Recent paper making the rounds:

> ["Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies"](https://aip.scitation.org/doi/10.1063/5.0009454), *Chaos*

This is non-logistic growth. Power-law is essentially an acceleration over time -- a non-autonomous differential equation -- in contrast to the classical autonomous differential equation to describe exponential contagion growth followed by a logistic asymptote.

https://ltcconline.net/greenl/courses/204/firstOrder/autonomous.htm

I mentioned autonomous vs non-autonomous growth in [comment above](https://forum.azimuthproject.org/discussion/comment/22022/#Comment_22022) and compared them in Mathematical Geoenergy

> " This kind of growth has an underlying mechanism of a constant acceleration term; in other words, the rate of

growth itself increases linearly with time. To first order, this explains scenarios that involve a rapidly increasing

uptake of resources and particularly those that spread by word of mouth. The growth of wiki words in Wikipedia

provides the best current‐day example of quadratic growth."

This was an early graph of wiki page (i.e. wiki word) growth

![](https://imagizer.imageshack.com/img924/1907/onAKOm.png)

It would be interesting to find out how many pages are added per day now, many years later

English articles: 6,067,626

https://en.wikipedia.org/wiki/Wikipedia:Size_of_Wikipedia#Graphs_of_size_and_growth_rate

[https://stats.wikimedia.org/#/en.wikipedia.org/content/pages-to-date/normal|table|all|page_type~content|monthly

](https://stats.wikimedia.org/#/en.wikipedia.org/content/pages-to-date/normal|table|all|page_type~content|monthly)

![](https://imagizer.imageshack.com/img923/6089/Hau3PR.png)

The power is still roughly 2 even though it appears to be slowing down. Note that this is plotted on a log-log scale -- contagion growth is plotted on a semi-log scale, which would have shown a more apparent flattened bend in the curve and earlier in the timeline.

There is an equivalent stochastic power-law "logistic" which may explain an asymptotic flattening -- as there are only so many words available in the english language to draw from (or human wikipedia editors to contribute). This is straightforward to derive in the same way that a stochastic logistic can be derived, mentioned in [comment #11](https://forum.azimuthproject.org/discussion/comment/21938/#Comment_21938).

[Example stochastic model fit](https://imagizer.imageshack.com/img923/7500/1v8Ukb.png)

[.. on semilog plot](https://imagizer.imageshack.com/img923/6352/5c1XS0.png)

I don't really know what implications this has for contagion growth modeling, as the exponential growth mechanism is well established.

> ["Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies"](https://aip.scitation.org/doi/10.1063/5.0009454), *Chaos*

This is non-logistic growth. Power-law is essentially an acceleration over time -- a non-autonomous differential equation -- in contrast to the classical autonomous differential equation to describe exponential contagion growth followed by a logistic asymptote.

https://ltcconline.net/greenl/courses/204/firstOrder/autonomous.htm

I mentioned autonomous vs non-autonomous growth in [comment above](https://forum.azimuthproject.org/discussion/comment/22022/#Comment_22022) and compared them in Mathematical Geoenergy

> " This kind of growth has an underlying mechanism of a constant acceleration term; in other words, the rate of

growth itself increases linearly with time. To first order, this explains scenarios that involve a rapidly increasing

uptake of resources and particularly those that spread by word of mouth. The growth of wiki words in Wikipedia

provides the best current‐day example of quadratic growth."

This was an early graph of wiki page (i.e. wiki word) growth

![](https://imagizer.imageshack.com/img924/1907/onAKOm.png)

It would be interesting to find out how many pages are added per day now, many years later

English articles: 6,067,626

https://en.wikipedia.org/wiki/Wikipedia:Size_of_Wikipedia#Graphs_of_size_and_growth_rate

[https://stats.wikimedia.org/#/en.wikipedia.org/content/pages-to-date/normal|table|all|page_type~content|monthly

](https://stats.wikimedia.org/#/en.wikipedia.org/content/pages-to-date/normal|table|all|page_type~content|monthly)

![](https://imagizer.imageshack.com/img923/6089/Hau3PR.png)

The power is still roughly 2 even though it appears to be slowing down. Note that this is plotted on a log-log scale -- contagion growth is plotted on a semi-log scale, which would have shown a more apparent flattened bend in the curve and earlier in the timeline.

There is an equivalent stochastic power-law "logistic" which may explain an asymptotic flattening -- as there are only so many words available in the english language to draw from (or human wikipedia editors to contribute). This is straightforward to derive in the same way that a stochastic logistic can be derived, mentioned in [comment #11](https://forum.azimuthproject.org/discussion/comment/21938/#Comment_21938).

[Example stochastic model fit](https://imagizer.imageshack.com/img923/7500/1v8Ukb.png)

[.. on semilog plot](https://imagizer.imageshack.com/img923/6352/5c1XS0.png)

I don't really know what implications this has for contagion growth modeling, as the exponential growth mechanism is well established.