Abstract for: Investigation into the Anomalous behavior of Adoption Rate in the simple SI Innovation Model
Adoption of new ideas or products usually follows an S shaped curve and therefore has been modeled based on the simple Susceptible-Infectious (SI) population System Dynamics model. While the model remains valid for lower values of Contact Rate, at higher values of Contact Rate the calculated Adoption Rate exceeds the corresponding stock of Potential Adopters. This behavior is anomalous as a flow (the calculated flow at an instant in the SD model) can never exceed the stock from which it originates. This paper attempts to understand the reason for this anomalous behavior by means of mathematical analysis. The analysis identified that the Adoption Rate must not be based on the average Contact Rate with Adopters but rather on the probability of contact with one Adopter. An equivalent Agent Based Model was used to better understand the problem and determine a solution. The solution identified is to replace Contact Rate with a new look up function namely Max. Fractional Adoption Rate which in turn is dependent on the proportion of Adopter population.