How to calculate risk of someone being infected at an event

[AssumptionFifer]

Hi all. I'm cross-posting this here from the LiveScience forums, in the hopes of starting a discussion on how to best estimate risks for events in the context of COVID. (Note that the numbers are accurate for when I wrote it, on June 20th.)

It is a longer post, addressed to those with more knowledge in epidemiological forecasting (unlike me, having very little knowledge here).
I live in Spain (Catalonia, specifically), and was recently invited to an event of 50 people happening mid-July over 3 days. I wanted to take the current data and try to estimate the risk that at least someone at the event is ill with COVID-19, and is able to spread it to others.

I did my best, but I'm sure that it will all look very amateurish to anyone with even a bit of experience. I would love to learn more about doing it as well as possible, so thank you in advance for all your feedback. Here's the method I followed, broadly:

1. Decide on the relevant window of time
2. Gather the current official data on spread of infections
3. From that, estimate the real number of current infections
4. From that, estimate the risk that someone will have and be able to transmit the virus during the event

Details:

1. Decide on the relevant window of time
My first question was the time window to consider — the number of days in the past which still show detected cases that are potentially infective today. At least according to the data I have, infectivity seems to drop a lot in the 8th day after symptoms appear (when they do appear; if we're talking about asymptomatic cases I don't think we really know how infectivity progresses), and in the first couple of days after infection infectivity seems to be low. Which is to say, if one wanted to estimate the "current number of infective people in Catalonia", I imagined one should consider:

1. the median incubation period (5-6 days to my knowledge) plus
2. 8 days after symptom onset during which people are still infective on average

Note that I did not subtract the first 1-2 days of the incubation period in which people are unlikely to be infective yet, because in this video the Spanish officials suggest that the time delay between a person being tested and their result appearing in the statistics is now around 1-2 days, so presumably by the time they arrive to be represented in the statistics they're already infectious.
So the total so far is 14 days.

To these 14 days I thought it made sense to add the three extra days to cover the whole event; the danger I imagined was that someone might have just contracted the virus before coming, and reached relevant infectivity levels by the second, third day or the morning of the last day. So in total it would be a window of 17 days.

2. Gather the current official data on spread of infections in Catalonia
I used this government website (clicking on "Mapa de calor de casos per regió sanitaria") to filter for the past 17 days. (I'll redo the calculations with today's data as I write this.) So, from the 3rd to the 19th of June we have 62685 suspicious, plus 2470 confirmed cases.

The challenge is with these "suspicious" cases, about which they say that there isn't a test to confirm or infirm the infection. One has to make an assumption about the percentage of these cases that are actual infections. Pulling a percentage a bit out of a hat, I said 30%. Which makes the grand total 18805 + 2470 = 21275 relevant cases.

3. From that, estimate the real number of current infections
This is where I felt most lost. I ended up using some equations I found on Wikipedia, and starting from the method detailed in this article:

"Now, use the average doubling time for the coronavirus (time it takes to double cases, on average). It’s 6.2. That means that, in the 17 days it took this person to die, the cases had to multiply by ~8 (=2^(17/6)). That means that, if you are not diagnosing all cases, one death today means 800 true cases today."

Assumptions:

• the estimated effective reproduction number Rt for the time between now and the event. Looking at its recent values in Spain I will choose 0.5, which is less than the recent plateau of ~0.8 and a bit more than the average of the last few days, which may not be representative for the medium term (although one hopes they are)
• a serial interval of 5.2 days (He et al. paper linked above)

So, using the formulas in the simple calculation heading in the Wikipedia article, we get:

1. K = ln(0.5) / 5.2= −0.133297535, which helps us find:
2. Doubling time = ln(2)/K = −5.2. (NO IDEA WHY IT'S NEGATIVE ), which helps us get to:
3. Estimated "real" cases = cases reported in last 17 days × 2^(17/5.2) = 21275 × 9.641320594 = 205119 cases that would be still infective today.

4. From that, estimate the risk that someone will have and be able to transmit the virus at the event

Assumptions

• estimate of how many have already had the virus: 7% of the population. I'm looking at this study, which suggested in Catalonia the number was 6.1% at the start of June, so I'm bumping it up just a bit (since the rate of infection has decreased a lot lately) to estimate that percentage at the start of the event in July.
• everyone who's gone through the disease has immunity to the virus, and this lasts at least four months. I am aware this is optimistic (and I would love to see some data on this, because I don't have any), but I don't think it affects the numbers much.

Calculations

1. First, find the number of potentially-infective cases in all of Catalonia throughout the event: current estimate of "real" cases * Rt^(days to event / serial interval) = 205119 × 0.5^(19/5.2) = 16296.
2. Now, determine the chances that one person in Catalonia is infective at any point during the event: estimate of infective cases / (total population - estimate of how many have already had the virus). So, plugging in the numbers, 16296 / (7727029 * 93%) = 0.226% chance that one person will be infective during the event.
3. Now, determine the chances that the event will be virus-free throughout: (1 − 0.0022677)^50 = ~0.893
4. Meaning, the chances that at least one person will be infective during the event is (1 - 0.894) * 100 = 10.7%

I'm looking forward to learning how to do this better, and thanks for reading so far!

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