Flattening the curve

Or why the Great Barrington Declaration makes sense

In “the game of epidemiological tag” and “epidemic the card game” each individual is as likely to be infected as each other. This “well mixed” population leads, when averaged over multiple simulations, to the standard SIR model where, at the end of the simulation, the population is split into acquired immunity and no immunity (herd immunity).

The contacts in the games form is what is known as a complete graph since each individual is connected to every other individual. Obviously this doesn’t scale much beyond the people in a room and in reality we have a sparse graph. There are lots of different way to construct sparse graphs. One particularly contrived way would be a domino derby in which each domino, when toppled, would topple two others leading to exponential growth. A more real world example would be a social network but how often do you meet your Facebook friends?

Scientists have studied the social network formed by voles in the English county of Northumberland. From this dataset it is possible to extract a network formed by 1610 antisocial individuals. The number of connections that an individual has is known as the degree and can be plotted to form the following histogram.

The game code was modified so that rather than pick from the whole set of other nodes it only picked from those it was connected to with each of those having equal chance. Simulations were started from each individual node 10 times with a value of two for the initial reproduction rate (R naught). The average of the results compared to the results for a complete graph is plotted as follows.

The voles network takes 105 generations and leaves 55% with no immunity whereas the well mixed population takes 25 generations and leaves 20% with no immunity. Hence flattening the curve results in the epidemic lasting much longer and increases the chances of a second wave when restrictions are eased.

This is why the curve should only be flattened in the subset of the population likely to have a severe reaction to the virus leaving the remainder to catch and recover as quickly as possible so that they can contribute to herd immunity for the vulnerable. In other words the Great Barrington Declaration makes sense.