## Archive for 2020-07-06

### Critique of “Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period” — Part 4: Modelling R, seasonality, immunity

In this post, fourth in a series (previous posts: Part 1, Part 2, Part 3), I’ll finally talk about some substantive conclusions of the following paper:

Kissler, Tedijanto, Goldstein, Grad, and Lipsitch, Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period, Science, vol. 368, pp. 860-868, 22 May 2020 (released online 14 April 2020). The paper is also available here, with supplemental materials here.

In my previous post, I talked about how the authors estimate the reproduction numbers (*R*) over time for the four common cold coronavirus, and how these estimates could be improved. In this post, I’ll talk about how Kissler et al. use these estimates for *R* to model immunity and cross-immunity for these viruses, and the seasonal effects on their transmission. These modelling results inform the later parts of the paper, in which they consider various scenarios for future transmission of SARS-CoV-2 (the coronavirus responsible for COVID-19), whose characteristics may perhaps resemble those of these other coronaviruses.

The conclusions that Kissler et al. draw from their model do not seem to me to be well supported. The problems start with the artifacts and noise in the proxy data and *R* estimates, which I discussed in Part 2 and Part 3. These issues with the *R* estimates induce Kissler et al. to model smoothed *R* estimates, which results in autocorrelated errors that invalidate their assessments of uncertainty. The noise in *R* estimates also leads them to limit their model to the 33 weeks of “flu season”; consequently, their model cannot possibly provide a full assessment of the degree of seasonal variation in *R*, which is one matter of vital importance. The conclusions Kissler et al. draw from their model regarding immunity and cross-immunity for the betacoronavirues are also flawed, because they ignore the effects of aggregation over the whole US, and because their model is unrealistic and inconsistent in its treatment of immunity during a season and at the start of a season. A side effect of this unrealistic immunity model is that the partial information on seasonality that their model produces is biased.

After justifying these criticisms of Kissler et al.’s results, I will explore what can be learned using better incidence proxies and *R* estimates, and better models of seasonality and immunity.

The code I use (written in R) is available here, with GPLv2 licence.