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I have been searching for a graph of the probability of infection (for covid 19) vs the number of days to the onset of symptoms. The following graph is taken from Namilae, et al (Multiscale model for pedestrian and infection dynamics during air travel): enter image description here

The above figure is for Ebola, adapted from CDC website.

I was thinking that at this stage of the pandemic, we would have this kind of data right now. Why would something like this not yet available after millions already infected?

Any insights? (Or anyone who has the lead to the probability of infection for covid?)

cgo
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  • I don't have any specific information, but as a complete guess I would say this issue is that it isn't as useful with COVID because there is a large body of individuals who are a-symptomatic. It's unclear how many this is, but some suggestions I've heard are between 40 - 80%. The second issue is that while it may seem like we are testing a lot of people for covid, are tests have high type I and type II error rates, so there is just a lot of uncertainty. In some ways the inability to make this graph is exactly why Covid is so difficult to deal with. – Tanner Phillips Oct 28 '20 at 11:51
  • This is a nice insight about symptomatic + asymptomatic patients. Would it be correct to say, if the graph above concerned Covid (and not ebola), then the 'true' probability of infection would have been higher because we need to consider both asymptomatic and symptomatic cases? (The graph above shows symptomatic patients only) – cgo Oct 28 '20 at 12:08
  • Yep, you got it. Ebola basically 100% of individuals are symptomatic. It's one (of many) reasons it didn't have large international spread. – Tanner Phillips Oct 28 '20 at 23:23

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Different types of intervals

There are several time periods that can be identified when person 'a' infects person 'b' (respectively the infector and infectee).

  • Serial interval: Time difference between symptoms of infector and infectee.
  • Generation interval: Time difference between infection times of infector and infectee
  • Incubation period: Time between getting infected and first symptoms.

plot

Serial interal

Often you see articles about the 'serial interval' (the symptoms are easier to track/observe than the time of infection). For covid-19 there are numerous articles that make estimates of this epidemiological parameter based on some model and set of observations.

For example, Ganyani et.el "Estimating the generation interval for COVID-19 based on symptom onset data" Euro Surveill. 2020 Apr 30

Computing infectiousness

In the article from Ganyani they have estimated the serial interval and the incubation time separately. They assume that these follow a gamma distribution.

Time distribution of infections relative to 1st symptoms in jnfector If X is the serial time and if Y is the incubation time for the infector, then X-Y is the time between infection of the infectee and the first symptoms of the infector (and this can be negative).

To get to the distribution of these times you can convolve the two gamma distributions (if the assumption is that X and Y are independent, which they often do in these models)

Infectiousness the above gives a time distribution of the infections (and sums up to 1). To get to the probability of infecting somebody you need to multiply this with the total number of people that get infected by somebody that is already infected. The $R_0$ or $R_t$ value.

Note that these distributions are constantly changing in time due to changes in measures like social distancing, increase (and simultaneously decrease) in immunity and possibly weather or other factors that change our health or the spreading potential of the virus.

The article from Ganyani estimates the curve by looking at data about infections and most others do the same. The article about ebola made the curve by using information about blood serum levels of the virus over the course of time (this sounds more rigorous, but note that this is based on very simple assumptions how blood serum levels relate to infection probability).

Sextus Empiricus
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