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30 March 2020 - 4 minute read

The disease caused by SARS-CoV-2, the novel coronavirus, was not previously endemic in the UK population - we have no prior immunity to it.

For a moment, however, imagine that SARS-CoV-2 was in fact endemic in the UK, like flu or the common cold. Continuing this thought experiment, and by using basic mathematical modelling and simulated data, we find that the very act of exponentially increasing testing would itself produce an apparent rapidly growing number of cases.

The graph below shows what this would look like if a constant 7% of the UK population had SARS-CoV-2 throughout the testing history:

Positive Tests if SARS-CoV-2 Was Endemic at 7% in the UK

If we assume 7% of the population had the virus, then 7% of tests would come back positive, which would result in a different growth trajectory in cases to that actually observed.

As we can see, testing ramped up much more quickly than cases initially, resulting in our curves not matching. However, around March 12 the UK government changed the way it went about testing people. Before this point “community testing” occurred where people could request testing if they had travelled to affected areas, or if they simply felt unwell.

After March 12, testing was confined to hospitalised patients only. Returning to our imaginary endemic scenario, the probability of testing positive for SARS-CoV-2 is:

P(having a respiratory disease) x P(SARS-CoV-2 | having a respiratory disease)

Clearly for patients hospitalised for respiratory disease, the first probability becomes 1.0. If we assume that nine out of 10 outpatients taking a test have nothing wrong with them, then hospital patients are 10 times more likely to have any disease. In other words, before March 12 we assume SARS-CoV-2 is 1% endemic in the test population; after, we assume it is 10% endemic in the test population. Now the chart would have looked like this:

Positive Tests if SARS-CoV-2 Endemic at 1%, with Test Policy Change

Taking in to account the policy change to only test hospital patients, then a 1% endemic disease that makes up 10% of hospitalised respiratory illness would produce test results much closer to what was observed.

The disease behaviour is entirely stationary throughout this. By contrast, the exponential curve on the chart is a direct result of non-stationary testing.

We can continue the thought experiment to consider deaths. Flu kills about 0.1% of those infected. But 1-5% of those infected seriously enough to be hospitalised will die. In our model above, we know that after March 12 most the positive tests come from hospitalised patients. If we assume 1% mortality for hospitalised patients, but 0.1% for all infected, then our simulated deaths versus actual would look like this:

Simulated Deaths for Endemic Flu-Like Disease

Using the same endemic assumptions, and assuming the 0.1% overall mortality but that 1% of hospitalized patients die, we simulate a similar number of deaths being identified as caused by the disease.

This is not to suggest that SAR-CoV-2 was already endemic in the population before testing began. The point is simply that the testing profile and a change in whom the tests target can together generate the observed data, even if the actual number infected and dying does not change through time. Given this, the current approach to testing provides little information about the true number of cases and the true mortality of the disease.