6 ms·
A nice 'visual' illustration of the threshold is found in Percolation theory https://en.wikipedia.org/wiki/Percolation_theory https://en.wikipedia.org/wiki/Perc
by fjfaase 5y ago
A nice 'visual' illustration of the threshold is found in Percolation theory https://en.wikipedia.org/wiki/Percolation_theory https://en.wikipedia.org/wiki/Percolation_theory where if you have an infinite grid of square rooms with either a wall or a door between each pair of rooms, that there is shift about what is connected when the percentage of door gets just over 50% as is visualized in this animation: https://en.wikipedia.org/wiki/Percolation_theory#/media/File:Transition_de_percolation_2.gif https://en.wikipedia.org/wiki/Percolation_theory#/media/File...
- ccbccccbbcccbb 5y agoI recommend everyone interested in percolation theory to also check https://meltingasphalt.com/interactive/going-critical/ https://meltingasphalt.com/interactive/going-critical/ and play with critical thresholds interactively!
- pietroppeter 5y agoGreat link, thanks for sharing!
- cecilpl2 5y agoThis was fascinating! It started with some simple simulations, but led into some very enlightening generalizations about why culture spreads more rapidly in cities than in the countryside, and why new language spreads more rapidly among adolescents.
- spiralx 4y agoThank you!
- feral 5y agoAnd, to give an example we've probably all become familiar with, this this is equivalent to how a disease becomes an epidemic as the R value crosses 1.
- scoot 5y agoThat seems more like a truism: If on average one case leads to more than one other (R > 1), the number of cases will grow. The R number therefore appears to be nothing more than a measure of growth or decline. What am I missing?
- joshocar 5y agoAs far as I understand it R is not a rate because it does not include time. Diseases that take on average a few days for you to pass on verses a few months will have different growth rates. For example, an STI might have an R factor of 3, but the rate is completely dependent on how often people have unprotected sex.
- scoot 5y agoGood point, R is often referred to as a rate both in media and academic publications, but "number" or "value" appears to be more correct. Fixed.
- rocqua 5y agoThis is essentially what is happening in the percolation case as well.
- deleted 5y ago[deleted]
- photochemsyn 5y agoR is not a measure of anything (i.e. real world data), it's more of a prediction based on a mathematical modeling procedure. It's not constant for a pathogen like Sars-CoV2, as it depends also on other conditions (environmental factors like temp/humidity, and social factors (norms like handshaking, etc.). The models used to generate R-numbers have some assumptions which may or may not be valid: (1) rectangular and stationary age distribution, and (2) homogeneous mixing of the population. Thus, the result is a fairly rough estimate. A major use is in getting a decent estimate of what percentage of a population needs to be vaccinated in order to halt the spread of a viral infection. However, this supposes 'sterilizing vaccination', i.e. vaccinated individuals are not asymptomatic carriers and spreaders of the infection. While this was the case for the smallpox vaccine, it doesn't seem to be the case with all known Covid19 vaccines, where there are many breakthrough cases (even though symptoms are reduced and hospitalization is minimal).
- raxxorraxor 5y agoSudden thresholds were just recently relevant with disease transmission and recoverability too.