Saturday, March 21, 2020

Controlavirus Spread Cannot Be Exponential: Real World Networks Have Limiting Structures

zdnet |  The media regularly refers to "exponential" growth in the number of cases of COVID-19 respiratory disease, and deaths from the disease, but the numbers suggest something else, a "small world" network that might have power law properties. That would be meaningfully different from the exponential growth path for the disease.

Is the spread of the respiratory infection known as COVID-19 happening in an "exponential" fashion?  

That's been the general contention of the media, which, as a public service, have explained at some length the basics of fast-growing quantities, such as disease, to hammer home how something like a virus can double in cases in a matter of days. 

However, the data on COVID-19 has a lot of puts and takes, and one of the factors not entirely considered is the graph of the infection. Graph theory has a lot to say about how phenomena can grow, such as the spread of infectious diseases. There are different graphs, or networks, of relations, and they can affect things such as the rate of propagation.  

One particular recent work calls into question the notion of the exponential growth of the disease. 
Scholars Anna Ziff and Robert Ziff, respectively of Duke University and the University of Michigan, earlier this month posted on the medrXiv pre-print server their curve-fitting exercise for COVID-19 confirmed cases and deaths, both in China and in the rest of the world, titled "Fractal kinetics of COVID-19 pandemic." 

As the authors write, "in standard epidemiological analysis, one assumes that the number of cases in diseases like this one grows exponentially, based upon the idea of a fixed reproduction rate."  

But that standard epidemiological view is not born out by the data. They found that while the numbers "display large growth, they do not, in fact, follow exponential behavior." Rather, the authors observed a period of initial exponential growth, followed by what's called a "power law," which is not the same thing.