Classroom Companion: Business

 
Chapter 18 · Digital Market Modeling

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18
18.5 
 Analysis of Real Markets
As shown, the temporal evolution of markets can be described mathematically 
using coupled sets of ordinary differential equations. In most cases, these equa-
tions cannot be solved using analytical methods. In the few cases in which analyti-
cal solutions can be found, it is necessary to treat all flow parameters as constants. 
Even the simple Bass equation cannot be solved analytically if the coefficients of 
innovation and imitation are functions of time.
Real markets are much more complicated than the three simple cases described 
in this chapter: system parameters are not constants but may be complex functions 
of time and the number of current customers; the model itself may be more com-
plex containing additional customer states (or compartments) and flows; and there 
may be more complex feedbacks from the market regulating the flows between 
states. Such complex cases can be analyzed using system dynamics. The method is 
briefly outlined in 
7
Box 
18.5
. The interested reader is advised to consult the spe-
cialized literature on system dynamics (e.g., the two books listed below) to learn 
more about this important method for the analysis of complex systems.
BPQ model are examples of such com-
partmental models in the digital econ-
omy. J. Cannarella and J. A. Spechler 
modified the SIR model by adding pos-
itive feedback to the recovery mecha-
nism. They called the model the irSIR 
model, where “ir” stands for “infectious 
recovery,” and used it to forecast the 
evolution of Facebook and Myspace 
(Cannarella & Spechler, 
2014
). The 
model fitted well with the evolution of 
Myspace but not for Facebook. The 
growth rate of Facebook had started to 
decline during 2013, and from this data, 
they predicted (in 2014) a rapid decline 
in Facebook users starting from 2017. 
The growth rate of Facebook regained 
its original speed in 2015, so the predic-
tion was based on too little data. This is 
similar to the problem the health 
authorities have to predict the evolu-
tion of COVID-19.