Saturday, May 09, 2009

Social News Modeled like Bacterial Growth

It's well known phenomena in biology that cells reproduce with cellular fission a process where one cell reproduces to two and two change to four and so forth. Growth proceeds exponentially until the environment can no longer support the growth or deaths begin to initiate. Ultimately the growth slows until it reaches a stationary phase and then finally a death phase will occur when deaths exceed new births.

Modeling this growth process can be accomplished by use of the modified Gompertz equation:


y = LN(N/No) - N is the final population count, No is the starting population.
mu(mean) - a rate constant indicating the maximum slope of the growth curve.
e - the mathematical constant approximately equal to 2.718
A - Represents a constant for the (peak value - the starting value)

This modified Gompertz equation was published in June 1990 by M.H. Zweitering, et al. in the Applied Environmental Microbiology. The article was entitled, "Modeling of the Bacterial Growth Curve".

OK so how does this apply to social media and Swine Flu or any other topic for that matter?

According to data obtained at the website, blog posts regarding the search terms "Swine Flu" took off beginning about April 22nd and reached a peak number of daily posts of 10884 on April 28th. Previous to this news event the average number of daily posts on the topic of swine flu was between four and five posts. Plotted on a trend chart the growth of the news expanded exponentially as depicted on the following chart.

The smoothed line on this curve represents the modeled equation for the Gompertz Curve. A quick linear regression of the growth portion of the curve shows a significant and high degree of correlation between the actual data and the modeled curve. Greater than 95% of the variance in the data can be accounted for with the Gompertz model.

There is an interesting kinetic parameter known as the doubling time. The doubling time represents the amount of time for a population to double. It is calculated as the LN(2)/slope or mean growth.

In this example of swine flu the doubling time works out to be 16.5 hours. The practical meaning of this is that recorded a doubling of swine flu blog mentions every 16 1/2 hours until it ultimately peaked on 4/28 and interest began to subside.

I would propose that different social news events and topics will grow exponentially at different rates and doubling times. Peak interest levels would also be different. Perhaps we have a way or can find a parameter that can compare one event to another. Doubling time is definitely one of these parameters.
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