Thread by @cesifoti

What is exponential growth?
It is growth that happens by multiplying rather than adding.
Consider linear growth that adds 10 & exponential growth that multiplies by 2:
Linear(+10):
10,20,30,40,50,...
Exponential(x2):
1,2,4,8,16,32,....
(Continues...) 1/

At the beginning exponential growth seems slow. It is only 32 after five cycles. But forward to 20 cycles. Linear growth gets just to 200 (20*10);
Exponential growth...
2048,
4096,
8192,
16,384
32,768
65,536
131,072
262,144
524,288
1,048,576=2^20
To More than a Million! 2/

In exponential growth, 1,000 is technically “halfway” to 1,000,000; so things can sneak up on you, since the same process that brought you to 1,000 cases (which seems manageable), can bring you to 1 million cases in the same amount of time. 3/

How do we defeat the epidemic? By multiplying by a smaller number. Imagine multiplying by 0.5 and halving the cases in each cycle instead of doubling them. But how do we bring that number down? 4/

The rate of spreading of an epidemic, the “2” I used in the first example, is a product of two numbers: the infection rate of the disease, and the connectivity of the network. The first number is one we cannot change right now, the second one (connectivity) is our strategy. 5/

If you are interested in learning more about spreading in networks, this classic paper by @alexvespi and Pastor-Satorras showed the importance of network structure in modulating the reach and spreading of a disease. It is a seminal contribution journals.aps.org/prl/pdf/10.110… /6

If you are interested in spreading that is more infectious for some populations (eg elderly) than others, in this paper @dsmilkov calculated the effects of “differential susceptibility” for populations with different mixing patterns nature.com/articles/srep0… 7/

Hope this threads helps. Stay at home, keep safe, and make this a moment of calm and reflection. /END