When should the last lockdown end?
We can estimate when it will be safe to end all lockdown restrictions in the UK using the Imperial SIR model (report 9). Life can return to normal once the natural (unmitigated) value of R falls below 1
As of today (22nd February) we know that
- About 13.5 million people have contracted COVID and recovered. They are therefore immune and extremely unlikely to be re-infected
- 17.5 million people have been vaccinated so by now roughly 15 million of these people are already immune.
- The latest ONS infection survey 19th Feb found that 550,000 people were currently infected with COVID
The UK population is 66.6 million so as of today we have the following split in numbers
Susceptible = ~37.5 million Recovered = ~ 28.5 million Infected = 0.55 million
Now taking the original Imperial College model (Report 9) we can see where we currently sit on their SIR curve.
Vaccinating 17.5 million people moves them from susceptible to recovered without infection thereby reducing the unmitigated value of R<1
The good news is that we have basically already beaten the epidemic. Even if we stopped all lockdown restrictions next week the disease would eventually peter out because it already can’t find enough susceptible people to infect in an unmitigated state (shown above). Of course infections would initially rise because of easing restrictions but this would soon stabilise and then fall naturally. The downside is that for a short period hospital admissions would rise before collapsing. We can avoid that initial panic by waiting until the number of vaccinated doubles to ~35 million by mid April then it is probably safe to end all restrictions.
The epidemic would then essentially all be over my mid May and normal life can resume.
The only question is whether Boris will have the guts to do it. Let’s hope so !
Postscript: Boris is taking a very cautious step by step approach with the goal of ending lockdown in July. This looks over cautious but he wants to minimise any risk of extra deaths until all adults have been vaccinated. He apparently got spooked again by the latest models of Fergusson et al. !
Quote: “Due to eligibility and vaccine hesitancy, vaccination alone will not be sufficient to keep the epidemic under control. NPIs must be lifted slowly and cautiously to minimise the number of deaths and prevent high hospital occupancy, with some baseline NPIs remaining in place (and adhered to) throughout 2021 and beyond.”
I wonder what they mean by “under control” ?
How do the numbers change if you have a strain with X% change in its transmissibility?
How did you get 15/17.5 million immune? That’s a bit higher immediate immunity than the beeb is reporting for “reduction in serious illness” after 4 weeks.
Vaccines are going out at a great rate so we must be close either way.
If a new strain emerges with say 20% more transmission then R increase by X% so I think we would just we need to vaccinate 20% more people. That means waiting a week or two longer.
15/17.5 was just a guess to correct for the delay of a week or so before immunity sets in.
Either way there is no point extending the lockdown beyond April IMHO.
Does timing scale with R like that? First step in my thoughts: theoretical “herd immunity” approximation for R=3.9 is an 11% increase in total infections versus R=3. Not sure how that relates to timing, and it looks like the eventual attack rate is generally a bit worse than from this equation, which might dampen the change in infections a bit.
I thought the vaccinations were being given to people even if they’d already had an infection? A random assumption would give ~20% of vaccines therefore being “wasted”, based on your 20% previously infected rate.
My rough model would be ~2 weeks from jab until we can count someone as covered. So in 2 weeks we’ll hit ~25 million (accounting for infection/vaccine overlap and using today’s 83% reported efficacy), and at 2.5 mil vaccines/week we’d hit your effective 28.5 million “recovered” around week of 22nd March.
April might be right but I’d want more detailed calcs to shift my opinion.
The higher the initial R the faster the epidemic proceeds and the faster it ends.
You are right that the NHS is also vaccinating people who have already recovered from Covid.
So that means there is some double counting. Interestingly in France the policy is to give only one vaccination
for those who have recovered from Covid. This makes sense because the first jab is essentially a booster (second jab)
to the infection (first jab).
Your numbers may be more realistic. However the main point though is once we pass this threshold the epidemic is essentially over even if temporarily number of cases increase as restrictions are lifted.
I also don’t get this comment:
“Even if we stopped all lockdown restrictions next week the disease would peter out because it already can’t find enough susceptible people to infect.”
Isn’t that true of every virus for which we develop immunity from infection?
I thought you meant we’d get R1.
So I think that bit of your post is really easy to misinterpret and could use some clearing up.
Assertions 1) and 2) are incorrect for a couple of reasons. Neither category is “immune” from being reinfected or infected. They can be be infected but will most likely be asymptomatic. But still able to infect others. There is not adequate data to determine how long this limited immunity will last for either case. It is highly likely tha we will need boosters on a regular basis.
Yes you are correct but the effect is small. Only a tiny fraction of cases have consequently been reinfected and could be corrected for. Likewise no vaccine is 100% efficient. The Israeli data shows that transmission is greatly reduced. “Data showed that the vaccine was 89 per cent effective at preventing infection of any kind and 94 per cent effective against symptomatic infection.
