Thread by @AlanBixter

COVID in NSW, Chaos and Strange Attractors (a stupidly long thread)
Chaos theory is a branch of mathematics focusing on the study of dynamic systems governed by deterministic laws involving feedback loops that are highly sensitive to initial conditions. /2

This sensitivity to initial conditions generates deterministic but apparently random systems. This behaviour is known as deterministic chaos. Chaotic systems are characterised by a set or field of initial conditions that can result in wildly oscillating behaviour. /3

In many cases chaotic behaviour is found only in a subset of these initial conditions as the field includes an attractor, a region of stability to which a large set of initial conditions eventually converge. /4

A classical chaotic model, the Hunter-Prey Model, involves in interaction between two species, one of prey, whose numbers rise when not predated on, and fall when hunted, and one of hunter, whose numbers fall when prey are rare, and rise when prey are plenty. /5

Depending on the initial conditions (numbers of prey, numbers of hunters, the effect of prey and hunter numbers on prey survival, the effect of prey and hunter numbers on hunter survival) the system often generates oscillations in prey and hunter numbers. /6

These oscillations are relatively stable for a period time before before increasing in magnitude of swing, and decreasing stability of periodicity. Many starting conditions eventually result in collapse into one or other of 2 attractors: death of all prey or death of hunters. /7

The Delta COVD outbreak in NSW has some remarkable characteristics that resemble the the Hunter-Prey Model. Numbers of infections rise when people crowd in public spaces; high case numbers discourage the crowing of people, social distancing reduce case numbers. /8

There are two obvious attractors - the virus can be eliminated, halting the chaotic system until virus is reseeded; or there is unconstrained spread, resulting in a collapse of social supports. /9

Between these two are a range of outcomes involving periodic swings in case numbers, which may convert to greater swings of less stable periodicity at they approach one of the attractors. /10

While this model can’t be used to accurately predict case numbers day-to-day, it can be used to draw general conclusions about the likely future if conditions are not altered in a meaningful way. /11

The current large oscillations in COVID case numbers in NSW, and loss of regular periodicity gives every indication of the State moving away from the previously experienced relative stability towards the attractor of unconstrained spread. /12

If this is a chaotic system, this behaviour is a direct result of the existing public health settings in the state, and failure to alter the public health settings will maintain progress to collapse into the attractor. /13

It would therefore be necessary to change the relationships between case numbers and human behaviour by the adoption of stronger public health measures that are not weakened in response to falls in infection numbers, but maintained until community infections are eradicated. <end>

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