**Summary**

**Friends**: Lockdown#2 began 22 days ago on 5th November, and this week’s data finally suggest that it is working!

**Last week I wrote that **if Lockdown#2 were working, then we would expect to see:

*The rate of***positive tests**falling.*5 to 10 days later,***hospital admissions**would fall.*After a further 5 to 10 days, the***rate of deaths**would fall.

**The latest data are discussed below** but the headline is this: *the rate of ***p****ositive tests ***is declining*. Consequently, the rate of **hospital** **admissions **and **deaths **should eventually fall too.

**Also, the rate at which positive tests **are falling is in line what I thought were the most optimistic assumptions conceivable. Basically – and this surprises me – based on these few day’s data, Lockdown#2 appears to be as effective as Lockdown#1.

**This is good news:**

**Restrictive though life is** under the current measures, there is much more activity than there was under Lockdown#1. Collectively we seem to have got better at social distancing and wearing masks and hand washing. This achievement offers us the prospect of a workable compromise between lives and livelihoods.

**But…**

- with a 7-day-average death rate of 460 people per day this is not a good situation. In fact it is amongst the worst in the world.
- with viral prevalence still around 1% there is an ongoing risk that the death rate could again increase rapidly if adherence to restrictive measures lapses, such as at Christmas.

**Let’s look at the data.**

**Data#1. Prevalence**

**Since late April** the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

**The number of people tested** and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 21st November 2020 on average 1.1% of the UK population were actively infected – 0.1% down on the previous week’s estimate.

**The raw count** of positive tests was:

- 2,040 from 169,333 people tested in the two weeks to 6th November,
- 1,974 from 158,308 people tested in the preceding two weeks, and
- 1,876 from 182,184 people tested in the two weeks preceding that.

**The data in the table** above are graphed below.

**Note these estimates **come from random survey tests (so-called Pillar 4 tests), not clinical tests.

**I have shown two curves **on the graph above.

- The
**black**dotted line (**– – –**) is the same curve I have plotted for the previous eleven weeks. (Link) - It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
- The
**blue continuous curve**is the ONS model for what is ‘really happening’.*I cannot explain how this estimate lies consistently below the data on which the model is based. Clearly there is something I have still not understood. I wrote to ONS 10 days ago requesting an explanation but I have not received an acknowledgement or a reply.*

**Data#2. Tests and Deaths**

**The graph below** shows three quantities on the same logarithmic scale:

**the number of positive tests per day****the number of people newly admitted to hospital each day****the number of deaths per day.**

**The data were downloaded** from the government’s ‘dashboard’ site.

- Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
- The deaths refer to deaths within 28 days of a test.
- Hospital admissions for the UK nations combined.

**All curves are** 7-day retrospective rolling averages of the data since July.

**The graph shows the data **alongside exponentially decreasing and then increasing trends shown as dotted lines.

**The**correspond to quantities halving every 21 days – the rate at which the epidemic declined during Lockdown#1.*declining*trends**The**correspond to quantities doubling every 15 days.*increasing*trends

**Back in July, the three data sets** initially fell with *similar* time-dependencies and then rose through the autumn.

**Data#3. Details and Projections**

**Because we are now** in the non-exponential phase of the epidemic, I have re-plotted recent data for **cases**, **admissions** and **deaths** on a linear scale below.

**I have also included some projections** (as dotted lines) taking *the most optimistic view possible*. I have imagined that:

- The effects of Lockdown#2 will begin to show through
,__on Day 324__*Looking back from Day 331, this seems to have been about right.*

- The declines will be as swift as in Lockdown#1 (halving every 21 days).
*Based on limited data, this too seems to be about right.*

- The declines will continue after the 2nd December end of Lockdown#2.
*The continued extensive and restrictive tiers announced this week means this is possible*

- The decline in hospital admissions is delayed 5 days with respect to cases
*There is some hint that this may be already visible.*

- The delay in deaths is delayed 5 days with respect to hospital admissions.
*A 5-day delay is the shortest conceivable and indeed deaths are still rising.*

**Here are this week’s updates.**

**The curved dotted-line projections** on the linear graphs above are effectively the same as the straight-line projections on the combined (logarithmic) graph. Please note that:

*These are guidelines not predictions*.- Look to see if quantities fall faster than this, or slower than this.

**Out of curiosity **I have also plotted the rate of **hospital admissions** relative to start of Lockdown for Lockdowns #1 and #2 below. We see that the 7-day averages rose for a clear two weeks after the start of Lockdown#1, and this has also happened in Lockdown#2.

**So…**

**I am allowing myself to feel briefly encouraged**: We have good vaccine news and seem to have found a way of living which – albeit highly restrictive – allows some economic and social activity while still driving down viral prevalence.

**Stay safe.**