Covid 19 Numbers – lag

Recording some thoughts about Covid 19 numbers.

Today’s figures

The Government says:

“As at 6.30am on 22 March 2020, there have been 1,098 confirmed cases of COVID-19 in Australia”.

The reference is https://www.health.gov.au/news/health-alerts/novel-coronavirus-2019-ncov-health-alert/coronavirus-covid-19-current-situation-and-case-numbers. However, that page is updated daily (ish), so don’t expect it to be the same if you check the reference.

Estimating Lag

If a person tests positive to the virus today, that means they were infected at some time in the past. So, what is the lag between infection and a positive test result?

Incubation Lag – about 5 days

When you are infected you don’t show symptoms immediately. Rather, there’s an incubation period before symptoms become apparent.  The time between being infected and developing symptoms varies from person to person, but most of the time a person shows symptoms after about 5 days (I recall seeing somewhere that 1 in a 1000 cases will develop symptoms after 14 days).

Presentation Lag – about 2 days

I think it’s fair to also assume that people are not presenting at testing immediately they become ill. It is probably taking them a couple of days from developing symptoms to actually get to the doctor – I read a story somewhere (have since lost the reference) about a young man who went to a party, then felt bad for days but didn’t go for a test until someone else from the party had returned a positive test.  Let’s assume there’s a mix of worried well and stoic types and call it 2 days from becoming symptomatic to seeking a test.

Referral Lag – about a day

Assuming that a GP is available straight away and recommends a test immediately, logistically there will still be most of a day taken up between deciding to see a doctor and having a test carried out.

Testing lag – about 2 days

The graph of infections “epi graph” today looks like this:

One thing you notice about the graph is that the new cases bars seem to increase for a couple of days, then decrease – so about 100 new cases in the last 24 hours, but almost 200 in the 24 hours before that. From the graph, the last 3 “dips” have been today (Sunday), last Thursday and last Sunday.  This seems to be happening every 3 to 4 days. I initially thought that the dips might mean fewer (or more) people presenting over weekends, but the period is inconsistent with that. I suspect, instead, that this actually means that testing is being batched.

That would mean that neither the peaks nor troughs is representative of infection surges/retreats, but is simply reflecting when tests are being processed. This seems to be a 4 day cycle, so, on average it seems that it would be about 2 days between having the test conducted and receiving a result. So a confirmed case count published today is actually showing confirmed cases as at about 2 days earlier.

Total lag

From the date someone is infected to the time that they receive a positive confirmation is about:

lag = time for symptoms to show+time to seek a test+referral time + time for the test to return a result

So, the published figures on confirmed infections are probably lagging actual infections in the community by about 10 days (5+2+1+2).

If there’s about a 10 day lag between infection and confirmation, then what a figure published today says is that about a week and a half ago there were about this many cases in the community.  So, the 22 March figure of 1098 infections is actually really a 12 March figure.

What the lag means for Physical (ie Social) Distancing

The main thing that the lag means is that if we were able to wave a magic wand today and stop all further infections, we would continue to record new infections for about 10 days (and the tail for longer). In practical terms, implementing physical distancing measures will not show any effect on new cases for about a week and a half. That’s because today there are infected people who are yet to be tested.

The silver lining to that is that the physical distancing measures that have been gaining prominence since 15 March should start to show up in the daily case numbers from the middle of the coming week, possibly offset by overseas entrants rushing to make the 20 March entry deadline.

Estimating Actual Infections as at Today

How many people are infected, but unconfirmed as at today? To estimate actual infections you’d need to have some idea of the rate at which infections are increasing. For example, if infections increased by 10% per day for 10 days, then you’d multiply the most recent figure by 1.1 raised to the power of 10 (ie about 2.5).  Unfortunately, the daily rate of increase (see table on the wiki page) has varied a fair bit (from 20% to 27%) over the most recent 10 days of data (that is, over the 10 days prior to 12 March, since the 22 March figures roughly correspond to 12 March infections) and there’s no guarantee that since that time the daily increase in infections will have remained stable, particularly in light of the implementation of physical distancing measures. At 23.5% per day, the factor is about 8.

There aren’t any reliable figures we can use to estimate the rate of infection during the current lag period (ie from 12 March to 22 March). This is because the vast majority of cases have not been from unexplained community transmission. Most of the cases are from people who have been overseas in the previous fortnight and they’re the cohort that has been most significantly impacted by recent physical distancing measures. From 15 March, they have been required to self isolate and from 20 March most of their entry into the country has stopped.  So I’d expect a surge in numbers up to about 30 March – ie reflecting infections in the cohort of people rushing to get into the country before the borders closed followed by a flattening. With the lag factor above, you’ll need to wait until 1 April or thereabouts to know for sure.

Note:

This post is just about accounting for the time lag between becoming infected and receiving a positive test result. It assumes, for example, that everyone who is infected seeks a test, and that everyone who is infected and seeks a test is, in fact, tested. As at today, neither of these things is true.