Main Focus

With the spread of COVID-19 in Italy and Europe, many analysis have been published, focusing mostly on modeling infections and deaths trends.

While it’s obviously relevant, it largely depends on:

  • the way data is gathered across different regions and countries;
  • a large number of exogenous variables, including (but not limited to) hard to measure restrictive policies and potential effects on weather / temperature on the virus diffusion.

This has resulted in models with good descriptive effectiveness but low prediction accuracy, at least in Italy (see for instance: https://www.ilsole24ore.com/art/coronavirus-governo-stima-92mila-contagi-picco-18-marzo-ADfgS9C).

Instead of focusing on forecasting, I think that a question at least as important has yet to be addressed directly and objectively: “Looking at today new reported positive cases, when did the actual infection start?”

This is crucial as it implies a second question: “When will we start to see the effects of the policies put in place on a given day?” - a key question as the public opinion expects quick results… but maybe it shouldn’t.

Modeling Approach

I consider 3 main phases:

  • Incubation: the time elapsed from exposure to the pathogen, to the onset of the first symptoms;
  • Time to testing and hospitalization: the time from the first symptoms (usually fever and cough) to testing (tampone) and eventually hospitalization
  • Result and publishing: the time needed for the result to be made available and be count in the official statistics

The overall time at the end of the analysis is given by the sum of these 3 different phases.

Incubation

Many studies have been recently published of COVID-19, including: https://annals.org/aim/fullarticle/2762808/incubation-period-coronavirus-disease-2019-covid-19-from-publicly-reported

Most studies agree on a median of roughly 5 days and a log-normal distribution with an IQR of (3.8, 6.7).

Time to testing and hospitalization

A recent (11 March) study on Lancet details the times from first symptoms to the onset of dyspnoea (difficulty to breathe) and to the admission to the hospital: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30566-3/fulltext

Given the purpose of this analysis and considering that the above study refers to a different health system (the Chinese one), it gets tricky to understand when the actual COVID-19 test is taken in the Italian scenario

I consider it safe to assume that:

  • tests are not performed right after the first symptoms, to see if the situation improves by itself and also to avoid further overcrowding of Italian hospitals
  • tests are performed when dyspnoea starts to occur (as a lower bound) and for sure when the patient reaches the hospital / medical structure (as an upper bound).

Median times and IQR are provided in the above link:

  • 7 days median time for dyspnoea (4, 9)
  • 11 days median time to admission to hospital (8, 14)

No insights on the actual distribution are given. For simplicity I assume two log-normal distributions with roughly similar median and IQR values.

Result and publishing

Tests have to be taken to labs and the actual outcome takes a few hours. Official figures are published once a day.

I consider it reasonable to take a constant 2 days into account for this phase (as many others, see for instance: https://datastudio.google.com/u/0/reporting/d9e404d5-e65e-4cd4-a455-c06fd11546c7/page/L7zIB)

Overall view

Here I’m providing an overall picture of the time from infection to actual publishing a new positive case for COVID-19. While different studies may lead to slightly different figures, the overall picture should roughly lead to similar results.

Key Figures

Some key figures can be easily extracted from the above scenarios.

On a given day, we can expect the Positive Cases related to infections started in the last 10 days to be between 0.2% and 9.99%, depending on the two scenarios (lower and upper bound) described above.

In simple words, cases registered any day are largely due to infections started at least 10 days before.

According to the model described so far, the median case registered on a given day is between 13 and 19 days old.

Conclusions

Looking at these figures the other way around, it takes time to see the effects of policies put in place on a given day on the number of new positive cases.

In order to properly evaluate the effectiveness of countermeasures, this study shows that it takes at least two weeks to be able to carry out a serious data-driven analysis.