 and week 30. Not only is the relationship between the prevalence of Delta and the epidemic’s reproduction number not linear, but there seems to be a clear period effect. In other words, part of that relationship appears to result from the fact that both the prevalence of Delta and the epidemic’s reproduction number have increased over time , while the relationship seems much weaker during any given period.

The parameter of interest is \alpha, Delta’s transmissibility advantage, for which I used a normal prior with a mean of 0 and a standard deviation of 1. This model is very similar to some of the models used in Abbott and Funk , a paper I mentioned above that used this approach to estimate Delta’s transmissibility advantage with English data. In the basic model, we just look at the relationship between the prevalence of Delta and the epidemic’s reproduction number. Since the epidemic’s reproduction number might change quasi-uniformly across departments for reasons that also have nothing to do with the prevalence of Delta, such as the rise in the prevalence of immunity due to vaccination , we add a national time-varying component in another version of the model.

It’s not obvious which version of the model is the best, so I’m trying a version in which the prevalence of Delta is the only independent variable, one in which there is also a department-level intercept, one in which there is a national time-varying component and finally one in which there is both a department-level intercept and a national time-varying component in addition to the prevalence of Delta. The estimates of Delta’s transmissibility advantage range from 26% to 44% depending on the model, but are often very imprecisely estimated. In fact, during the period for which Delta’s transmissibility advantage is the most precisely estimated , the model finds that Delta is 38% less transmissible than the other variants. To be clear, I don’t actually believe that Delta is less transmissible, I just point that out to emphasize that estimates of a variant’s relative transmissibility obtained with this kind of method or indeed with any other method that people use to estimate it should be taken with a grain of salt the size of Jupiter.

The truth is that we don’t have enough background knowledge about the data generating process to be confident that we can estimate relative transmissibility with that kind of approach. Thus, instead of trying to estimate Delta’s transmissibility advantage with a model that attempts to control for various potential confounding factors but that we have no reason to be confident will recover causal effects, we can use the other approach I described in my review of the literature and estimate Delta’s transmission advantage in France. As we shall see, this will actually cast further doubt on the idea that Delta’s transmissibility advantage is as high as people claim. Since we can estimate the prevalence of Delta at different points in time, we can use that to estimate the number of cases associated with Delta and non-delta variants over time in France.

In turn, this can be used to estimate the growth rates for Delta and non-Delta variants, which as I explained in the previous section can be converted into reproduction numbers and used to estimate Delta’s transmission advantage.

We can also perform this analysis at the department level and this shows the same pattern

19 The fact that estimates of Delta’s transmission advantage vary so much across departments is actually noteworthy. Some of that is no doubt measurement error, which is more of a concern at the department level because in some departments there are weeks during which few positive samples were tested for the presence of L452R, but most of that variation is probably real. 20 This suggests that other factors beside the intrinsic characteristics of the different variants play a huge role in explaining how fast they grow relative to each other, which in turn highlights the danger of interpreting estimates of Delta’s transmission advantage in a particular context as reflecting a transmissibility advantage.

What should we make of all this?

As I have explained, it’s very difficult to estimate Delta’s transmissibility relative to the other strains of the virus, because we only observe transmission. In practice, the estimates of Delta’s transmissibility advantage in the literature were obtained from the variant’s transmission advantage during the initial expansion of the lineage in various countries. As we have seen, in some cases, experts actually estimate a much larger transmissibility advantage. For instance, in the models they use to make projections for the French government, the epidemiologists I mentioned above assume that Delta is between 2.5 and 3.5 times more transmissible than the original strain of the virus, which implies a basic reproduction number somewhere between 6.4 and 8.7.

The problem is that, not only are estimates of Delta’s transmission advantage during the initial expansion of the lineage highly variable depending on the context and the method used, but as we have seen in the case of France, it sometimes almost completely disappears. If we used the transmission advantage they had in the latest data to estimate their transmissibility advantage over the previously established variants, instead of using the transmission advantage measured during their initial expansion, we’d reach the conclusion that Delta is at most 44% more transmissible than the original strain and has a basic reproduction number somewhere between 2.5 and 3.6 if we assume that it was 2.5 for the original strain of the virus. To be clear, I’m not saying that Delta’s transmissibility advantage over the original strain is no larger than 44%, this upper bound was obtained by looking at the variant’s transmission advantage after the initial expansion of the lineage and as I have explained there is no straightforward way to infer transmissibility from transmission. You could argue that if people infected by Delta don’t seem to have been infecting more people on average than people infected by another variant in France during the past month, it’s because Delta is now circulating in contexts that make it more difficult for it to spread than the contexts in which the other variants are circulating, so that other things are not equal.

In fact, as I will briefly touch upon in the conclusion of this essay, there are good reasons to expect that the transmission advantage of a variant during its initial expansion overestimates its transmissibility advantage. The point I’m trying to make here is just that it’s a bad idea to assume that Delta’s transmission advantage during its initial expansion is a good estimate of its transmissibility advantage, just as it was a bad idea to do it with Alpha and as it will be a bad idea to do it with the next variant that takes over after Delta, because a variant’s transmission advantage over the other variants depends not just on its transmissibility advantage but also on the contexts in which those variants are circulating and, with both Alpha and Delta, we have seen that whatever their transmissibility advantage the contexts in which the various strains are circulating clearly dominates since otherwise the transmission advantage would not vary so widely across different contexts. While I have focused on French data, this wide variability of Delta’s transmission advantage across contexts is not limited to France. Even between-country variation seems to be huge, with estimates ranging from ~25% to ~180% across countries in the study based on GISAID sequences I mentioned in my review of the literature, and those are pooled estimates over several weeks of data, so there would no doubt be even more variation if we estimated Delta’s transmission advantage in each country during each period separately.

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Source: Philippe Lemoine | CSPI

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