That’s the sort of question that the later parts of the Kissler, et al. paper try to answer. I’ll be discussing those parts in a future post. I haven’t finished examining what they did, so I can’t say exactly what I’ll conclude about that.

Leaving aside the particulars of this paper, though, I think it’s reasonable to see COVID-19 staying around as a seasonal (in temperate regions) disease as one possible scenario. If so, it might also evolve to become serious (though of course in many people it is already not serious). I think it’s pretty hard to make definite predictions.

]]>I think you’ve reversed “ILI” and “non-ILI” in your second paragraph. The seasonality of non-ILI visits seems to be tied to calendar events, such as the start of school. The ILI seasonality seems to be tied to virus dynamics, which has a general seasonality, but with peaks that aren’t precisely timed by the calendar (varying by several weeks, perhaps because of the weather that year, or whatever). In both cases, there could be a bit of the other kind of seasonality, but putting in both kinds for both ILI and non-ILI visits seems too complicated.

The ability of sums of sin and cos to produce any phase is important to getting the calendar sort of seasonality to have peaks in the right places, but doesn’t help if the peaks move around from year to year. One could build a model with an AR(2) component (which can exhibit oscillations of around some period, but not precisely fixed), but that seems too elaborate in this context.

]]>where is the observed count or index at time point , is the periodic, is some zero mean noise, and is a deterministic function of which describes the upramp/downramp of LI visits, probably a ratio of sums of exponentials. Over the course of a season the net contribution from is zero.

On the second point, okay, but per “Unlike for non-ILI visits, the seasonality for ILI visits is not firmly fixed to the calendar — the time of the peak varies in different years by several weeks — so a Fourier representation of seasonality that is common to all years is not appropriate”, mightn’t there be departures season by season even for ILI? Or does the uniform distribution for phase take care of that? And if it doesn’t, why doesn’t it take care of it for non-ILI?

]]>Allowing a linear combination of sin and cos doesn’t impose phase restrictions, since you can get a sine wave with any phase that way. In fact, even in a Bayesian context, this scheme works fine, since independent Gaussian priors for the regression coefficients on the sin and cos components results in a uniform distribution for the phase of the combined wave.

]]>On the seasonal, rather than use early terms of Fourier series, might do as done in state space modeling and declare that for any seasonal component , for , with samples in a season, then:

This would liberate, too, from the phase restrictions which and impose.

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