The current models of viral marketing for the business community are seriously flawed and fail to reflect the real world. But, if we are really looking for a model for viral growth for our businesses, the perfect analogue is a model for the spread of disease. Allow me to explain. . .
A Better Model for Viral Marketing
The classic model on the spread of disease is the SIR model, developed by Kermack and McKendrick. (Author’s note: Sorry I couldn’t link to the original paper. You can buy it for $54.50 here — blame the academic publishing industry). I’ve applied this model to viral marketing by drawing analogies between a disease and a product. The desired outcomes are very different, but the math is the same:
Under the SIR model, the general population is divided into three parts.
- S – The number of people susceptible to the disease (potential customers)
- I – The number of people who are infected with the disease (current customers)
- R – The number of people who have recovered from the disease (former customers)
For a viral marketing analogue, the market for your offering can be divided into three subpopulations.
- S – The number of potential customers
- I – The number of current customers
- R – The number of former customers
The number of people in these three subpopulations change over time. In the disease model, people who are susceptible become infected. And people who are infected recover.
The population of the market for your product changes the same way: potential customers become current customers, and some customers decide to stop using your product, becoming former customers.
For the time being, we’re going to ignore the way the population of your market changes for simplicity’s sake. In other words, the total market (N=S+I+R) will be treated as a static market. And we’ll assume (just for now) that former customers are immune, and won’t return to being customers again.
the total market for your product = the number of potential customers + the number current customers + the number of former customers
this is represented as N = S + I + R
The Point of Viral Marketing is to Spread the Message and Interest in the Product
The point of viral marketing is to make the message spread, so it “infects” as many “susceptible” people as possible. The parameters that govern spread of disease are:
- β – The infection rate (sharing rate)
- γ – The recovery rate (churn rate)
Viral marketing is spread by “sharing” (instead of infection).
Assuming that current customers (I) and potential customers (S) communicate with each other at an average rate that is proportional to their numbers (as governed by the Law of Mass Action), the number of new customers, in any unit of time, that are “infected” due to word of mouth or online sharing is
the sharing rate * the number of potential customers * the number of current customers
this is represented as βSI
As the number of new customers grows by βSI, the number of potential customers shrinks. In the SIR model, current customers become former customers at a rate defined by the parameter γ.
In other words, γ is the fraction of current customers who become former customers in any unit of time. It has the dimensions of inverse time (1/t), and 1/γ represents the average time a user remains a user.
So, if γ=1% of users lost per day, then the average length of time a user remains active is 100 days.
What this means is that there will be a growing customer base as long as:
the sharing rate * the number of potential customers/the churn rate is > 1
The differential equations governing viral spread (or the possible ways the slope of the viral model might look) are:
- dS/dt=−βSI (the derivative of the number of potential customers relative to time = the sharing rate * the number of potential customers * the number of current customers, represented as a negative slope)
- dI/dt=βSI–γI (the derivative of the current users relative to time = the sharing rate * the number of potential customers – the churn rate of existing customers)
- dR/dt=γI (the derivative of the number of former users relative to time = the churn rate * current customers)
But note, differential equations are (lots of times) impossible to solve. Still, they’re helpful in thinking about how your product can go viral, even if you have a small sharing rate.
The Bottom Line: Your Product Can Go Viral Even if the Sharing Rate is Small
This SIR model shows that with a big enough market, you can go viral even with a small β (sharing rate) so long as your γ (churn rate) is also small.
It also shows that the effects of churn cannot be ignored, even very early in viral growth.
Learn how to apply this formula to your own company and chart a path to viral growth and take a more detailed look into Valerie’s better model for Viral Growth on the Data Community DC Blog. Stay tuned for her next post in the series.