Probability an infected person would be in crowds of various sizes
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This spreadsheet simply calculates the probability that at least one person infected with Covid-19 is in a crowd of a given size, assuming a community infection rate.
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Assuming crowd members aren't psychopaths or idiots, the appropriate infection rate is for people who do not yet know that they are infected.
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It is important to note that nobody knows what that rate is so it's just a tool to test the implications of your assumptions.
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The calculation also assumes that the people who show up are a random subset of the population whose infection probabilities are independent.
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In other words, it does not apply to a group of 20 people stepping off a cruise ship or arriving from the same province in Italy.
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What is likelihood someone infected with COVID-19 is at your event?
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Probability that at least one participant is infected as function of number of participants and community infection rate
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Undetected community infection rate is 1 in …
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Expressed as Percent# of participants
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10301002501,00035,000
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1,000,0000.0001%0.00%0.00%0.01%0.02%0.10%3.44%
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100,0000.001%0.01%0.03%0.10%0.25%1.00%29.53%
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10,0000.01%0.10%0.30%1.00%2.47%9.52%96.98%
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1,0000.1%1.00%2.96%9.52%22.13%63.23%100.00%
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1001.0%9.56%26.03%63.40%91.89%100.00%100.00%
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1010.0%65.13%95.76%100.00%100.00%100.00%100.00%
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520.0%89.26%99.88%100.00%100.00%100.00%100.00%
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User can change highlighted cells2.540.0%99.40%100.00%100.00%100.00%100.00%100.00%
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FYI, the formula is 1 - (1-p)^n, where p is the community infection rate (column c) and n is the number of participants (row 11). (1-p)*n is the probability that nobody is infected. So 1 - (1-p)^n is the probability that at least one person is infected. You could also figure the probability distribution for the number of infected people, but that is a more complex calculation.
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Source: Len Burman (who is not an epidemiologist or infectious disease expert, but does know some probability and statistics)
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@lenburman
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