Someone check my maths, please.
I'm trying to simplify 2 scenarios - say you have a limited amount of time to restrict growth of the virus due to economic implications.
Scenario 1: r0 = 2 for 5 iterations, r0 = 1.5 for the next 5 iterations
1: 2, 4, 8, 16, 32 at r0 = 2, then 47, 72, 108, 162, 243 at r0 = 1,5
Scenario 2: r0 = 1.5 for 5 iterations, r0 = 2 for the next 5 iterations.
1: 2, 2, 3, 5, 8 at r0 = 1.5, then 15, 30, 61, 122, 243 at r0 = 2
Obviously, the final number of fresh infections on the last cycle is equal in both cases, as its 25 x 21.5 in both.
But the sum of the sequence in scenario 1 is 696, and the sum of the sequence in scenario 2 is 492, a 29% reduction in total cases.
My interpretation of this is that as soon as virus spread becomes smoothly exponential, we should implement the harshest isolation policies as early as possible, to limit the total amount of people infected. This implies it is better to act when cases are as low as possible, rather than wait to act until cases appear more dramatic.
I realise my model is very limited, but can anyone find anything that would sway it away from the conclusion that early action on minimal cases is better that later action on larger numbers of cases?
I -think- it means I'd support shutting schools earlier, rather than later, to be honest. But I'd actually like someone else to be doing this maths, with more info, and then explaining it down to me.