Here is a stochastic analogy to epidemic growth -- the rate at which popcorn popping follows a similar logistic sigmoid as an ensemble of contagions. This is the familiar slow initial popping of a few kernels leading up to a maximum popping rate followed by a decline of popping as the population of kernels impacted saturates.

Click on the PDF on the link below and go to section C.4:

https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.app3

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/9781119434351.app3

The rationale for including this example in our book is because it describes the Hubbert logistic curve not directly related to resource extraction, yet provides a real world analogy that can be easily set up as a controlled lab experiment.

It also doesn't hold as a perfect analogy to contagion, as the accelerated growth is controlled as an Arrhenius rate activated by temperature instead of as a multiplicative contagion, i.e. an individual kernel does not pop because its neighbor pops but because of the temperature of the medium. In the figure below, the fraction unpopped is simply the complement of the fraction popped to convert to the familiar S-curve.

![](https://imagizer.imageshack.com/img923/7695/cO2M7C.png)

The usual observation in virus epidemic growth is that the contagiousness *decreases* with increased temperature instead of what might be expected as an increase if it was a thermally activated complex obeying the laws of statistical mechanics. This behavior apparently is not completely understood but there is some thought it might be related to the increased intensity of UV light during the summer months killing any airborne virus : https://www.webmd.com/cold-and-flu/news/20180212/can-uv-light-be-used-to-kill-airborne-flu-virus-#1 or that buildings have more air circulation and people tend to congregate less indoors during the summer. Considering that humans have a thermally stabilized environment controlled by their regulated body temperature, it would be hard to make sense of a thermally activated mechanism once the virus enters the body.

This is a recent paper on COVID-19 based on available geographic/climate correlation
[High Temperature and High Humidity Reduce the Transmission of COVID-19](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3551767)

PS: The popcorn experiment is interesting in that the controlled conditions were set up as a *single* isolated popcorn kernel was monitored as it was heated up, not by monitoring an aggregation of kernels. The statistical distribution resembling a logistic sigmoid was only found by compiling the results of thousands of individual kernel measurements. So this is essentially characterizing the stochastic uncertainty of a single kernel.