So yes these need correcting but the overall message is the same. We can safely end lockdown in May.
A brilliant and clear take-down of the Ferguson model. Ferguson, if he were looking in, would have to either accept the conclusion or retract his team’s model.
I’m interested in endemic effects longer term – it is likely about a million people will enter the UK every year who have no protection, mainly ‘cos people make babies but also by immigration. To maintain an ongoing endemic equilibrium absent a vaccine around half would have to catch the virus, and hopefully they wouldn’t notice as babies and immigrants tend to be young, naturellement. But it won’t happen that way because there’s too much population immunity and the virus can’t get an entry point..
Until say after 20 years when we’ve added 20 million susceptibles to the UK population and most of the over-65s today have died or are about to. And Sars-Cov-2 is back
So the vaccine programmes are here to stay. Even the last of those starting trials now could be the preferred one for the long term.
Thanks.
You’re right that it looks like we will all have to have a yearly booster jab if the virus continues to mutate.
As long as the majority of the population maintain immunity it should protect the young and newly arrived migrants.
One other worry is the reluctance of some ethnic groups to vaccination in general. Certain jobs should require vaccination.
On November 30th you accused Boris of being “frightened of being blamed so it is easier to him to “follow the science and wait for a “vaccine””” because at the time Covid infections were dropping… of course, one month later, Covid infections surpassed their November peak on their way to more than doubling November’s numbers by early January.
Perhaps it is better to be on the safe side and actually wait to see the number of currently infected people drop to very low levels before opening. Maybe those low levels will indeed be reached by May, but in Boris’ position I would not be relying on handwaving based on using the number of vaccinated people plus the number of recovered Covid infections to derive a calculated R value of less than 1.
Also, while I’m pretty confident in vaccinations reducing transmission by somewhere on the order of 90%, I am actually less confident about actual Covid infections doing the same, particularly when the initial case was mild. E.g., see https://www.scientificamerican.com/article/why-the-u-s-is-underestimating-covid-reinfection/, but I also have anecdata in the case of my cousin who got a mild case of Covid back in April, and a rather severe case last month.
Reposting: I think including a link made my last post get hung up.
I basically noted 2 things:
First, you have a history of underestimating the pandemic.
November 30th: you noted that infection rates peaked on November 18th, and accused Boris of being frightened of re-opening. Observation: by December 20th the UK passed the November peak on its way to more than doubling that peak by January 9th.
October 31st: you claimed current measures were enough, that cases would turn a corner within a week.
June 17th: You guess that IFR is about 0.5% or maybe less. Observations: hard to tell, but in the US we have several states whose death rates are 0.2% of total population (including states like North Dakota which didn’t get hit in the first wave when one could argue that IFR was artificially high due to poor treatment), and I doubt that any of these states had more than a third of their population infected, so… I’m guessing 0.6% is a lower bound on IFR, and 1% is more likely.
Second, there is evidence that there is reinfection in some weak, early cases of Covid (google it). Anecdata: two of my cousins had mild cases of Covid in April, and then both got infected again in early January (with more serious symptoms, though both are recovering).
The thing is, it was hard to predict the emergence of the UK strain
The big unknown is whether more new strains will emerge as a result of vaccination. I heard (on TWIV) that these strains (UK, Brazil, South Africa) were always there but there was no positive selection of them until immunity began to build up -the implication being that people got the bug twice, at least enough to pass it on – the second bout being the new strain.
My guess is that new strain(s) will emerge enough to worry everyone, but not enough to have much effect. That’s because seasonality will kick in very soon – as soon as temperatures rise. (We’d probably like some new vaxs by autumn though.)
Seasonality explained – it’s not so mysterious:
https://www.preprints.org/manuscript/202101.0389/v1
PS I don’t think models like the Imperial College one really try to deal with seasonality. I think they just use a very crude fudge factor. They also don’t deal with dormant infections – both are major shortcomings.
Posting this picture tomorrow, accompanying my letter to Rishi Sunak (UK Chancellor of The Exchequer), with the Subject:
Insane, perpetual £31.83 billion/year cost of renewables in the Sixth Carbon Budget is self-harm economics.
This Blogpost refers: https://colin-megson.medium.com/by-2050-the-cccs-sixth-carbon-budget-calls-for-635-twh-year-of-despatchable-electricity-from-d1cac83a213
Search for: “by 2050, the ccc sixth carbon budget calls for 635 twh/year”
With WASPP technologies it will cost £31.83 billion each and every year, FOREVER!
With advanced NPPs it will cost just £8.41 billion per year.