Sunday, March 22, 2020

Mitigation vs suppression

Next thing to do is look at suppression. Vallance recently made an absolutely terrible comment that I find hard to excuse, describing the difference between mitigation and suppression as "semantic". It is not, the distinction is absolutely fundamental to the overall strategy.

The only excuse I can find for his comment is if he just meant we have to make strong efforts to reduce R0 as much as practicable in either case. But still, mitigation (R0 greater than 1) gives us an epidemic, perhaps slowed to some extent ("flattening the curve") but still spreading through a large part of the population until it burns out through herd immunity. Whereas suppression (R0 less than 1) means we control the epidemic, immediately reducing its spread from the moment controls are introduced (though it may take a week or two to see this clearly in the statistics). This threshold of R0=1 is a clear "tipping point" in the system, much more so than is apparent in just about any climate science I've seen. It is extremely implausible that a mitigation scenario would not exceed the figure of 20,000 deaths that Whitty talked about - it would almost certainly be upwards of 100,000 unless there are serious errors in the understanding of data currently available.

Here is a comparison between mitigation and suppression. At the day indicated by the vertical line, a policy is introduce which changes R0 from the base level of 2.5 (odd final digit just for convenience) to the values shown in the legend. The epidemics play out as shown. You may be a little bit puzzled that the number of visible lines doesn't match the legend.

Let's blow up the plot around the imposition of the controls. Oh there they are! All the R0 < 1 values drop away rapidly after a small delay of a few days. 

This also shows up strongly in the number of total cases over the duration of the epidemic. Mitigation (unless you get very close to 1 indeed) always ends up with a substantial proportion of the population infected. Suppression never does. They are as different as apples and kippers. By the way, the total population here is taken to be 67 million, so the R0=2.5 case gets about 90% of us. The suppression strategies are all well under 1%.

Suppression does need to be continued basically indefinitely however, at least until some external change to the paradigm like vaccines are produced. And it may be impossible to keep R0 under 1 indefinitely, due to economic realities. But at a minimum, it bears carefully looking at. It appears to be the current policy of the govt, but is not compatible with Johnson's claim that this will all be over in 12 weeks. That's what happens when you elect an incompetent buffoon to be PM. He might be able to bluff his way through a late-night essay crisis with a bit of cod Latin (haven't we all done that in our time) but when faced with a technical problem that requires attention to detail he is utterly out of his depth.

Ferguson et al describes some suppression controls (basically the current policy of widespread social distancing, plus case isolation and home quarantining) which together achieve R0 less than 1 in their model. Let's have a look at their figures and try to work out how effective they think these suppression policies should be. Their Fig 4 is the clearest guide - assuming a basic value of R0=2.2, they claim to keep a lid on the epidemic with policies in place for about 2/3rds of the time and off for the remaining 1/3 of the time. 

The plot suggests the policies need to be in place a bit more than that I think, but let's take their word for it. I further assume that the "off" state means no controls at all, ie reverting back to R0=2.2. Back of the envelope calculation suggests that the suppressed state should correspond to R0=sqrt(1/2.2) = 0.67 but that turns out to not quite be adequate and even R0=0.6 gives a very gradual rise over time with the drops seen during 20 days of the controls not quite cancelling out the growth in the uncontrolled 10 day periods. I haven't bothered to implement the thresholding procedure as described in Ferguson et al, just done a straightforward 20 days on, 10 days off to see what happens.

The vertical dashed line is drawn 3 days after the change in policy and roughly coincides with the turning point in the epidemic, showing the lag inherent to the system. I think the lag in this model is unrealistically short due to various reasons which are quite obvious when you look at the equations. It isn't designed to simulate changes over such short time scales as a few days. It would take even longer to observe in reality due to observing, testing and reporting delays. It would probably take at least a week to really see it.

Note that this calculation made the possibly optimistic assumption of R0=2.2. If we revert back to the original R0=2.4, and assume the suppressed state has an equivalently scaled value of 2.4/2.2* 0.6 = 0.65 (just my simple assumption but it seems a reasonable starting point), then in order to keep a lid on things we need to impose the controls for 22 days in every 30 days period and only have 8 days off, which is what is shown below. Or you could perhaps say 3 weeks on, one off. That's 3/4 of the time rather than 2/3rds. On the other hand I'm sure I saw someone estimate R0=0.3 from Wuhan during the lockdown. I can't find a link to that right now though and it did require very draconian control that we probably wouldn't tolerate.
Perhaps it would be more realistic to find a more sustainable approach which just kept moderate control maintaining R0 ~ 1 indefinitely. Even R0=1.3 would be a huge relief and buy us many months according to my top plots. That's one for the behavioural policy experts and epidemiologists jointly to work out. I have to say I'm not optimistic about the chances of the current govt and population collectively being able to control the epidemic indefinitely though I could imagine that widespread cheap and fast testing (for the virus, or better still, for antibodies) would radically change policy options and make control much easier to achieve.


Ben McMillan said...

Once you have got the cases down enough, you have enough resources to do large-scale contact tracing, extended quarantine for incomers and mass testing. Test anyone with a fever, anyone in contact with a known case, and regularly test health-care professionals.

That's worth probably a big factor in R0, so the rate of reduction (in relative terms) increases as you reduce the number of active cases.

Getting it to essentially zero over three months seems more practical than an indefinite yo-yo approach. In other words, it is not too late for the South Korea approach: but extensive suppression is needed first.

James Annan said...

Yes I agree 100% with that and it does provide a theoretical pathway to sustaining R0 below 1 without too much social order to get there from here, we probably need a month at least of R0=0.5 and I am somewhat sceptical of our abilities to do this. If we'd started earlier and got the testing sorted, it might have been a different story.

(hate that blogger can't handle less than or greater than signs properly, confusing them with html...was frustrating trying to write the post until I just gave up and spelt it out!)

Phil said...

The Hammer and the Dance.

Grant said...

The assumption is that suppression methodologies are applied carte blanche across age groups. However it seems feasible to test whether relaxing restrictions on a cohort up to age 55 but maintaining a social distancing strategy for the 55 to 75 grouping would modify substantially the time delta between trigger points in the adaptive suppression methodology.

I suggest the 55 to 75 age group for the obvious reasons .. they are more likely to be ICU candidates .. but also more likely to have n=2 per household .. and because I'm bracketed by that demographic!. They might also be more inclined to follow such guidance.