Yes hospitalisations also useful.
I don't think we can have a second wave at the moment. I mean I think it is not possible.
Unfortunately the ONS declines to publish the raw numbers being tested and found positive/negative for covid-19
The data are here
www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/5june2020/relateddata
There are no data there on test counts and test dates!
However the ONS say the number being found newly infected is 'too small to publish' (!), and the number currently infected (not necessarily within the last week) is falling sharply.
So R must have been very close to zero for considerable periods of time.... Because we know that at LEAST 2.9 million people have been infected in England (based on antibodies), and now only around 60,000 are positive. As this has been going on for only 10 weeks, it's clear that the number infected was at one point MUCH higher. I.e. late March. The earliest estimate published was 150,000 positive, between 27 April and 10 May.
So we would have had say 100 people arriving from China or Spain or Italy or wherever infected with covid-19, and at one point that was displaying perfect exponential growth doubling every 3 days, until we reached a peak of current infections that was far over half a million. Some would have already recovered at the peak of infections of course, so don't forget that, and they all add into our 2.9 million, but clearly in the exponential growth stage, infectious people are infecting others before many have recovered.
Anyway, we locked the country down, and whereas previously the growth might have gone something like:
1 March - 10,000
4 March - 20,000
7 March - 40,000
10 March - 80,000
13 March - 160,000
16 March - 320,000
19 March - 640,000 (possible peak?)
So if we all went back to our dogging and rock concerts and what have you, our brains having been wiped by some sinister force, then in a week the infections could quadruple from their current level. And in 11 days or so you could get back to the peak.
But clearly that's not possible.
We now have data that were in March not available.
We are not going back to full on sweaty orgies tomorrow.
We are exercising caution.
And if it turned out that infections went from 60k this week to 65k next week that wouldn't necessarily be disastrous. Because clearly there are 'excess deaths' now with covid-19 afflicting 0.1% of the population. And if that were to go up to 0.15% there would be more deaths (not 50% more than now necessarily because of the way that current deaths may have been in hospital for months, and were infected when infection rates were higher).
But there isn't a number written in stone where we have to shut the country down again. We 'unlock' certain activities. We wait, we watch the numbers. Then if that's ok, we continue and maybe unlock more. And if the numbers start going up again then we re-evaluate.
But given major behavioural changes full exponential growth is very unlikely and we'd catch it before it could get back to normal levels. Note that we are seeing signs of boredom with this shit, in mass protests, which wouldnt have taken place in April under the same circumstances, and some people realising that covid-19 is not at all a threat to them (assuming they are young and healthy).
So we could at some point see infections going up again, but for now we have had continually declining infection counts (where that is active infections, not necessarily in the last 7 days) and very low new infections (except they are not publishing the raw data), but it doesn't seem like it's something that could just explode.