isee systems blog
Last summer I had the opportunity to see students from Diana Fisher’s dynamic modeling class at Wilson High School in Portland, Oregon present their modeling projects to participants of the International System Dynamics Society Conference in Albuquerque. The parallel session was filled with educators and professionals from different fields, many of whom are renowned system dynamicists. I think it is safe …
This is part two of a three part series on Limits to Growth. Part one can be accessed here and part three can be accessed here.
In part one of this series, I explained the Limits to Growth archetype and gave examples in epidemiology and ecology. This part introduces the Bass diffusion model, an effective way to implement the capture of customers in a developing market. This is also used to implement what Kim Warren calls Type 1 rivalry in his book Strategy Management Dynamics, that is, rivalry between multiple companies in an emerging market.
The Bass Diffusion Model
The Bass diffusion model is very similar to the SIR model shown in part one. Since we do not usually track customers who have “recovered” from using our product, the model only has two stocks, corresponding loosely to the Susceptible and Infected stocks. New customers are acquired through contact with existing customers, just as an infection spreads, but in this context this is called word of mouth (wom). This is, however, not sufficient to spread the news of a good product, so the Bass diffusion model also includes a constant rate of customer acquisition through advertising. This is shown below (and can be downloaded by clicking here).
The feedback loops B1 and R are the same as the balancing and reinforcing loops between Susceptible and Infected in the SIR model. Instead of an infection rate, there is a wom multiplier which is the product of the Bass diffusion model’s contact rate and the adoption rate. If you are examining policies related to these variables, it would be important to separate them out in the model.
The additional feedback loop, B2, starts the ball rolling and helps a steady stream of customers come in the door. If you examine the SIR model closely, you will see that the initial value of Infected is one. If no one is infected, the disease cannot spread. Likewise, if no one is a customer, there is no one to tell others how great the product is so they want to become customers also. By advertising, awareness of the product is created in the market and some people will become customers without having encountered other customers who are happy with the product.
The behavior of this model is shown below. Note it is not different in character from the SIR model or the simple population model.
This post is written by Rolf Olsen, a participant in our Introduction to Dynamic Modeling with iThink and STELLA workshop held last month in Colorado Springs. We thought Rolf’s perspective would offer insights for those of you who are new to Systems Thinking or curious about applying dynamic modeling to real-world issues.
I was very excited about a last-minute chance to attend the introductory iThink/STELLA workshop, but to be honest, on the flight to Colorado Springs, I started to become apprehensive. Who was I trying to kid? Sure, I’d heard the terms “stock” and “flow” and I understood their roles as the nouns and verbs of the software. I’d even read a few chapters in Barry Richmond’s Introduction to Systems Thinking. But the first time I started up the software and stared at that blank workspace, I had no clue where to begin! Adding to my anguish, I was quite certain there would be others there who were much smarter than me and really knew what they were doing.
In college I spent most of my time and energy studying English and French, language, literature, cinema, art history, and so forth. I managed to avoid all higher math like the plague (although I did reasonably well in basic statistics). My engineer father often reminded me that my degree in Humanities prepared me for almost nothing. After college, I stumbled into a career in marketing – quite fertile territory for exploring system dynamics and modeling, as it turns out. I spent a few formative years in an ad agency and at a regional banking system, before finding my stride marketing and managing nonprofit arts and culture organizations. Today I work in marketing and communication in a large academic medical center.
For years I’ve used spreadsheets to model various ‘what if’ scenarios. In the arts, I used spreadsheets to create budgets and set ticket prices, always seeking ways to better predict revenue from ticket sales at different prices, for different types of performances (e.g., modern dance, string quartet, jazz ensemble), or on different days of the week.
Preparing for the iThink/STELLA workshop, I decided I’d like to try to model demand in a market area for laser vision correction surgery, popularly known as LASIK or PRK. That seemed simple enough. I might be able to bluff my way through this workshop after all!
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