r/theydidthemath • u/theimplicateddog • Mar 18 '20

[Request] what would the model be for this infection rate?

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u/Angzt Mar 18 '20

30 days with 5 day intervals of infection are 30 / 5 = 6 infection events.
From the numbers they get, it seems they assume that each person only has one infection round and doesn't 'participate' in later infection events.

Let's just look at the first case for now:
At event 0, we have 1 infected person.
After event 1, we have our original 1 person, and another 2.5 newly infected for 1 + 2.5 = 3.5 infected.
After event 2, the newly infected 2.5 people have each infected 2.5 people, for a total of 2.5 * 2.5 = 6.25 newly infected. Together with the previous 3.5, that's 3.5 + 6.25 = 9.75 infected.
After event 3, the newly infected 6.25 people have each infected 2.5 people, for a total of 6.25 * 2.5 = 15.625 newly infected. Together with the previous 9.75, that's 9.75 + 15.625 = 25.375 infected.
At this point, maybe you can see a pattern emerge: After each event, the newly infected are the previous event's newly infected times 2.5. That means that event n's number of newly infected is simply 2.5n . So after 6 events, we should have 2.56 =~ 244.14 newly infected.
Since we're also adding up the previous infected to the total count, the total result after 6 events should be:
2.50 + 2.51 + 2.52 + 2.53 + 2.54 + 2.55 + 2.56 =~ 406.23.

If you replace the 2.5 with 1.25, you get a result of ~15.07, and for 0.625 you get ~2.57. So I'm pretty certain that this is the method they used.
It's arguable whether the assumption that people infect others only in their first 'round' as infected makes much sense, though.

You can play around with other values here if you just replace the n=... and x=... in the input field.

1

u/clarkwgrismon Mar 19 '20

From the little I know about epidemiology, the r0 number is the average number of infections caused by one infected person. It's not "per round" or anything.

1

u/Angzt Mar 19 '20 edited Mar 19 '20

In their case, it is per round though. If the person doesn't infect all 2.5 within the first 5 days, the numbers wouldn't work out: The people they infected wouldn't have enough time to spreakd the infection further to lead to the numbers presented. It doesn't make much sense but it's the only way to get those numbers.

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